0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule --cpu-limit=%d %s 0.03/0.24 % Computer : n140.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 06:15:55 CDT 2018 0.03/0.24 % CPUTime : 0.03/0.24 # Version: 2.2pre001 0.07/0.39 # No SInE strategy applied 0.07/0.39 # Trying AutoSched0 for 151 seconds 10.26/10.50 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_AE_CS_SP_PS_S0Y 10.26/10.50 # and selection function SelectMaxLComplexAvoidPosPred. 10.26/10.50 # 10.26/10.50 # Preprocessing time : 1.136 s 10.26/10.50 # Presaturation interreduction done 10.26/10.50 10.26/10.50 # Proof found! 10.26/10.50 # SZS status Theorem 10.26/10.50 # SZS output start CNFRefutation 10.26/10.50 fof(fact_bex__UNIV, axiom, ![X37, X9]:(?[X21]:(hBOOL(hAPP(hAPP(c_member(X9),X21),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))&hBOOL(hAPP(X37,X21)))<=>?[X91]:hBOOL(hAPP(X37,X91))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__UNIV)). 10.26/10.50 fof(fact_UNIV__I, axiom, ![X11, X9]:hBOOL(hAPP(hAPP(c_member(X9),X11),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__I)). 10.26/10.50 fof(fact_empty__def, axiom, ![X9]:c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))=hAPP(c_Set_OCollect(X9),hAPP(c_COMBK(tc_HOL_Obool,X9),c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__def)). 10.26/10.50 fof(fact_Collect__def, axiom, ![X37, X9]:hAPP(c_Set_OCollect(X9),X37)=X37, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__def)). 10.26/10.50 fof(help_c__fNot__2, axiom, ![X37]:(hBOOL(hAPP(c_fNot,X37))|~(~(hBOOL(X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__2)). 10.26/10.50 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J, axiom, ![X11, X23]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11),X23))=>c_Nat__Transfer_Ois__nat(X11))<=c_Nat__Transfer_Onat__set(X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J)). 10.26/10.50 fof(fact_mem__def, axiom, ![X23, X11, X9]:(hBOOL(hAPP(X23,X11))<=>hBOOL(hAPP(hAPP(c_member(X9),X11),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__def)). 10.26/10.50 fof(fact_number__of__is__id, axiom, ![X29]:X29=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__is__id)). 10.26/10.50 fof(fact_Collect__neg__eq, axiom, ![X37, X9]:hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9),c_fNot),X37))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 10.26/10.50 fof(fact_vimage__Collect__eq, axiom, ![X37, X12, X13, X9]:hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBB(X13,tc_HOL_Obool,X9),X37),X12))=hAPP(c_Set_Ovimage(X9,X13,X12),hAPP(c_Set_OCollect(X13),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Collect__eq)). 10.26/10.50 fof(fact_empty__Collect__eq, axiom, ![X37, X9]:(hAPP(c_Set_OCollect(X9),X37)=c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))<=>![X21]:~(hBOOL(hAPP(X37,X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Collect__eq)). 10.26/10.50 fof(help_c__COMBK__1, axiom, ![X218, X219, X9, X19]:X219=hAPP(hAPP(c_COMBK(X19,X9),X219),X218), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBK__1)). 10.26/10.50 fof(fact_UNIV__def, axiom, ![X9]:c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))=hAPP(c_Set_OCollect(X9),hAPP(c_COMBK(tc_HOL_Obool,X9),c_fTrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__def)). 10.26/10.50 fof(fact_is__nat__def, axiom, ![X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))<=>c_Nat__Transfer_Ois__nat(X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__nat__def)). 10.26/10.50 fof(fact_neg__number__of__Min, axiom, hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Min)). 10.26/10.50 fof(fact_double__complement, axiom, ![X23, X9]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),X23))=X23, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__complement)). 10.26/10.50 fof(fact_vimage__id, axiom, ![X23, X9]:X23=hAPP(c_Set_Ovimage(X9,X9,c_Fun_Oid(X9)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__id)). 10.26/10.50 fof(fact_Compl__empty__eq, axiom, ![X9]:c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 10.26/10.50 fof(fact_someI, axiom, ![X9, X11, X37]:(hBOOL(hAPP(X37,X11))=>hBOOL(hAPP(X37,c_Hilbert__Choice_OEps(X9,X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_someI)). 10.26/10.50 fof(fact_Pls__def, axiom, c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pls__def)). 10.26/10.50 fof(fact_rel__simps_I20_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I20_J)). 10.26/10.50 fof(fact_ex__in__conv, axiom, ![X23, X9]:(X23!=c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))<=>?[X21]:hBOOL(hAPP(hAPP(c_member(X9),X21),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__in__conv)). 10.26/10.50 fof(fact_nat__set__def, axiom, ![X79]:(c_Nat__Transfer_Onat__set(X79)<=>![X21]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21),X79))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__set__def)). 10.26/10.50 fof(fact_ext, axiom, ![X61, X12]:(X12=X61<=![X21]:hAPP(X12,X21)=hAPP(X61,X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ext)). 10.26/10.50 fof(help_c__fNot__1, axiom, ![X37]:(~(hBOOL(hAPP(c_fNot,X37)))|~(hBOOL(X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__1)). 10.26/10.50 fof(help_c__COMBB__1, axiom, ![X50, X75, X37, X24, X9, X13]:hAPP(hAPP(hAPP(c_COMBB(X13,X9,X24),X37),X75),X50)=hAPP(X37,hAPP(X75,X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBB__1)). 10.26/10.50 fof(fact_id__apply, axiom, ![X44, X19]:X44=hAPP(c_Fun_Oid(X19),X44), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__apply)). 10.26/10.50 fof(fact_compl__bot__eq, axiom, ![X19]:(class_Lattices_Oboolean__algebra(X19)=>hAPP(c_Groups_Ouminus__class_Ouminus(X19),c_Orderings_Obot__class_Obot(X19))=c_Orderings_Otop__class_Otop(X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__bot__eq)). 10.26/10.50 fof(fact_bot__fun__def, axiom, ![X11, X13, X9]:(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X13,X9)),X11)=c_Orderings_Obot__class_Obot(X9)<=class_Orderings_Obot(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__fun__def)). 10.26/10.50 fof(fact_exE__some, axiom, ![X9, X16, X37]:((X16=c_Hilbert__Choice_OEps(X9,X37)=>hBOOL(hAPP(X37,X16)))<=?[X91]:hBOOL(hAPP(X37,X91))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exE__some)). 10.26/10.50 fof(arity_HOL__Obool__Lattices_Oboolean__algebra, axiom, class_Lattices_Oboolean__algebra(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Oboolean__algebra)). 10.26/10.50 fof(arity_HOL__Obool__Orderings_Obot, axiom, class_Orderings_Obot(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Obot)). 10.26/10.50 fof(help_c__fTrue__1, axiom, hBOOL(c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fTrue__1)). 10.26/10.50 fof(fact_compl__top__eq, axiom, ![X19]:(hAPP(c_Groups_Ouminus__class_Ouminus(X19),c_Orderings_Otop__class_Otop(X19))=c_Orderings_Obot__class_Obot(X19)<=class_Lattices_Oboolean__algebra(X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__top__eq)). 10.26/10.50 fof(fact_top__apply, axiom, ![X11, X13, X9]:(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,X9)),X11)=c_Orderings_Otop__class_Otop(X9)<=class_Orderings_Otop(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__apply)). 10.26/10.50 fof(fact_finite, axiom, ![X23, X9]:(class_Finite__Set_Ofinite(X9)=>hBOOL(hAPP(c_Finite__Set_Ofinite(X9),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite)). 10.26/10.50 fof(arity_HOL__Obool__Orderings_Otop, axiom, class_Orderings_Otop(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Otop)). 10.26/10.50 fof(fact_finite__set, axiom, ![X20, X9]:hBOOL(hAPP(c_Finite__Set_Ofinite(X9),hAPP(c_List_Oset(X9),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__set)). 10.26/10.50 fof(arity_HOL__Obool__Finite__Set_Ofinite, axiom, class_Finite__Set_Ofinite(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Finite__Set_Ofinite)). 10.26/10.50 fof(fact_Collect__mem__eq, axiom, ![X23, X9]:hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBC(X9,tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool),c_member(X9)),X23))=X23, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__mem__eq)). 10.26/10.50 fof(help_c__COMBC__1, axiom, ![X50, X75, X37, X9, X24, X13]:hAPP(hAPP(X37,X50),X75)=hAPP(hAPP(hAPP(c_COMBC(X13,X24,X9),X37),X75),X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBC__1)). 10.26/10.50 fof(fact_Inter__UNIV, axiom, ![X9]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X9,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__UNIV)). 10.26/10.50 fof(fact_Nats__0, axiom, ![X9]:(hBOOL(hAPP(hAPP(c_member(X9),c_Groups_Ozero__class_Ozero(X9)),c_Nat_Osemiring__1__class_ONats(X9)))<=class_Rings_Osemiring__1(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__0)). 10.26/10.50 fof(arity_Int__Oint__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__1)). 10.26/10.50 fof(fact_not__neg__0, axiom, ~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__0)). 10.26/10.50 fof(help_c__fFalse__1, axiom, ~(hBOOL(c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fFalse__1)). 10.26/10.50 fof(c_0_46, plain, ![X1809, X1810, X1811, X1809, X1813, X1810]:((~hBOOL(hAPP(hAPP(c_member(X1810),X1811),c_Orderings_Otop__class_Otop(tc_fun(X1810,tc_HOL_Obool))))|~hBOOL(hAPP(X1809,X1811))|hBOOL(hAPP(X1809,esk46_1(X1809))))&((hBOOL(hAPP(hAPP(c_member(X1810),esk47_2(X1809,X1810)),c_Orderings_Otop__class_Otop(tc_fun(X1810,tc_HOL_Obool))))|~hBOOL(hAPP(X1809,X1813)))&(hBOOL(hAPP(X1809,esk47_2(X1809,X1810)))|~hBOOL(hAPP(X1809,X1813))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__UNIV])])])])])])])). 10.26/10.50 fof(c_0_47, plain, ![X7791, X7792]:hBOOL(hAPP(hAPP(c_member(X7792),X7791),c_Orderings_Otop__class_Otop(tc_fun(X7792,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__I])). 10.26/10.50 fof(c_0_48, plain, ![X12107]:c_Orderings_Obot__class_Obot(tc_fun(X12107,tc_HOL_Obool))=hAPP(c_Set_OCollect(X12107),hAPP(c_COMBK(tc_HOL_Obool,X12107),c_fFalse)), inference(variable_rename,[status(thm)],[fact_empty__def])). 10.26/10.50 fof(c_0_49, plain, ![X13288, X13289]:hAPP(c_Set_OCollect(X13289),X13288)=X13288, inference(variable_rename,[status(thm)],[fact_Collect__def])). 10.26/10.50 cnf(c_0_50, plain, (hBOOL(hAPP(X3,esk46_1(X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_46])). 10.26/10.50 cnf(c_0_51, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_47])). 10.26/10.50 fof(c_0_52, plain, ![X13468]:(hBOOL(hAPP(c_fNot,X13468))|hBOOL(X13468)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__2])])). 10.26/10.50 fof(c_0_53, plain, ![X7677, X7678]:(~c_Nat__Transfer_Onat__set(X7678)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X7677),X7678))|c_Nat__Transfer_Ois__nat(X7677))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])])])). 10.26/10.50 fof(c_0_54, plain, ![X6892, X6893, X6894, X6892, X6893, X6894]:((~hBOOL(hAPP(X6892,X6893))|hBOOL(hAPP(hAPP(c_member(X6894),X6893),X6892)))&(~hBOOL(hAPP(hAPP(c_member(X6894),X6893),X6892))|hBOOL(hAPP(X6892,X6893)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])])])). 10.26/10.50 fof(c_0_55, plain, ![X9039]:X9039=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9039), inference(variable_rename,[status(thm)],[fact_number__of__is__id])). 10.26/10.50 fof(c_0_56, plain, ![X3206, X3207]:hAPP(c_Set_OCollect(X3207),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3207),c_fNot),X3206))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3207,tc_HOL_Obool)),hAPP(c_Set_OCollect(X3207),X3206)), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 10.26/10.50 fof(c_0_57, plain, ![X3608, X3609, X3610, X3611]:hAPP(c_Set_OCollect(X3611),hAPP(hAPP(c_COMBB(X3610,tc_HOL_Obool,X3611),X3608),X3609))=hAPP(c_Set_Ovimage(X3611,X3610,X3609),hAPP(c_Set_OCollect(X3610),X3608)), inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq])). 10.26/10.50 fof(c_0_58, plain, ![X5104, X5105, X5106, X5104, X5105]:((hAPP(c_Set_OCollect(X5105),X5104)!=c_Orderings_Obot__class_Obot(tc_fun(X5105,tc_HOL_Obool))|~hBOOL(hAPP(X5104,X5106)))&(hBOOL(hAPP(X5104,esk165_1(X5104)))|hAPP(c_Set_OCollect(X5105),X5104)=c_Orderings_Obot__class_Obot(tc_fun(X5105,tc_HOL_Obool)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq])])])])])])])). 10.26/10.50 fof(c_0_59, plain, ![X6195, X6196, X6197, X6198]:X6196=hAPP(hAPP(c_COMBK(X6198,X6197),X6196),X6195), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 10.26/10.51 cnf(c_0_60, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))), inference(split_conjunct,[status(thm)],[c_0_48])). 10.26/10.51 cnf(c_0_61, plain, (hAPP(c_Set_OCollect(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_49])). 10.26/10.51 fof(c_0_62, plain, ![X8943]:c_Orderings_Otop__class_Otop(tc_fun(X8943,tc_HOL_Obool))=hAPP(c_Set_OCollect(X8943),hAPP(c_COMBK(tc_HOL_Obool,X8943),c_fTrue)), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 10.26/10.51 cnf(c_0_63, plain, (hBOOL(hAPP(X1,esk46_1(X1)))|~hBOOL(hAPP(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])). 10.26/10.51 cnf(c_0_64, plain, (hBOOL(hAPP(c_fNot,X1))|hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_52])). 10.26/10.51 fof(c_0_65, plain, ![X9270, X9270]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9270))|c_Nat__Transfer_Ois__nat(X9270))&(~c_Nat__Transfer_Ois__nat(X9270)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9270)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])])])])). 10.26/10.51 cnf(c_0_66, plain, (c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_53])). 10.26/10.51 cnf(c_0_67, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_54])). 10.26/10.51 cnf(c_0_68, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))), inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min])). 10.26/10.51 cnf(c_0_69, plain, (X1=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_55])). 10.26/10.51 fof(c_0_70, plain, ![X3572, X3573]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3573,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3573,tc_HOL_Obool)),X3572))=X3572, inference(variable_rename,[status(thm)],[fact_double__complement])). 10.26/10.51 cnf(c_0_71, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_56])). 10.26/10.51 fof(c_0_72, plain, ![X11928, X11929]:X11928=hAPP(c_Set_Ovimage(X11929,X11929,c_Fun_Oid(X11929)),X11928), inference(variable_rename,[status(thm)],[fact_vimage__id])). 10.26/10.51 cnf(c_0_73, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4))=hAPP(c_Set_Ovimage(X1,X2,X4),hAPP(c_Set_OCollect(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_57])). 10.26/10.51 cnf(c_0_74, plain, (hBOOL(hAPP(X1,esk165_1(X1)))|hAPP(c_Set_OCollect(X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_58])). 10.26/10.51 cnf(c_0_75, plain, (X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_59])). 10.26/10.51 cnf(c_0_76, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_60, c_0_61])). 10.26/10.51 fof(c_0_77, plain, ![X5762]:c_Orderings_Otop__class_Otop(tc_fun(X5762,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5762,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5762,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 10.26/10.51 cnf(c_0_78, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue))), inference(split_conjunct,[status(thm)],[c_0_62])). 10.26/10.51 fof(c_0_79, plain, ![X10519, X10520, X10521]:(~hBOOL(hAPP(X10521,X10520))|hBOOL(hAPP(X10521,c_Hilbert__Choice_OEps(X10519,X10521)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])])). 10.26/10.51 cnf(c_0_80, plain, (hBOOL(hAPP(c_fNot,esk46_1(c_fNot)))|hBOOL(X1)), inference(spm,[status(thm)],[c_0_63, c_0_64])). 10.26/10.51 cnf(c_0_81, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_65])). 10.26/10.51 cnf(c_0_82, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_Pls__def])). 10.26/10.51 cnf(c_0_83, plain, (c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(X2,X1))), inference(spm,[status(thm)],[c_0_66, c_0_67])). 10.26/10.51 cnf(c_0_84, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))), inference(rw,[status(thm)],[c_0_68, c_0_69])). 10.26/10.51 fof(c_0_85, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J])). 10.26/10.51 fof(c_0_86, plain, ![X12272, X12273, X12272, X12273, X12275]:((X12272=c_Orderings_Obot__class_Obot(tc_fun(X12273,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X12273),esk425_2(X12272,X12273)),X12272)))&(~hBOOL(hAPP(hAPP(c_member(X12273),X12275),X12272))|X12272!=c_Orderings_Obot__class_Obot(tc_fun(X12273,tc_HOL_Obool)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])])])). 10.26/10.51 fof(c_0_87, plain, ![X14582, X14583, X14582]:((~c_Nat__Transfer_Onat__set(X14582)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X14583),X14582))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14583))))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk505_1(X14582)),X14582))|c_Nat__Transfer_Onat__set(X14582))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk505_1(X14582)))|c_Nat__Transfer_Onat__set(X14582)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__set__def])])])])])])])). 10.26/10.51 fof(c_0_88, plain, ![X8226, X8227]:(hAPP(X8227,esk283_2(X8226,X8227))!=hAPP(X8226,esk283_2(X8226,X8227))|X8227=X8226), inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ext])])])])])])). 10.26/10.51 cnf(c_0_89, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_70])). 10.26/10.51 cnf(c_0_90, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)=hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_61]), c_0_61])). 10.26/10.51 cnf(c_0_91, plain, (X1=hAPP(c_Set_Ovimage(X2,X2,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_72])). 10.26/10.51 cnf(c_0_92, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_61]), c_0_61])). 10.26/10.51 fof(c_0_93, plain, ![X5012]:(~hBOOL(hAPP(c_fNot,X5012))|~hBOOL(X5012)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 10.26/10.51 cnf(c_0_94, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk165_1(X1)))), inference(rw,[status(thm)],[c_0_74, c_0_61])). 10.26/10.51 cnf(c_0_95, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)=c_fFalse), inference(spm,[status(thm)],[c_0_75, c_0_76])). 10.26/10.51 fof(c_0_96, plain, ![X10850, X10851, X10852, X10853, X10854, X10855]:hAPP(hAPP(hAPP(c_COMBB(X10855,X10854,X10853),X10852),X10851),X10850)=hAPP(X10852,hAPP(X10851,X10850)), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 10.26/10.51 cnf(c_0_97, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_77])). 10.26/10.51 cnf(c_0_98, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_78, c_0_61])). 10.26/10.51 cnf(c_0_99, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_79])). 10.26/10.51 cnf(c_0_100, plain, (hBOOL(hAPP(c_fNot,esk46_1(c_fNot)))), inference(ef,[status(thm)],[c_0_80])). 10.26/10.51 cnf(c_0_101, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~c_Nat__Transfer_Ois__nat(X1)), inference(rw,[status(thm)],[c_0_81, c_0_82])). 10.26/10.51 cnf(c_0_102, plain, (c_Nat__Transfer_Ois__nat(c_Int_OMin)|~c_Nat__Transfer_Onat__set(c_Nat__Numeral_Oneg)), inference(spm,[status(thm)],[c_0_83, c_0_84])). 10.26/10.51 cnf(c_0_103, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_85])). 10.26/10.51 cnf(c_0_104, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|X3!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_86])). 10.26/10.51 cnf(c_0_105, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk505_1(X1)),X1))|c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_87])). 10.26/10.51 cnf(c_0_106, plain, (X1=X2|hAPP(X1,esk283_2(X2,X1))!=hAPP(X2,esk283_2(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_88])). 10.26/10.51 fof(c_0_107, plain, ![X415, X416]:X415=hAPP(c_Fun_Oid(X416),X415), inference(variable_rename,[status(thm)],[fact_id__apply])). 10.26/10.51 cnf(c_0_108, plain, (hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90]), c_0_90])). 10.26/10.51 cnf(c_0_109, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2), inference(rw,[status(thm)],[c_0_91, c_0_92])). 10.26/10.51 cnf(c_0_110, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_93])). 10.26/10.51 cnf(c_0_111, plain, (c_fFalse=X1|hBOOL(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_94]), c_0_95]), c_0_75])). 10.26/10.51 fof(c_0_112, plain, ![X3388]:(~class_Lattices_Oboolean__algebra(X3388)|hAPP(c_Groups_Ouminus__class_Ouminus(X3388),c_Orderings_Obot__class_Obot(X3388))=c_Orderings_Otop__class_Otop(X3388)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])). 10.26/10.51 fof(c_0_113, plain, ![X8670, X8671, X8672]:(~class_Orderings_Obot(X8672)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(X8671,X8672)),X8670)=c_Orderings_Obot__class_Obot(X8672)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot__fun__def])])])). 10.26/10.51 fof(c_0_114, plain, ![X894, X895, X896, X897]:(~hBOOL(hAPP(X896,X897))|(X895!=c_Hilbert__Choice_OEps(X894,X896)|hBOOL(hAPP(X896,X895)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_exE__some])])])])])])). 10.26/10.51 cnf(c_0_115, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_96])). 10.26/10.51 cnf(c_0_116, plain, (hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_97, c_0_90])). 10.26/10.51 cnf(c_0_117, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)=c_fTrue), inference(spm,[status(thm)],[c_0_75, c_0_98])). 10.26/10.51 cnf(c_0_118, plain, (hBOOL(hAPP(c_fNot,c_Hilbert__Choice_OEps(X1,c_fNot)))), inference(spm,[status(thm)],[c_0_99, c_0_100])). 10.26/10.51 cnf(c_0_119, plain, (~c_Nat__Transfer_Onat__set(c_Nat__Numeral_Oneg)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_103])). 10.26/10.51 cnf(c_0_120, plain, (c_Nat__Transfer_Onat__set(X1)|X1!=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))), inference(spm,[status(thm)],[c_0_104, c_0_105])). 10.26/10.51 cnf(c_0_121, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(X1,esk283_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1))!=c_fFalse), inference(spm,[status(thm)],[c_0_106, c_0_95])). 10.26/10.51 cnf(c_0_122, plain, (X1=hAPP(c_Fun_Oid(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_107])). 10.26/10.51 cnf(c_0_123, plain, (c_Fun_Oid(tc_HOL_Obool)=hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot)), inference(spm,[status(thm)],[c_0_108, c_0_109])). 10.26/10.51 cnf(c_0_124, plain, (hAPP(c_fNot,X1)=c_fFalse|~hBOOL(X1)), inference(spm,[status(thm)],[c_0_110, c_0_111])). 10.26/10.51 cnf(c_0_125, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_112])). 10.26/10.51 cnf(c_0_126, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra])). 10.26/10.51 cnf(c_0_127, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3)=c_Orderings_Obot__class_Obot(X1)|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_113])). 10.26/10.51 cnf(c_0_128, plain, (class_Orderings_Obot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot])). 10.26/10.51 cnf(c_0_129, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,X2))|X3!=c_Hilbert__Choice_OEps(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_114])). 10.26/10.51 cnf(c_0_130, plain, (hAPP(c_fNot,c_fFalse)=c_fTrue), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_117]), c_0_95])). 10.26/10.51 cnf(c_0_131, plain, (hBOOL(c_fTrue)), inference(split_conjunct,[status(thm)],[help_c__fTrue__1])). 10.26/10.51 cnf(c_0_132, plain, (~hBOOL(c_Hilbert__Choice_OEps(X1,c_fNot))), inference(spm,[status(thm)],[c_0_110, c_0_118])). 10.26/10.51 cnf(c_0_133, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_119, c_0_120])). 10.26/10.51 cnf(c_0_134, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(spm,[status(thm)],[c_0_121, c_0_95])). 10.26/10.51 cnf(c_0_135, plain, (hAPP(c_fNot,hAPP(c_fNot,X1))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_115])). 10.26/10.51 cnf(c_0_136, plain, (hAPP(c_fNot,X1)=c_fFalse|c_fFalse=X1), inference(spm,[status(thm)],[c_0_124, c_0_111])). 10.26/10.51 fof(c_0_137, plain, ![X12436]:(~class_Lattices_Oboolean__algebra(X12436)|hAPP(c_Groups_Ouminus__class_Ouminus(X12436),c_Orderings_Otop__class_Otop(X12436))=c_Orderings_Obot__class_Obot(X12436)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__top__eq])])])). 10.26/10.51 cnf(c_0_138, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))=c_Orderings_Otop__class_Otop(tc_HOL_Obool)), inference(spm,[status(thm)],[c_0_125, c_0_126])). 10.26/10.51 cnf(c_0_139, plain, (c_Orderings_Obot__class_Obot(tc_HOL_Obool)=c_fFalse), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128]), c_0_95])). 10.26/10.51 fof(c_0_140, plain, ![X13905, X13906, X13907]:(~class_Orderings_Otop(X13907)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13906,X13907)),X13905)=c_Orderings_Otop__class_Otop(X13907)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_top__apply])])])). 10.26/10.51 cnf(c_0_141, plain, (hBOOL(hAPP(c_fNot,X1))|X1!=c_Hilbert__Choice_OEps(X2,c_fNot)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_131])])). 10.26/10.51 cnf(c_0_142, plain, (c_Hilbert__Choice_OEps(X1,c_fNot)=c_fFalse), inference(spm,[status(thm)],[c_0_132, c_0_111])). 10.26/10.51 fof(c_0_143, plain, ![X6590, X6591]:(~class_Finite__Set_Ofinite(X6591)|hBOOL(hAPP(c_Finite__Set_Ofinite(X6591),X6590))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])])). 10.26/10.51 cnf(c_0_144, plain, (hAPP(c_Set_OCollect(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_58])). 10.26/10.51 cnf(c_0_145, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_133, c_0_134])). 10.26/10.51 cnf(c_0_146, plain, (c_fFalse=X1|c_fTrue=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136]), c_0_130])). 10.26/10.51 cnf(c_0_147, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_137])). 10.26/10.51 cnf(c_0_148, plain, (c_Orderings_Otop__class_Otop(tc_HOL_Obool)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse)), inference(rw,[status(thm)],[c_0_138, c_0_139])). 10.26/10.51 cnf(c_0_149, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3)=c_Orderings_Otop__class_Otop(X1)|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_140])). 10.26/10.51 cnf(c_0_150, plain, (class_Orderings_Otop(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop])). 10.26/10.51 fof(c_0_151, plain, ![X2113, X2114]:hBOOL(hAPP(c_Finite__Set_Ofinite(X2114),hAPP(c_List_Oset(X2114),X2113))), inference(variable_rename,[status(thm)],[fact_finite__set])). 10.26/10.51 cnf(c_0_152, plain, (hBOOL(hAPP(c_fNot,X1))|X1!=c_fFalse), inference(rw,[status(thm)],[c_0_141, c_0_142])). 10.26/10.51 cnf(c_0_153, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_143])). 10.26/10.51 cnf(c_0_154, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite])). 10.26/10.51 cnf(c_0_155, plain, (X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_144, c_0_61])). 10.26/10.51 cnf(c_0_156, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_fFalse|c_fTrue!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_145, c_0_146])). 10.26/10.51 cnf(c_0_157, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse))=c_fFalse), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_126]), c_0_148]), c_0_139])). 10.26/10.51 cnf(c_0_158, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse)=c_fTrue), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150]), c_0_117]), c_0_148])). 10.26/10.51 cnf(c_0_159, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_151])). 10.26/10.51 cnf(c_0_160, plain, (X1!=c_fFalse|~hBOOL(X1)), inference(spm,[status(thm)],[c_0_110, c_0_152])). 10.26/10.51 cnf(c_0_161, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),X1))), inference(spm,[status(thm)],[c_0_153, c_0_154])). 10.26/10.51 cnf(c_0_162, plain, (c_fTrue!=c_Nat__Numeral_Oneg|X1!=c_fFalse|~hBOOL(hAPP(X1,X2))), inference(spm,[status(thm)],[c_0_155, c_0_156])). 10.26/10.51 cnf(c_0_163, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fTrue)=c_fFalse), inference(rw,[status(thm)],[c_0_157, c_0_158])). 10.26/10.51 cnf(c_0_164, plain, (hBOOL(hAPP(X1,esk47_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_46])). 10.26/10.51 cnf(c_0_165, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk46_1(c_Finite__Set_Ofinite(X1))))), inference(spm,[status(thm)],[c_0_63, c_0_159])). 10.26/10.51 cnf(c_0_166, plain, (hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),X1)!=c_fFalse), inference(spm,[status(thm)],[c_0_160, c_0_161])). 10.26/10.51 cnf(c_0_167, plain, (c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool)!=c_fFalse|c_fTrue!=c_Nat__Numeral_Oneg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_158]), c_0_131])])). 10.26/10.51 cnf(c_0_168, plain, (hAPP(c_fTrue,c_fTrue)=c_fFalse|c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool)=c_fFalse), inference(spm,[status(thm)],[c_0_163, c_0_146])). 10.26/10.51 cnf(c_0_169, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk47_2(c_Finite__Set_Ofinite(X1),X2)))), inference(spm,[status(thm)],[c_0_164, c_0_165])). 10.26/10.51 cnf(c_0_170, plain, (c_Finite__Set_Ofinite(tc_HOL_Obool)=c_fFalse|hAPP(c_fTrue,X1)!=c_fFalse), inference(spm,[status(thm)],[c_0_166, c_0_146])). 10.26/10.51 cnf(c_0_171, plain, (hAPP(c_fTrue,c_fTrue)=c_fFalse|c_fTrue!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_167, c_0_168])). 10.26/10.51 cnf(c_0_172, plain, (c_Finite__Set_Ofinite(X1)!=c_fFalse|c_fTrue!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_162, c_0_169])). 10.26/10.51 cnf(c_0_173, plain, (c_fTrue!=c_Nat__Numeral_Oneg), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_172])). 10.26/10.51 fof(c_0_174, plain, ![X12545, X12546]:hAPP(c_Set_OCollect(X12546),hAPP(hAPP(c_COMBC(X12546,tc_fun(X12546,tc_HOL_Obool),tc_HOL_Obool),c_member(X12546)),X12545))=X12545, inference(variable_rename,[status(thm)],[fact_Collect__mem__eq])). 10.26/10.51 cnf(c_0_175, plain, (c_fFalse=X1|X1!=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_173, c_0_146])). 10.26/10.51 fof(c_0_176, plain, ![X12815, X12816, X12817, X12818, X12819, X12820]:hAPP(hAPP(X12817,X12815),X12816)=hAPP(hAPP(hAPP(c_COMBC(X12820,X12819,X12818),X12817),X12816),X12815), inference(variable_rename,[status(thm)],[help_c__COMBC__1])). 10.26/10.51 cnf(c_0_177, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_174])). 10.26/10.51 fof(c_0_178, plain, ![X12411]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X12411,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12411,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X12411,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Inter__UNIV])). 10.26/10.51 cnf(c_0_179, plain, (c_fFalse=c_Nat__Numeral_Oneg), inference(er,[status(thm)],[c_0_175])). 10.26/10.51 fof(c_0_180, plain, ![X14407]:(~class_Rings_Osemiring__1(X14407)|hBOOL(hAPP(hAPP(c_member(X14407),c_Groups_Ozero__class_Ozero(X14407)),c_Nat_Osemiring__1__class_ONats(X14407)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__0])])])). 10.26/10.51 cnf(c_0_181, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_COMBC(X4,X5,X6),X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_176])). 10.26/10.51 cnf(c_0_182, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)=X2), inference(rw,[status(thm)],[c_0_177, c_0_61])). 10.26/10.51 cnf(c_0_183, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_178])). 10.26/10.51 cnf(c_0_184, plain, (c_fTrue=X1|c_Nat__Numeral_Oneg=X1), inference(rw,[status(thm)],[c_0_146, c_0_179])). 10.26/10.51 cnf(c_0_185, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_180])). 10.26/10.51 cnf(c_0_186, plain, (hAPP(hAPP(c_member(X1),X2),X3)=hAPP(X3,X2)), inference(spm,[status(thm)],[c_0_181, c_0_182])). 10.26/10.51 cnf(c_0_187, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_fTrue), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183, c_0_184]), c_0_183]), c_0_145])). 10.26/10.51 cnf(c_0_188, plain, (hBOOL(hAPP(c_Nat_Osemiring__1__class_ONats(X1),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[c_0_185, c_0_186])). 10.26/10.51 cnf(c_0_189, plain, (class_Rings_Osemiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1])). 10.26/10.51 fof(c_0_190, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__0])). 10.26/10.51 cnf(c_0_191, plain, (X1!=c_fTrue|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_155, c_0_187])). 10.26/10.51 cnf(c_0_192, plain, (hBOOL(hAPP(c_Nat_Osemiring__1__class_ONats(tc_Int_Oint),c_Int_OPls))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188, c_0_82]), c_0_189])])). 10.26/10.51 cnf(c_0_193, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_190])). 10.26/10.51 fof(c_0_194, plain, ~hBOOL(c_fFalse), inference(fof_simplification,[status(thm)],[help_c__fFalse__1])). 10.26/10.51 cnf(c_0_195, plain, (c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)!=c_fTrue), inference(spm,[status(thm)],[c_0_191, c_0_192])). 10.26/10.51 cnf(c_0_196, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls))), inference(rw,[status(thm)],[c_0_193, c_0_82])). 10.26/10.51 cnf(c_0_197, plain, (~hBOOL(c_fFalse)), inference(split_conjunct,[status(thm)],[c_0_194])). 10.26/10.51 cnf(c_0_198, plain, (c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)=c_Nat__Numeral_Oneg), inference(spm,[status(thm)],[c_0_195, c_0_184])). 10.26/10.51 cnf(c_0_199, plain, (hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)=c_fFalse), inference(spm,[status(thm)],[c_0_196, c_0_111])). 10.26/10.51 cnf(c_0_200, plain, (~hBOOL(c_Nat__Numeral_Oneg)), inference(rw,[status(thm)],[c_0_197, c_0_179])). 10.26/10.51 cnf(c_0_201, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192, c_0_198]), c_0_199]), c_0_179]), c_0_200]), ['proof']). 10.26/10.51 # SZS output end CNFRefutation 10.26/10.51 # Proof object total steps : 202 10.26/10.51 # Proof object clause steps : 118 10.26/10.51 # Proof object formula steps : 84 10.26/10.51 # Proof object conjectures : 0 10.26/10.51 # Proof object clause conjectures : 0 10.26/10.51 # Proof object formula conjectures : 0 10.26/10.51 # Proof object initial clauses used : 48 10.26/10.51 # Proof object initial formulas used : 46 10.26/10.51 # Proof object generating inferences : 48 10.26/10.51 # Proof object simplifying inferences : 50 10.26/10.51 # Training examples: 0 positive, 0 negative 10.26/10.51 # Parsed axioms : 5230 10.26/10.51 # Removed by relevancy pruning/SinE : 0 10.26/10.51 # Initial clauses : 7569 10.26/10.51 # Removed in clause preprocessing : 229 10.26/10.51 # Initial clauses in saturation : 7340 10.26/10.51 # Processed clauses : 23646 10.26/10.51 # ...of these trivial : 481 10.26/10.51 # ...subsumed : 9409 10.26/10.51 # ...remaining for further processing : 13756 10.26/10.51 # Other redundant clauses eliminated : 293 10.26/10.51 # Clauses deleted for lack of memory : 0 10.26/10.51 # Backward-subsumed : 381 10.26/10.51 # Backward-rewritten : 3969 10.26/10.51 # Generated clauses : 277119 10.26/10.51 # ...of the previous two non-trivial : 270129 10.26/10.51 # Contextual simplify-reflections : 1732 10.26/10.51 # Paramodulations : 276645 10.26/10.51 # Factorizations : 6 10.26/10.51 # Equation resolutions : 473 10.26/10.51 # Propositional unsat checks : 0 10.26/10.51 # Propositional check models : 0 10.26/10.51 # Propositional check unsatisfiable : 0 10.26/10.51 # Propositional clauses : 0 10.26/10.51 # Propositional clauses after purity: 0 10.26/10.51 # Propositional unsat core size : 0 10.26/10.51 # Current number of processed clauses : 3270 10.26/10.51 # Positive orientable unit clauses : 1393 10.26/10.51 # Positive unorientable unit clauses: 117 10.26/10.51 # Negative unit clauses : 418 10.26/10.51 # Non-unit-clauses : 1342 10.26/10.51 # Current number of unprocessed clauses: 113816 10.26/10.51 # ...number of literals in the above : 218140 10.26/10.51 # Current number of archived formulas : 0 10.26/10.51 # Current number of archived clauses : 10437 10.26/10.51 # Clause-clause subsumption calls (NU) : 11948094 10.26/10.51 # Rec. Clause-clause subsumption calls : 4245270 10.26/10.51 # Non-unit clause-clause subsumptions : 9492 10.26/10.51 # Unit Clause-clause subsumption calls : 321922 10.26/10.51 # Rewrite failures with RHS unbound : 308 10.26/10.51 # BW rewrite match attempts : 38431 10.26/10.51 # BW rewrite match successes : 1583 10.26/10.51 # Condensation attempts : 0 10.26/10.51 # Condensation successes : 0 10.26/10.51 # Termbank termtop insertions : 7785487 10.33/10.53 10.33/10.53 # ------------------------------------------------- 10.33/10.53 # User time : 10.053 s 10.33/10.53 # System time : 0.234 s 10.33/10.53 # Total time : 10.287 s 10.33/10.53 # Maximum resident set size: 10800 pages 10.33/10.53 EOF