%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV138^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n110.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 13:33:47 EDT 2014 % Result : Theorem 20.35s % Output : Proof 20.35s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV138^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n110.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 08:12:46 CDT 2014 % % CPUTime : 20.35 % 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 0xad4878>, <kernel.Type object at 0xad4830>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) of role conjecture named cTHM150_pme % Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))):Prop % Parameter a_DUMMY:a. % We need to prove ['(forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))))'] % Parameter a:Type. % Trying to prove (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) % Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4:(Xq Xz) % Found (fun (x5:((Xr Xu) Xv))=> x4) as proof of (Xq Xz) % Found (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4) as proof of (((Xr Xu) Xv)->(Xq Xz)) % Found (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4) as proof of ((Xq Xz)->(((Xr Xu) Xv)->(Xq Xz))) % Found (and_rect10 (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4)) as proof of (Xq Xz) % Found ((and_rect1 (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4)) as proof of (Xq Xz) % Found (((fun (P:Type) (x4:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4)) as proof of (Xq Xz) % Found (fun (x3:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x4:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4))) as proof of (Xq Xz) % Found (fun (Xv:a) (x3:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x4:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4))) as proof of (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz)) % Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x4:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found (fun (Xu:a) (Xv:a) (x3:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x4:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x4) x3)) (Xq Xz)) (fun (x4:(Xq Xz)) (x5:((Xr Xu) Xv))=> x4))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x5:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x5 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x6:(Xq Xz) % Found (fun (x7:((Xr Xu) Xv))=> x6) as proof of (Xq Xz) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of (((Xr Xu) Xv)->(Xq Xz)) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of ((Xq Xz)->(((Xr Xu) Xv)->(Xq Xz))) % Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (fun (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (Xq Xz) % Found (fun (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz)) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x2 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x6:(Xq Xz) % Found (fun (x7:((Xr Xu) Xv))=> x6) as proof of (Xq Xz) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of (((Xr Xu) Xv)->(Xq Xz)) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of ((Xq Xz)->(((Xr Xu) Xv)->(Xq Xz))) % Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (fun (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (Xq Xz) % Found (fun (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz)) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x5:((Xr Xy) Xw) % Instantiate: Xu:=Xy:a % Found x5 as proof of ((Xr Xu) Xw) % Found x5:((Xr Xy) Xw) % Instantiate: Xu:=Xy:a % Found x5 as proof of ((Xr Xu) Xw) % Found x6:(Xq Xz) % Found (fun (x7:((Xr Xu) Xv))=> x6) as proof of (Xq Xz) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of (((Xr Xu) Xv)->(Xq Xz)) % Found (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6) as proof of ((Xq Xz)->(((Xr Xu) Xv)->(Xq Xz))) % Found (and_rect20 (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found ((and_rect2 (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6)) as proof of (Xq Xz) % Found (fun (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (Xq Xz) % Found (fun (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz)) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found (fun (Xu:a) (Xv:a) (x5:((and (Xq Xz)) ((Xr Xu) Xv)))=> (((fun (P:Type) (x6:((Xq Xz)->(((Xr Xu) Xv)->P)))=> (((((and_rect (Xq Xz)) ((Xr Xu) Xv)) P) x6) x5)) (Xq Xz)) (fun (x6:(Xq Xz)) (x7:((Xr Xu) Xv))=> x6))) as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xz)) ((Xr Xu) Xv))->(Xq Xz))) % Found x4:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x4 as proof of (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))) % Found x5:((Xr Xy) Xw) % Instantiate: Xu:=Xy:a % Found x5 as proof of ((Xr Xu) Xw) % Found x5:((Xr Xy) Xw) % Instantiate: Xu:=Xy:a % Found x5 as proof of ((Xr Xu) Xw) % Found x5:((Xr Xy) Xw) % Instantiate: Xu:=Xy:a % Found x5 as proof of ((Xr Xu) Xw) % Found x300:=(x30 x0):(Xq Xy) % Found (x30 x0) as proof of (Xq Xu) % Found ((x3 Xq) x0) as proof of (Xq Xu) % Found ((x3 Xq) x0) as proof of (Xq Xu) % Found ((conj10 ((x3 Xq) x0)) x5) as proof of ((and (Xq Xu)) ((Xr Xu) Xw)) % Found (((conj1 ((Xr Xu) Xw)) ((x3 Xq) x0)) x5) as proof of ((and (Xq Xu)) ((Xr Xu) Xw)) % Found ((((conj (Xq Xu)) ((Xr Xu) Xw)) ((x3 Xq) x0)) x5) as proof of ((and (Xq Xu)) ((Xr Xu) Xw)) % Found ((((conj (Xq Xu)) ((Xr Xu) Xw)) ((x3 Xq) x0)) x5) as proof of ((and (Xq Xu)) ((Xr Xu) Xw)) % Found (x200 ((((conj (Xq Xu)) ((Xr Xu) Xw)) ((x3 Xq) x0)) x5)) as proof of (Xq Xw) % Found ((x20 Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)) as proof of (Xq Xw) % Found (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)) as proof of (Xq Xw) % Found (fun (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5))) as proof of (Xq Xw) % Found (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5))) as proof of (((Xr Xy) Xw)->(Xq Xw)) % Found (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5))) as proof of (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw))) % Found ((conj00 (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2) as proof of ((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) % Found (((conj0 (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2) as proof of ((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) % Found ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2) as proof of ((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) % Found ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2) as proof of ((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) % Found (x40 ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)) as proof of (Xq Xz) % Found ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)) as proof of (Xq Xz) % Found (fun (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))) as proof of (Xq Xz) % Found (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))) as proof of ((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->(Xq Xz)) % Found (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))) as proof of ((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->(Xq Xz))) % Found (and_rect10 (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))) as proof of (Xq Xz) % Found ((and_rect1 (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))) as proof of (Xq Xz) % Found (((fun (P:Type) (x3:((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))->((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))->P)))=> (((((and_rect (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))) as proof of (Xq Xz) % Found (fun (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))->((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))->P)))=> (((((and_rect (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))) as proof of (Xq Xz) % Found (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))->((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))->P)))=> (((((and_rect (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))) as proof of ((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->(Xq Xz)) % Found (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))->((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))->P)))=> (((((and_rect (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))) as proof of ((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->(Xq Xz))) % Found (and_rect00 (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))->((forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))->P)))=> (((((and_rect (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))))) as proof of (Xq Xz) % Found ((and_rect0 (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))))) as proof of (Xq Xz) % Found (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2)))))) as proof of (Xq Xz) % Found (fun (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (Xq Xz) % Found (fun (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)) % Found (fun (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))) % Found (fun (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz)))) % Found (fun (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (forall (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) % Found (fun (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (forall (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) % Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) % Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) as proof of (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))->(forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) % Got proof (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) % Time elapsed = 19.797193s % node=2638 cost=1354.000000 depth=38 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xy)))) (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))->(Xq Xz))))) (Xq:(a->Prop)) (x0:((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))))=> (((fun (P:Type) (x1:((forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))->((forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))->P)))=> (((((and_rect (forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) P) x1) x0)) (Xq Xz)) (fun (x1:(forall (Xw:a), (((Xr Xx) Xw)->(Xq Xw)))) (x2:(forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv))))=> (((fun (P:Type) (x3:((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))->((forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))->P)))=> (((((and_rect (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz)))) P) x3) x)) (Xq Xz)) (fun (x3:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xx) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xy)))) (x4:(forall (Xq0:(a->Prop)), (((and (forall (Xw:a), (((Xr Xy) Xw)->(Xq0 Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq0 Xu)) ((Xr Xu) Xv))->(Xq0 Xv))))->(Xq0 Xz))))=> ((x4 Xq) ((((conj (forall (Xw:a), (((Xr Xy) Xw)->(Xq Xw)))) (forall (Xu:a) (Xv:a), (((and (Xq Xu)) ((Xr Xu) Xv))->(Xq Xv)))) (fun (Xw:a) (x5:((Xr Xy) Xw))=> (((fun (Xu:a)=> ((x2 Xu) Xw)) Xy) ((((conj (Xq Xy)) ((Xr Xy) Xw)) ((x3 Xq) x0)) x5)))) x2))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------