TSTP Solution File: ALG270^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------