%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV137^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n116.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 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 : SEV137^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n116.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 08:12:36 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 0x120b6c8>, <kernel.Type object at 0x1202b00>) 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 (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) of role conjecture named cTHM204_pme % Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))):Prop % Parameter a_DUMMY:a. % We need to prove ['(forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))'] % Parameter a:Type. % Trying to prove (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) % Found x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0))) % Found x0 as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0))) % Found x2000:=(x200 x1):(Xx0 Xy) % Found (x200 x1) as proof of (Xx0 Xy) % Found ((x20 x0) x1) as proof of (Xx0 Xy) % Found (((x2 Xx0) x0) x1) as proof of (Xx0 Xy) % Found (((x2 Xx0) x0) x1) as proof of (Xx0 Xy) % Found ((x30 x0) (((x2 Xx0) x0) x1)) as proof of (Xx0 Xz) % Found (((x3 Xx0) x0) (((x2 Xx0) x0) x1)) as proof of (Xx0 Xz) % Found (fun (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of (Xx0 Xz) % Found (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of ((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz))))->(Xx0 Xz)) % Found (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of ((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))->((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz))))->(Xx0 Xz))) % Found (and_rect00 (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz) % Found ((and_rect0 (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz) % Found (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz) % Found (fun (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (Xx0 Xz) % Found (fun (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of ((Xx0 Xx)->(Xx0 Xz)) % Found (fun (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))) % Found (fun (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))) % Found (fun (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))) % Found (fun (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) % Found (fun (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) % Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) % Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) % Got proof (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) % Time elapsed = 0.288848s % node=40 cost=345.000000 depth=20 % :::::::::::::::::::::: % % 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 (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------