%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : ALG270^5 : 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 13:18:21 EDT 2014 % Result : Theorem 29.49s % Output : Proof 29.49s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : ALG270^5 : 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 09:03:31 CDT 2014 % % CPUTime : 29.49 % 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 0x24d0908>, <kernel.Type object at 0x22594d0>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0x24d0680>, <kernel.DependentProduct object at 0x1f60998>) of role type named c_star % Using role type % Declaring c_star:(a->(a->a)) % FOF formula ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))->(forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z)))))) of role conjecture named cTHM23_pme % Conjecture to prove = ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))->(forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z)))))):Prop % Parameter a_DUMMY:a. % We need to prove ['((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))->(forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z))))))'] % Parameter a:Type. % Parameter c_star:(a->(a->a)). % Trying to prove ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))->(forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z)))))) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star ((c_star ((c_star W) X)) Y)) Z))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star ((c_star ((c_star W) X)) Y)) Z))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star ((c_star ((c_star W) X)) Y)) Z))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star ((c_star ((c_star W) X)) Y)) Z))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref00:=(eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))):(((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star W) X)) ((c_star Y) Z)))->(P ((c_star ((c_star W) X)) ((c_star Y) Z)))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref0 ((c_star ((c_star W) X)) ((c_star Y) Z))) P) as proof of (P0 ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found (((eq_ref a) ((c_star ((c_star W) X)) ((c_star Y) Z))) P) as proof of (P0 ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found (((eq_ref a) ((c_star ((c_star W) X)) ((c_star Y) Z))) P) as proof of (P0 ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found eq_ref000:=(eq_ref00 P):((P ((c_star W) ((c_star ((c_star X) Y)) Z)))->(P ((c_star W) ((c_star ((c_star X) Y)) Z)))) % Found (eq_ref00 P) as proof of (P0 ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref0 ((c_star W) ((c_star ((c_star X) Y)) Z))) P) as proof of (P0 ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found (((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) P) as proof of (P0 ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found (((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) P) as proof of (P0 ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found eq_ref00:=(eq_ref0 ((c_star W) ((c_star ((c_star X) Y)) Z))):(((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found (eq_ref0 ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found eq_ref00:=(eq_ref0 ((c_star W) ((c_star ((c_star X) Y)) Z))):(((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found (eq_ref0 ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found ((eq_ref a) ((c_star W) ((c_star ((c_star X) Y)) Z))) as proof of (((eq a) ((c_star W) ((c_star ((c_star X) Y)) Z))) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found x000:=(x00 ((c_star Y) Z)):(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x000 as proof of (((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x0:(P ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Instantiate: b:=((c_star ((c_star ((c_star W) X)) Y)) Z):a % Found x0 as proof of (P0 b) % Found eq_ref00:=(eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))):(((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star ((c_star X) Y)) Z))) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref00:=(eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((eq_ref a) b) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x000:=(x00 ((c_star Y) Z)):(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x000 as proof of (((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x000:=(x00 ((c_star Y) Z)):(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found x000 as proof of (((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found eq_ref00:=(eq_ref0 b):(((eq a) b) b) % Found (eq_ref0 b) as proof of (P b) % Found ((eq_ref a) b) as proof of (P b) % Found ((eq_ref a) b) as proof of (P b) % Found ((eq_ref a) b) as proof of (P b) % Found eq_ref00:=(eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))):(((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (eq_ref0 ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found ((eq_ref a) ((c_star W) ((c_star X) ((c_star Y) Z)))) as proof of (((eq a) ((c_star W) ((c_star X) ((c_star Y) Z)))) b) % Found eq_ref000:=(eq_ref00 P):((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star ((c_star ((c_star W) X)) Y)) Z))) % Found (eq_ref00 P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found ((eq_ref0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P) as proof of (P0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) % Found x000:=(x00 Z):(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z))) % Found (x00 Z) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found ((x0 Y) Z) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found (((x ((c_star W) X)) Y) Z) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found (((x ((c_star W) X)) Y) Z) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found (((x ((c_star W) X)) Y) Z) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) % Found x000:=(x00 ((c_star Y) Z)):(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (x00 ((c_star Y) Z)) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found ((x0 X) ((c_star Y) Z)) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (((x W) X) ((c_star Y) Z)) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (((x W) X) ((c_star Y) Z)) as proof of (((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (((eq_trans00000 (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (((eq_trans00000 (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b)) (x1:(((eq a) b) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((eq_trans0000 x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> ((((eq_trans000 ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((eq_trans00 b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> (((eq_trans0 ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P)) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z)))) % Found (fun (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of (forall (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of (forall (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (W:a) (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of (forall (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (x:(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))) (W:a) (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of (forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z))))) % Found (fun (x:(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))) (W:a) (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))->(forall (W:a) (X:a) (Y:a) (Z:a), (((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star W) ((c_star X) ((c_star Y) Z)))))) % Got proof (fun (x:(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))) (W:a) (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) % Time elapsed = 28.986532s % node=4746 cost=787.000000 depth=17 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:(forall (Xx:a) (Xy:a) (Xz:a), (((eq a) ((c_star ((c_star Xx) Xy)) Xz)) ((c_star Xx) ((c_star Xy) Xz))))) (W:a) (X:a) (Y:a) (Z:a) (P:(a->Prop))=> ((((fun (x0:(((eq a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) ((c_star ((c_star W) X)) ((c_star Y) Z)))) (x1:(((eq a) ((c_star ((c_star W) X)) ((c_star Y) Z))) ((c_star W) ((c_star X) ((c_star Y) Z)))))=> (((((fun (b:a)=> ((((eq_trans a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) b) ((c_star W) ((c_star X) ((c_star Y) Z))))) ((c_star ((c_star W) X)) ((c_star Y) Z))) x0) x1) (fun (x3:a)=> ((P ((c_star ((c_star ((c_star W) X)) Y)) Z))->(P x3))))) (((x ((c_star W) X)) Y) Z)) (((x W) X) ((c_star Y) Z))) (((eq_ref a) ((c_star ((c_star ((c_star W) X)) Y)) Z)) P))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF 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