%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV310^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n107.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 13:34:01 EDT 2014 % Result : Theorem 2.16s % Output : Proof 2.16s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV310^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n107.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 08:48:16 CDT 2014 % % CPUTime : 2.16 % 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 0xd583f8>, <kernel.Type object at 0xd76c20>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0xfd93b0>, <kernel.DependentProduct object at 0xd76cf8>) of role type named cK % Using role type % Declaring cK:((a->Prop)->(a->Prop)) % FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))) of role conjecture named cTHM90A_pme % Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) 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), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))))'] % Parameter a:Type. % Parameter cK:((a->Prop)->(a->Prop)). % Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))) % Found x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0) % Instantiate: X:=(cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))):(a->Prop) % Found x1 as proof of ((cK X) Xx0) % Found x3:(X Xx1) % Found x3 as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))) % Found (fun (x3:(X Xx1))=> x3) as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))) % Found (fun (Xx1:a) (x3:(X Xx1))=> x3) as proof of ((X Xx1)->(forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)))) % Found (fun (Xx1:a) (x3:(X Xx1))=> x3) as proof of (forall (Xx:a), ((X Xx)->(forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx))))) % Found x2:(X Xx0) % Found x2 as proof of (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))) % Found (fun (x2:(X Xx0))=> x2) as proof of (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))) % Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->(forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0)))) % Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->(forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx))))) % Found x2:((cK (cK X)) Xx0) % Instantiate: X0:=(cK X):(a->Prop) % Found x2 as proof of ((cK X0) Xx0) % Found x2:((cK (cK X)) Xx0) % Instantiate: X0:=(cK X):(a->Prop) % Found x2 as proof of ((cK X0) Xx0) % Found x4:(X0 Xx1) % Found x4 as proof of (X Xx1) % Found (fun (x4:(X0 Xx1))=> x4) as proof of (X Xx1) % Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of ((X0 Xx1)->(X Xx1)) % Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx))) % Found x2:(X0 Xx0) % Found x2 as proof of (X Xx0) % Found (fun (x2:(X0 Xx0))=> x2) as proof of (X Xx0) % Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx))) % Found x3:(X Xx1) % Instantiate: X0:=(fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))):(a->Prop) % Found x3 as proof of ((cK X0) Xx1) % Found x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))) % Instantiate: X0:=(cK S0):(a->Prop) % Found x30 as proof of (forall (Xx:a), ((X0 Xx)->(S0 Xx))) % Found x20:(X0 Xx0) % Instantiate: X:=X0:(a->Prop) % Found (fun (x20:(X0 Xx0))=> x20) as proof of (X Xx0) % Found (fun (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of (((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)->((X0 Xx0)->(X Xx0))) % Found (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of (forall (Xx00:a), (((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)->((X0 Xx0)->(X Xx0)))) % Found (x00 (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20)) as proof of ((X0 Xx0)->(X Xx0)) % Found ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20)) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx0:a)=> ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20))) as proof of ((X0 Xx0)->(X Xx0)) % Found (fun (Xx0:a)=> ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20))) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx))) % Found x500:=(x50 x30):(S0 Xx2) % Found (x50 x30) as proof of (S0 Xx2) % Found ((x5 S0) x30) as proof of (S0 Xx2) % Found (fun (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of (S0 Xx2) % Found (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of ((X0 Xx2)->(S0 Xx2)) % Found (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of (forall (Xx:a), ((X0 Xx)->(S0 Xx))) % Found ((x400 (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1) % Found (((x40 S0) (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1) % Found ((((x4 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1) % Found (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1) % Found (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1) % Found (x300 (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)) as proof of (S0 Xx1) % Found ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)) as proof of (S0 Xx1) % Found (fun (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (S0 Xx1) % Found (fun (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)) % Found (fun (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))) % Found (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of ((X Xx1)->(forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)))) % Found (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (forall (Xx:a), ((X Xx)->(forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx))))) % Found ((x200 (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0) % Found (((x20 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0) % Found ((((x2 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (fun (Xx1:a) (x3:((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0) % Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0) % Found (fun (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0) % Found (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of (((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0)->((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)) % Found (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of (forall (Xx0:a), (((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0)->((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0))) % Found (x00 (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx) % Found ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx) % Found (fun (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx) % Found (fun (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) % Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of (forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))) % Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))) % Got proof (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) % Time elapsed = 1.831115s % node=343 cost=1482.000000 depth=29 % :::::::::::::::::::::: % % 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), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------