TSTP Solution File: SEV296^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV296^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n041.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 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:27:24 EDT 2015
% Result : Unknown 272.39s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV296^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.01/1.07 % Computer : n041.star.cs.uiowa.edu
% 0.01/1.07 % Model : x86_64 x86_64
% 0.01/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.01/1.07 % Memory : 32286.75MB
% 0.01/1.07 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.01/1.07 % CPULimit : 300
% 0.01/1.07 % DateTime : Thu Apr 16 12:16:47 CDT 2015
% 0.01/1.07 % CPUTime :
% 0.01/1.09 Python 2.7.5
% 0.29/1.50 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cbb90>, <kernel.DependentProduct object at 0x22cb4d0>) of role type named c_plus_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring c_plus:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)))
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x24a9050>, <kernel.DependentProduct object at 0x22cb830>) of role type named c_star_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring c_star:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)))
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb878>, <kernel.DependentProduct object at 0x22cb3b0>) of role type named cONE_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cONE:((fofType->Prop)->Prop)
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb488>, <kernel.Sort object at 0x21aeef0>) of role type named cPLUS_AXIOMS_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cPLUS_AXIOMS:Prop
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb830>, <kernel.DependentProduct object at 0x22cb368>) of role type named cSUCC_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cSUCC:(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb638>, <kernel.Sort object at 0x21aeef0>) of role type named cTIMES_AXIOMS_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cTIMES_AXIOMS:Prop
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb518>, <kernel.DependentProduct object at 0x22cb3f8>) of role type named cTWO_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cTWO:((fofType->Prop)->Prop)
% 0.29/1.50 FOF formula (<kernel.Constant object at 0x22cb878>, <kernel.DependentProduct object at 0x22cb488>) of role type named cZERO_type
% 0.29/1.50 Using role type
% 0.29/1.50 Declaring cZERO:((fofType->Prop)->Prop)
% 0.29/1.50 FOF formula (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))) of role definition named cZERO_def
% 0.29/1.50 A new definition: (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)))
% 0.29/1.50 Defined: cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))
% 0.29/1.50 FOF formula (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))) of role definition named cSUCC_def
% 0.29/1.50 A new definition: (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))))
% 0.29/1.50 Defined: cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))
% 0.29/1.50 FOF formula (((eq ((fofType->Prop)->Prop)) cONE) (cSUCC cZERO)) of role definition named cONE_def
% 0.29/1.50 A new definition: (((eq ((fofType->Prop)->Prop)) cONE) (cSUCC cZERO))
% 0.29/1.50 Defined: cONE:=(cSUCC cZERO)
% 0.29/1.50 FOF formula (((eq ((fofType->Prop)->Prop)) cTWO) (cSUCC cONE)) of role definition named cTWO_def
% 0.29/1.50 A new definition: (((eq ((fofType->Prop)->Prop)) cTWO) (cSUCC cONE))
% 0.29/1.50 Defined: cTWO:=(cSUCC cONE)
% 0.29/1.50 FOF formula (((eq Prop) cPLUS_AXIOMS) ((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) cZERO)) X))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) (cSUCC Y))) (cSUCC ((c_plus X) Y)))))) of role definition named cPLUS_AXIOMS_def
% 0.29/1.50 A new definition: (((eq Prop) cPLUS_AXIOMS) ((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) cZERO)) X))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) (cSUCC Y))) (cSUCC ((c_plus X) Y))))))
% 0.29/1.50 Defined: cPLUS_AXIOMS:=((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) cZERO)) X))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) (cSUCC Y))) (cSUCC ((c_plus X) Y)))))
% 8.09/9.32 FOF formula (((eq Prop) cTIMES_AXIOMS) ((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) cZERO)) cZERO))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) (cSUCC Y))) ((c_plus ((c_star X) Y)) Y))))) of role definition named cTIMES_AXIOMS_def
% 8.09/9.32 A new definition: (((eq Prop) cTIMES_AXIOMS) ((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) cZERO)) cZERO))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) (cSUCC Y))) ((c_plus ((c_star X) Y)) Y)))))
% 8.09/9.32 Defined: cTIMES_AXIOMS:=((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) cZERO)) cZERO))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) (cSUCC Y))) ((c_plus ((c_star X) Y)) Y))))
% 8.09/9.32 FOF formula (((and cPLUS_AXIOMS) cTIMES_AXIOMS)->(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) ((c_plus cTWO) cTWO))) of role conjecture named cFOUR_THEOREM_B
% 8.09/9.32 Conjecture to prove = (((and cPLUS_AXIOMS) cTIMES_AXIOMS)->(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) ((c_plus cTWO) cTWO))):Prop
% 8.09/9.32 Parameter fofType_DUMMY:fofType.
% 8.09/9.32 We need to prove ['(((and cPLUS_AXIOMS) cTIMES_AXIOMS)->(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) ((c_plus cTWO) cTWO)))']
% 8.09/9.32 Parameter fofType:Type.
% 8.09/9.32 Parameter c_plus:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))).
% 8.09/9.32 Parameter c_star:(((fofType->Prop)->Prop)->(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))).
% 8.09/9.32 Definition cONE:=(cSUCC cZERO):((fofType->Prop)->Prop).
% 8.09/9.32 Definition cPLUS_AXIOMS:=((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) cZERO)) X))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_plus X) (cSUCC Y))) (cSUCC ((c_plus X) Y))))):Prop.
% 8.09/9.32 Definition cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))):(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)).
% 8.09/9.32 Definition cTIMES_AXIOMS:=((and (forall (X:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) cZERO)) cZERO))) (forall (X:((fofType->Prop)->Prop)) (Y:((fofType->Prop)->Prop)), (((eq ((fofType->Prop)->Prop)) ((c_star X) (cSUCC Y))) ((c_plus ((c_star X) Y)) Y)))):Prop.
% 8.09/9.32 Definition cTWO:=(cSUCC cONE):((fofType->Prop)->Prop).
% 8.09/9.32 Definition cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)):((fofType->Prop)->Prop).
% 8.09/9.32 Trying to prove (((and cPLUS_AXIOMS) cTIMES_AXIOMS)->(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) ((c_plus cTWO) cTWO)))
% 8.09/9.32 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 8.09/9.32 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 8.09/9.32 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 8.09/9.32 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 8.09/9.32 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 8.09/9.32 Found eta_expansion000:=(eta_expansion00 ((c_star cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) (fun (x:(fofType->Prop))=> (((c_star cTWO) cTWO) x)))
% 8.09/9.32 Found (eta_expansion00 ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 8.09/9.32 Found ((eta_expansion0 Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 8.09/9.32 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 8.09/9.32 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 8.09/9.32 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 43.71/44.96 Found x00:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found x00:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found x00:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x00:(P ((c_star cTWO) cTWO)))=> x00) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 43.71/44.96 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 43.71/44.96 Found eq_ref00:=(eq_ref0 ((c_star cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) ((c_star cTWO) cTWO))
% 43.71/44.96 Found (eq_ref0 ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 43.71/44.96 Found x20:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 43.71/44.96 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 43.71/44.96 Found eq_ref00:=(eq_ref0 ((c_plus cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) ((c_plus cTWO) cTWO))
% 43.71/44.96 Found (eq_ref0 ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 43.71/44.96 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 43.71/44.96 Found x20:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found x20:(P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P ((c_star cTWO) cTWO))
% 43.71/44.96 Found (fun (x20:(P ((c_star cTWO) cTWO)))=> x20) as proof of (P0 ((c_star cTWO) cTWO))
% 43.71/44.96 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x0)):(((eq Prop) (((c_star cTWO) cTWO) x0)) (((c_star cTWO) cTWO) x0))
% 43.71/44.96 Found (eq_ref0 (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 43.71/44.96 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 43.71/44.96 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 43.71/44.96 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 43.71/44.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 43.71/44.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x0)):(((eq Prop) (((c_star cTWO) cTWO) x0)) (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found (eq_ref0 (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 64.42/65.60 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 64.42/65.60 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 64.42/65.60 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 64.42/65.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.42/65.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 64.42/65.60 Found x00:(P ((c_plus cTWO) cTWO))
% 64.42/65.60 Found (fun (x00:(P ((c_plus cTWO) cTWO)))=> x00) as proof of (P ((c_plus cTWO) cTWO))
% 64.42/65.60 Found (fun (x00:(P ((c_plus cTWO) cTWO)))=> x00) as proof of (P0 ((c_plus cTWO) cTWO))
% 64.42/65.60 Found x00:(P ((c_plus cTWO) cTWO))
% 64.42/65.60 Found (fun (x00:(P ((c_plus cTWO) cTWO)))=> x00) as proof of (P ((c_plus cTWO) cTWO))
% 64.42/65.60 Found (fun (x00:(P ((c_plus cTWO) cTWO)))=> x00) as proof of (P0 ((c_plus cTWO) cTWO))
% 64.42/65.60 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 64.42/65.60 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found x10:(P (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found (fun (x10:(P (((c_star cTWO) cTWO) x0)))=> x10) as proof of (P (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found (fun (x10:(P (((c_star cTWO) cTWO) x0)))=> x10) as proof of (P0 (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found x10:(P (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found (fun (x10:(P (((c_star cTWO) cTWO) x0)))=> x10) as proof of (P (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found (fun (x10:(P (((c_star cTWO) cTWO) x0)))=> x10) as proof of (P0 (((c_star cTWO) cTWO) x0))
% 64.42/65.60 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 64.42/65.60 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 64.42/65.60 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 64.42/65.60 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found x300:=(x30 cONE):(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) (cSUCC cONE))) ((c_plus ((c_star cTWO) cONE)) cONE))
% 64.42/65.60 Found (x30 cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 64.42/65.60 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 64.42/65.60 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 64.42/65.60 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 64.42/65.60 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 64.42/65.60 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 64.42/65.60 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 102.34/103.56 Found eta_expansion000:=(eta_expansion00 ((c_star cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) (fun (x:(fofType->Prop))=> (((c_star cTWO) cTWO) x)))
% 102.34/103.56 Found (eta_expansion00 ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 102.34/103.56 Found ((eta_expansion0 Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 102.34/103.56 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 102.34/103.56 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 102.34/103.56 Found (((eta_expansion (fofType->Prop)) Prop) ((c_star cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 102.34/103.56 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 102.34/103.56 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 102.34/103.56 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 102.34/103.56 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 102.34/103.56 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 102.34/103.56 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 102.34/103.56 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 102.34/103.56 Found eq_ref00:=(eq_ref0 ((c_plus cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) ((c_plus cTWO) cTWO))
% 102.34/103.56 Found (eq_ref0 ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 102.34/103.56 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 102.34/103.56 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 102.34/103.56 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found eq_ref00:=(eq_ref0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))):(((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found (eq_ref0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 119.03/120.28 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x2)):(((eq Prop) (((c_star cTWO) cTWO) x2)) (((c_star cTWO) cTWO) x2))
% 119.03/120.28 Found (eq_ref0 (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.03/120.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x2)):(((eq Prop) (((c_star cTWO) cTWO) x2)) (((c_star cTWO) cTWO) x2))
% 119.03/120.28 Found (eq_ref0 (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x2)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x2)) b)
% 119.03/120.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.03/120.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x2))
% 119.03/120.28 Found x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 119.03/120.28 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 119.03/120.28 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 119.03/120.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 119.03/120.28 Found eq_ref00:=(eq_ref0 ((c_plus cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) ((c_plus cTWO) cTWO))
% 119.03/120.28 Found (eq_ref0 ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 161.34/162.51 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 161.34/162.51 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 161.34/162.51 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 161.34/162.51 Found x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found x20:(P ((c_plus cTWO) cTWO))
% 161.34/162.51 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P ((c_plus cTWO) cTWO))
% 161.34/162.51 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P0 ((c_plus cTWO) cTWO))
% 161.34/162.51 Found x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found (fun (x00:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x00) as proof of (P0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 161.34/162.51 Found x20:(P ((c_plus cTWO) cTWO))
% 161.34/162.51 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P ((c_plus cTWO) cTWO))
% 161.34/162.51 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P0 ((c_plus cTWO) cTWO))
% 161.34/162.51 Found x30:(P (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found (fun (x30:(P (((c_star cTWO) cTWO) x2)))=> x30) as proof of (P (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found (fun (x30:(P (((c_star cTWO) cTWO) x2)))=> x30) as proof of (P0 (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found x30:(P (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found (fun (x30:(P (((c_star cTWO) cTWO) x2)))=> x30) as proof of (P (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found (fun (x30:(P (((c_star cTWO) cTWO) x2)))=> x30) as proof of (P0 (((c_star cTWO) cTWO) x2))
% 161.34/162.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 161.34/162.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found eq_ref00:=(eq_ref0 (((c_plus cTWO) cTWO) x0)):(((eq Prop) (((c_plus cTWO) cTWO) x0)) (((c_plus cTWO) cTWO) x0))
% 161.34/162.51 Found (eq_ref0 (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found eq_ref00:=(eq_ref0 (((c_plus cTWO) cTWO) x0)):(((eq Prop) (((c_plus cTWO) cTWO) x0)) (((c_plus cTWO) cTWO) x0))
% 161.34/162.51 Found (eq_ref0 (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 161.34/162.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 161.34/162.51 Found eq_ref00:=(eq_ref0 (((c_plus cTWO) cTWO) x0)):(((eq Prop) (((c_plus cTWO) cTWO) x0)) (((c_plus cTWO) cTWO) x0))
% 161.34/162.51 Found (eq_ref0 (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 161.34/162.51 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.46/207.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found eq_ref00:=(eq_ref0 (((c_plus cTWO) cTWO) x0)):(((eq Prop) (((c_plus cTWO) cTWO) x0)) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found (eq_ref0 (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_plus cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_plus cTWO) cTWO) x0)) b)
% 206.46/207.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.46/207.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x0)):(((eq Prop) (((c_star cTWO) cTWO) x0)) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found (eq_ref0 (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.46/207.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found eq_ref00:=(eq_ref0 (((c_star cTWO) cTWO) x0)):(((eq Prop) (((c_star cTWO) cTWO) x0)) (((c_star cTWO) cTWO) x0))
% 206.46/207.68 Found (eq_ref0 (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found ((eq_ref Prop) (((c_star cTWO) cTWO) x0)) as proof of (((eq Prop) (((c_star cTWO) cTWO) x0)) b)
% 206.46/207.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.46/207.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((c_plus cTWO) cTWO) x0))
% 206.46/207.68 Found x20:(P ((c_plus cTWO) cTWO))
% 206.46/207.68 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P ((c_plus cTWO) cTWO))
% 206.46/207.68 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P0 ((c_plus cTWO) cTWO))
% 206.46/207.68 Found x20:(P ((c_plus cTWO) cTWO))
% 206.46/207.68 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P ((c_plus cTWO) cTWO))
% 206.46/207.68 Found (fun (x20:(P ((c_plus cTWO) cTWO)))=> x20) as proof of (P0 ((c_plus cTWO) cTWO))
% 206.46/207.68 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 206.46/207.68 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 206.46/207.68 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 206.46/207.68 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found eq_ref00:=(eq_ref0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))):(((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found (eq_ref0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 254.88/256.05 Found x10:(P (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x10:(P (((c_plus cTWO) cTWO) x0)))=> x10) as proof of (P (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x10:(P (((c_plus cTWO) cTWO) x0)))=> x10) as proof of (P0 (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found x10:(P (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x10:(P (((c_plus cTWO) cTWO) x0)))=> x10) as proof of (P (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x10:(P (((c_plus cTWO) cTWO) x0)))=> x10) as proof of (P0 (((c_plus cTWO) cTWO) x0))
% 254.88/256.05 Found x30:(P (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x30:(P (((c_star cTWO) cTWO) x0)))=> x30) as proof of (P (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x30:(P (((c_star cTWO) cTWO) x0)))=> x30) as proof of (P0 (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found x30:(P (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x30:(P (((c_star cTWO) cTWO) x0)))=> x30) as proof of (P (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found (fun (x30:(P (((c_star cTWO) cTWO) x0)))=> x30) as proof of (P0 (((c_star cTWO) cTWO) x0))
% 254.88/256.05 Found x20:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found (fun (x20:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x20) as proof of (P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found (fun (x20:(P ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))))=> x20) as proof of (P0 ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 254.88/256.05 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 254.88/256.05 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 254.88/256.05 Found eta_expansion_dep000:=(eta_expansion_dep00 ((c_plus cTWO) cTWO)):(((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) (fun (x:(fofType->Prop))=> (((c_plus cTWO) cTWO) x)))
% 254.88/256.05 Found (eta_expansion_dep00 ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 254.88/256.05 Found ((eta_expansion_dep0 (fun (x5:(fofType->Prop))=> Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 254.88/256.05 Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 254.88/256.05 Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 254.88/256.05 Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) ((c_plus cTWO) cTWO)) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 254.88/256.05 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 254.88/256.05 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 254.88/256.05 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star cTWO) cTWO))
% 272.39/273.57 Found x300:=(x30 cONE):(((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) (cSUCC cONE))) (cSUCC ((c_plus cTWO) cONE)))
% 272.39/273.57 Found (x30 cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 272.39/273.57 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 272.39/273.57 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 272.39/273.57 Found ((x3 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus cTWO) cTWO)) b)
% 272.39/273.57 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 272.39/273.57 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found eq_ref000:=(eq_ref00 P):((P ((c_star cTWO) cTWO))->(P ((c_star cTWO) cTWO)))
% 272.39/273.57 Found (eq_ref00 P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref0 ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found (((eq_ref ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) P) as proof of (P0 ((c_star cTWO) cTWO))
% 272.39/273.57 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 272.39/273.57 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_plus cTWO) cTWO))
% 272.39/273.57 Found x500:=(x50 cONE):(((eq ((fofType->Prop)->Prop)) ((c_star cTWO) (cSUCC cONE))) ((c_plus ((c_star cTWO) cONE)) cONE))
% 272.39/273.57 Found (x50 cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 272.39/273.57 Found ((x5 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 272.39/273.57 Found ((x5 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 272.39/273.57 Found ((x5 cTWO) cONE) as proof of (((eq ((fofType->Prop)->Prop)) ((c_star cTWO) cTWO)) b)
% 272.39/273.57 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 272.39/273.57 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) ((c_star (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 272.39/273.57 Found eq_ref00:=(eq_ref0 ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))):(((eq ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO))))
% 272.39/273.57 Found (eq_ref0 ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) as proof of (((eq ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO))) (cSUCC (cSUCC cZERO)))) b)
% 272.39/273.57 Found ((eq_ref ((fofType->Prop)->Prop)) ((c_plus (cSUCC (cSUCC cZERO)))
%------------------------------------------------------------------------------