%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEV017^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n179.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 13:33:35 EDT 2014 % Result : Theorem 0.64s % Output : Proof 0.64s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEV017^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n179.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 07:30:21 CDT 2014 % % CPUTime : 0.64 % 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 0xdbe830>, <kernel.Type object at 0xdbed40>) 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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))) of role conjecture named cTHM514_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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))):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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))))'] % 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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))) % Found x0:((Xr Xx) Xy) % Instantiate: Xy0:=Xy:a % Found x0 as proof of ((Xr Xx) Xy0) % Found x1:((Xr Xy) Xz) % Instantiate: Xy0:=Xy:a % Found x1 as proof of ((Xr Xy0) Xz) % Found ((conj00 x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) % Found (((conj0 ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) % Found ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) % Found ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) % Found (x3000 ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1)) as proof of ((Xr Xx) Xz) % Found ((x300 Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz) % Found (((fun (Xy0:a)=> ((x30 Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz) % Found (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz) % Found (fun (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) as proof of ((Xr Xx) Xz) % Found (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) as proof of ((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0)))->((Xr Xx) Xz)) % Found (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) 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) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0)))->((Xr Xx) Xz))) % Found (and_rect00 (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz) % Found ((and_rect0 ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz) % Found (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz) % Found (fun (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of ((Xr Xx) Xz) % Found (fun (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (((Xr Xy) Xz)->((Xr Xx) Xz)) % Found (fun (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))) % Found (fun (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))) % Found (fun (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))) % 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) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))) % 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) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) 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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))) % 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) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) 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) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))) % 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) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) % Time elapsed = 0.320395s % node=47 cost=642.000000 depth=22 % :::::::::::::::::::::: % % 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) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((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) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------