%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV014^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n099.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 13:33:34 EDT 2014 % Result : Theorem 0.48s % Output : Proof 0.48s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV014^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n099.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 07:29:31 CDT 2014 % % CPUTime : 0.48 % 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 0x1725710>, <kernel.Type object at 0x17257a0>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))) of role conjecture named cTHM513_pme % Conjecture to prove = (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))):Prop % Parameter a_DUMMY:a. % We need to prove ['(forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx))))'] % Parameter a:Type. % Trying to prove (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))) % Found x20:=(x2 Xx):((Xr Xx) Xx) % Found (x2 Xx) as proof of ((Xr Xx) Xx) % Found (fun (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((Xr Xx) Xx) % Found (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->((Xr Xx) Xx)) % Found (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->((Xr Xx) Xx))) % Found (and_rect10 (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx) % Found ((and_rect1 ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx) % Found (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx) % Found (fun (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of ((Xr Xx) Xx) % Found (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz)))->((Xr Xx) Xx)) % Found (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of (((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz)))->((Xr Xx) Xx))) % Found (and_rect00 (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx) % Found ((and_rect0 ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx) % Found (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx) % Found (fun (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of ((Xr Xx) Xx) % Found (fun (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (forall (Xx:a), ((Xr Xx) Xx)) % Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx))) % Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))) % Got proof (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) % Time elapsed = 0.165021s % node=19 cost=123.000000 depth=16 % :::::::::::::::::::::: % % 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))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------