%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SET201^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n186.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 13:30:22 EDT 2014 % Result : Theorem 0.87s % Output : Proof 0.87s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SET201^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n186.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 09:25:21 CDT 2014 % % CPUTime : 0.87 % 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 0x1e307e8>, <kernel.Type object at 0x1e30200>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0x1919b90>, <kernel.DependentProduct object at 0x1e30128>) of role type named cV % Using role type % Declaring cV:(a->Prop) % FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) of role conjecture named cBOOL_PROP_41_pme % Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))):Prop % Parameter a_DUMMY:a. % We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))'] % Parameter a:Type. % Parameter cV:(a->Prop). % Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) % Found x200:=(x20 x4):(cV Xx) % Found (x20 x4) as proof of (cV Xx) % Found ((x2 Xx) x4) as proof of (cV Xx) % Found ((x2 Xx) x4) as proof of (cV Xx) % Found x100:=(x10 x3):(Y Xx) % Found (x10 x3) as proof of (Y Xx) % Found ((x1 Xx) x3) as proof of (Y Xx) % Found ((x1 Xx) x3) as proof of (Y Xx) % Found ((conj00 ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx)) % Found (((conj0 (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx)) % Found ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((Z Xx)->((and (Y Xx)) (cV Xx))) % Found (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((X Xx)->((Z Xx)->((and (Y Xx)) (cV Xx)))) % Found (and_rect10 (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx)) % Found ((and_rect1 ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx)) % Found (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((forall (Xx0:a), ((Z Xx0)->(cV Xx0)))->((and (Y Xx)) (cV Xx))) % Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((forall (Xx0:a), ((X Xx0)->(Y Xx0)))->((forall (Xx0:a), ((Z Xx0)->(cV Xx0)))->((and (Y Xx)) (cV Xx)))) % Found (and_rect00 (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx)) % Found ((and_rect0 ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx)) % Found (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of ((and (Y Xx)) (cV Xx)) % Found (fun (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))) % Found (fun (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))) % Found (fun (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))) % Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) % Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) % Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) % Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) % Time elapsed = 0.545291s % node=114 cost=568.000000 depth=24 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------