%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV311^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n114.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 13:34:02 EDT 2014 % Result : Theorem 0.61s % Output : Proof 0.61s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV311^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n114.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 08:48:26 CDT 2014 % % CPUTime : 0.61 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % FOF formula (<kernel.Constant object at 0x275c830>, <kernel.Type object at 0x275cc68>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0x275c9e0>, <kernel.DependentProduct object at 0x275bf80>) of role type named cF % Using role type % Declaring cF:((a->Prop)->(a->Prop)) % FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))) of role conjecture named cTHM521_pme % Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))):Prop % Parameter a_DUMMY:a. % We need to prove ['((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))))'] % Parameter a:Type. % Parameter cF:((a->Prop)->(a->Prop)). % Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))) % Found x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))) % Instantiate: X:=(cF S):(a->Prop) % Found x1 as proof of (forall (Xx:a), ((X Xx)->(S Xx))) % Found x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx) % Instantiate: X:=(fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))):(a->Prop) % Found x0 as proof of ((cF X) Xx) % Found x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx) % Instantiate: X0:=(fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))):(a->Prop) % Found x0 as proof of ((cF X0) Xx) % Found x3:(X0 Xx0) % Found x3 as proof of (X Xx0) % Found (fun (x3:(X0 Xx0))=> x3) as proof of (X Xx0) % Found (fun (Xx0:a) (x3:(X0 Xx0))=> x3) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx0:a) (x3:(X0 Xx0))=> x3) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx))) % Found x400:=(x40 x1):(forall (Xx:a), (((cF X) Xx)->((cF S) Xx))) % Found (x40 x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1))) % Found ((x4 S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1))) % Found (((x X) S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1))) % Found (((x X) S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1))) % Found (x30 (((x X) S) x1)) as proof of (X Xx0) % Found ((x3 X) (((x X) S) x1)) as proof of (X Xx0) % Found (fun (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of (X Xx0) % Found (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx))) % Found ((x210 (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx) % Found (((x21 X) (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx) % Found ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx) % Found ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx) % Found ((x200 x1) ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0)) as proof of ((cF S) Xx) % Found (((x20 S) x1) ((((x2 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0)) as proof of ((cF S) Xx) % Found ((((x2 (cF S)) S) x1) ((((x2 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx) % Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx) % Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx) % Found (x10 (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))) as proof of (S Xx) % Found ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))) as proof of (S Xx) % Found (fun (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (S Xx) % Found (fun (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)) % Found (fun (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))) % Found (fun (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))) % Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))) % Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))) % Got proof (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) % Time elapsed = 0.296557s % node=66 cost=1449.000000 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:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------