%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV401^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n097.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 13:34:09 EDT 2014 % Result : Theorem 1.38s % Output : Proof 1.38s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV401^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n097.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 09:07:31 CDT 2014 % % CPUTime : 1.38 % 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 0x1f316c8>, <kernel.Type object at 0x1f312d8>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0x1f31c68>, <kernel.DependentProduct object at 0x1f11320>) of role type named cF % Using role type % Declaring cF:((a->Prop)->(a->Prop)) % FOF formula (<kernel.Constant object at 0x1c1c0e0>, <kernel.DependentProduct object at 0x1f11908>) of role type named cG % Using role type % Declaring cG:((a->Prop)->(a->Prop)) % FOF formula (((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))->(forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))) of role conjecture named cTHM67_pme % Conjecture to prove = (((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))->(forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))):Prop % Parameter a_DUMMY:a. % We need to prove ['(((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))->(forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))))'] % Parameter a:Type. % Parameter cF:((a->Prop)->(a->Prop)). % Parameter cG:((a->Prop)->(a->Prop)). % Trying to prove (((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))->(forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))) % Found x300:=(x30 Xx):(((cF S) Xx)->((cF (cG (cF S))) Xx)) % Found (x30 Xx) as proof of (((cF S) Xx)->((cF (cG (cF S))) Xx)) % Found ((x3 (cF S)) Xx) as proof of (((cF S) Xx)->((cF (cG (cF S))) Xx)) % Found ((x3 (cF S)) Xx) as proof of (((cF S) Xx)->((cF (cG (cF S))) Xx)) % Found x10:=(x1 S):(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))) % Found (x1 S) as proof of (forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))) % Found (x1 S) as proof of (forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))) % Found (x2000 (x1 S)) as proof of (((cF (cG (cF S))) Xx)->((cF S) Xx)) % Found ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((x200 x4) Xx)) (x1 S)) as proof of (((cF (cG (cF S))) Xx)->((cF S) Xx)) % Found ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> (((x20 (cG (cF S))) x4) Xx)) (x1 S)) as proof of (((cF (cG (cF S))) Xx)->((cF S) Xx)) % Found ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S)) as proof of (((cF (cG (cF S))) Xx)->((cF S) Xx)) % Found ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S)) as proof of (((cF (cG (cF S))) Xx)->((cF S) Xx)) % Found ((conj00 ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (((conj0 (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))) as proof of ((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) % Found (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))) as proof of ((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))) % Found (and_rect10 (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found ((and_rect1 ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))) as proof of ((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0)))->((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) % Found (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))) as proof of (((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0)))->((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))) % Found (and_rect00 (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found ((and_rect0 ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx)))))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) as proof of ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)) % Found (fun (S:(a->Prop)) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) as proof of (forall (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) % Found (fun (x:((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))) (S:(a->Prop)) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) as proof of (forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) % Found (fun (x:((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))) (S:(a->Prop)) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) as proof of (((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))->(forall (S:(a->Prop)) (Xx:a), ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx)))) % Got proof (fun (x:((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))) (S:(a->Prop)) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) % Time elapsed = 1.048334s % node=168 cost=540.000000 depth=25 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:((and ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx))))) (S:(a->Prop)) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))->((forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))->P)))=> (((((and_rect ((and (forall (S:(a->Prop)) (T:(a->Prop)), ((forall (Xx:a), ((S Xx)->(T Xx)))->(forall (Xx:a), (((cF T) Xx)->((cF S) Xx)))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cF (cG S)) Xx))))) (forall (S:(a->Prop)) (Xx:a), ((S Xx)->((cG (cF S)) Xx)))) P) x0) x)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x0:((and (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))) (x1:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cG (cF S0)) Xx0))))=> (((fun (P:Type) (x2:((forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))->((forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))->P)))=> (((((and_rect (forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0)))) P) x2) x0)) ((iff ((cF (cG (cF S))) Xx)) ((cF S) Xx))) (fun (x2:(forall (S0:(a->Prop)) (T:(a->Prop)), ((forall (Xx0:a), ((S0 Xx0)->(T Xx0)))->(forall (Xx0:a), (((cF T) Xx0)->((cF S0) Xx0)))))) (x3:(forall (S0:(a->Prop)) (Xx0:a), ((S0 Xx0)->((cF (cG S0)) Xx0))))=> ((((conj (((cF (cG (cF S))) Xx)->((cF S) Xx))) (((cF S) Xx)->((cF (cG (cF S))) Xx))) ((fun (x4:(forall (Xx0:a), ((S Xx0)->((cG (cF S)) Xx0))))=> ((((x2 S) (cG (cF S))) x4) Xx)) (x1 S))) ((x3 (cF S)) Xx))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------