TSTP Solution File: ALG273^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG273^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n100.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 13:18:22 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG273^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n100.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 09:04:16 CDT 2014
% % CPUTime : 300.03
% 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 0x118f518>, <kernel.Type object at 0x118f638>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0xe84bd8>, <kernel.DependentProduct object at 0x118fab8>) of role type named cGROUP2_type
% Using role type
% Declaring cGROUP2:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x118f758>, <kernel.DependentProduct object at 0x118fab8>) of role type named cGROUP3_type
% Using role type
% Declaring cGROUP3:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x118f1b8>, <kernel.DependentProduct object at 0xfb6f80>) of role type named cGRP_ASSOC_type
% Using role type
% Declaring cGRP_ASSOC:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0x118f9e0>, <kernel.DependentProduct object at 0xfb6f80>) of role type named cGRP_LEFT_INVERSE_type
% Using role type
% Declaring cGRP_LEFT_INVERSE:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x118f248>, <kernel.DependentProduct object at 0xfb6c68>) of role type named cGRP_LEFT_UNIT_type
% Using role type
% Declaring cGRP_LEFT_UNIT:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x118f1b8>, <kernel.DependentProduct object at 0xfb6d40>) of role type named cGRP_RIGHT_INVERSE_type
% Using role type
% Declaring cGRP_RIGHT_INVERSE:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x118f9e0>, <kernel.DependentProduct object at 0xfb6b48>) of role type named cGRP_RIGHT_UNIT_type
% Using role type
% Declaring cGRP_RIGHT_UNIT:((g->(g->g))->(g->Prop))
% FOF formula (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))) of role definition named cGRP_ASSOC_def
% A new definition: (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))))
% Defined: cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe)))))) of role definition named cGRP_LEFT_INVERSE_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))))))
% Defined: cGRP_LEFT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))) of role definition named cGRP_LEFT_UNIT_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))))
% Defined: cGRP_LEFT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))) of role definition named cGRP_RIGHT_INVERSE_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))))
% Defined: cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))) of role definition named cGRP_RIGHT_UNIT_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))))
% Defined: cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGROUP2) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe)))) of role definition named cGROUP2_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGROUP2) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe))))
% Defined: cGROUP2:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe)))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))) of role definition named cGROUP3_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))))
% Defined: cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))
% FOF formula (forall (Xf:(g->(g->g))) (Xe:g), ((iff ((cGROUP2 Xf) Xe)) ((cGROUP3 Xf) Xe))) of role conjecture named cEQUIV_02_03
% Conjecture to prove = (forall (Xf:(g->(g->g))) (Xe:g), ((iff ((cGROUP2 Xf) Xe)) ((cGROUP3 Xf) Xe))):Prop
% Parameter g_DUMMY:g.
% We need to prove ['(forall (Xf:(g->(g->g))) (Xe:g), ((iff ((cGROUP2 Xf) Xe)) ((cGROUP3 Xf) Xe)))']
% Parameter g:Type.
% Definition cGROUP2:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe))):((g->(g->g))->(g->Prop)).
% Definition cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))):((g->(g->g))->(g->Prop)).
% Definition cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))):((g->(g->g))->Prop).
% Definition cGRP_LEFT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))))):((g->(g->g))->(g->Prop)).
% Definition cGRP_LEFT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))):((g->(g->g))->(g->Prop)).
% Definition cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))):((g->(g->g))->(g->Prop)).
% Definition cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))):((g->(g->g))->(g->Prop)).
% Trying to prove (forall (Xf:(g->(g->g))) (Xe:g), ((iff ((cGROUP2 Xf) Xe)) ((cGROUP3 Xf) Xe)))
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of (((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of ((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of (((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2) as proof of ((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x2) x0)) (cGRP_ASSOC Xf)) (fun (x2:(cGRP_ASSOC Xf)) (x3:((cGRP_LEFT_UNIT Xf) Xe))=> x2)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of (((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_LEFT_UNIT Xf) Xe)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe)) P) x4) x0)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_LEFT_UNIT Xf) Xe))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found x2:(cGRP_ASSOC Xf)
% Found x2 as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))):(((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))
% Found (eq_ref0 (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) as proof of (((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) b)
% Found ((eq_ref (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) as proof of (((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) b)
% Found ((eq_ref (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) as proof of (((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) b)
% Found ((eq_ref (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) as proof of (((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))):(((eq (g->Prop)) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe)))
% Found (eq_ref0 (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))) as proof of (((eq (g->Prop)) (fun (
% EOF
%------------------------------------------------------------------------------