0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -jar mcs_epr.jar %d %s 0.02/0.24 % Computer : n118.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 06:18:10 CDT 2018 0.02/0.24 % CPUTime : 0.08/0.31 openjdk version "1.8.0_144" 0.08/0.31 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.08/0.31 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.15/0.43 start to proof:theBenchmark.p 11.46/11.62 % Version : CSE_E---1.0 11.46/11.62 % Problem : theBenchmark.p 11.46/11.62 % Proof found! 11.46/11.62 % SZS status Theorem for theBenchmark.p 11.46/11.62 % SZS output start Proof 11.46/11.62 fof(fact_empty__def, axiom, (![X14]:hAPP(c_Set_OCollect(X14),hAPP(c_COMBK(tc_HOL_Obool,X14),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__def)). 11.46/11.62 fof(fact_Collect__def, axiom, (![X39]:![X14]:X39=hAPP(c_Set_OCollect(X14),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__def)). 11.46/11.62 fof(fact_Collect__neg__eq, axiom, (![X39]:![X14]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14,tc_HOL_Obool)),hAPP(c_Set_OCollect(X14),X39))=hAPP(c_Set_OCollect(X14),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14),c_fNot),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 11.46/11.62 fof(fact_vimage__Collect__eq, axiom, (![X39]:![X37]:![X38]:![X14]:hAPP(c_Set_OCollect(X14),hAPP(hAPP(c_COMBB(X38,tc_HOL_Obool,X14),X39),X37))=hAPP(c_Set_Ovimage(X14,X38,X37),hAPP(c_Set_OCollect(X38),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Collect__eq)). 11.46/11.62 fof(fact_Collect__empty__eq, axiom, (![X39]:![X14]:(![X15]:~(hBOOL(hAPP(X39,X15)))<=>hAPP(c_Set_OCollect(X14),X39)=c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 11.46/11.62 fof(help_c__COMBK__1, axiom, (![X235]:![X236]:![X14]:![X7]:X236=hAPP(hAPP(c_COMBK(X7,X14),X236),X235)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBK__1)). 11.46/11.62 fof(fact_double__complement, axiom, (![X32]:![X14]:X32=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14,tc_HOL_Obool)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__complement)). 11.46/11.62 fof(fact_vimage__id, axiom, (![X32]:![X14]:X32=hAPP(c_Set_Ovimage(X14,X14,c_Fun_Oid(X14)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__id)). 11.46/11.62 fof(fact_UNIV__def, axiom, (![X14]:hAPP(c_Set_OCollect(X14),hAPP(c_COMBK(tc_HOL_Obool,X14),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__def)). 11.46/11.63 fof(fact_add__eq__self__zero, axiom, (![X29]:![X12]:(X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X29)=>X29=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 11.46/11.63 fof(fact_transfer__nat__int__numerals_I1_J, axiom, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__numerals_I1_J)). 11.46/11.63 fof(fact_Pls__def, axiom, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pls__def)). 11.46/11.63 fof(fact_nat_Osimps_I3_J, axiom, (![X272]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X272)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osimps_I3_J)). 11.46/11.63 fof(help_c__fNot__1, axiom, (![X39]:(~(hBOOL(hAPP(c_fNot,X39)))|~(hBOOL(X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__1)). 11.46/11.63 fof(fact_Compl__empty__eq, axiom, (![X14]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 11.46/11.63 fof(fact_add__Suc__right, axiom, (![X29]:![X12]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc__right)). 11.46/11.63 fof(fact_id__apply, axiom, (![X5]:![X7]:X5=hAPP(c_Fun_Oid(X7),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__apply)). 11.46/11.63 fof(help_c__COMBB__1, axiom, (![X11]:![X119]:![X39]:![X65]:![X14]:![X38]:hAPP(hAPP(hAPP(c_COMBB(X38,X14,X65),X39),X119),X11)=hAPP(X39,hAPP(X119,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBB__1)). 11.46/11.63 fof(fact_Nat_Oadd__0__right, axiom, (![X12]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 11.46/11.63 fof(fact_n__not__Suc__n, axiom, (![X29]:hAPP(c_Nat_OSuc,X29)!=X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__not__Suc__n)). 11.46/11.63 fof(c_0_20, plain, (![X15]:hAPP(c_Set_OCollect(X15),hAPP(c_COMBK(tc_HOL_Obool,X15),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_empty__def])). 11.46/11.63 fof(c_0_21, plain, (![X40]:![X41]:X40=hAPP(c_Set_OCollect(X41),X40)), inference(variable_rename,[status(thm)],[fact_Collect__def])). 11.46/11.63 fof(c_0_22, plain, (![X40]:![X41]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X41,tc_HOL_Obool)),hAPP(c_Set_OCollect(X41),X40))=hAPP(c_Set_OCollect(X41),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X41),c_fNot),X40))), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 11.46/11.63 fof(c_0_23, plain, (![X40]:![X41]:![X42]:![X43]:hAPP(c_Set_OCollect(X43),hAPP(hAPP(c_COMBB(X42,tc_HOL_Obool,X43),X40),X41))=hAPP(c_Set_Ovimage(X43,X42,X41),hAPP(c_Set_OCollect(X42),X40))), inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq])). 11.46/11.63 fof(c_0_24, plain, (![X40]:![X41]:![X40]:![X41]:![X43]:((hBOOL(hAPP(X40,esk66_1(X40)))|hAPP(c_Set_OCollect(X41),X40)=c_Orderings_Obot__class_Obot(tc_fun(X41,tc_HOL_Obool)))&(hAPP(c_Set_OCollect(X41),X40)!=c_Orderings_Obot__class_Obot(tc_fun(X41,tc_HOL_Obool))|~hBOOL(hAPP(X40,X43))))), 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_Collect__empty__eq])])])])])])])). 11.46/11.63 fof(c_0_25, plain, (![X237]:![X238]:![X239]:![X240]:X238=hAPP(hAPP(c_COMBK(X240,X239),X238),X237)), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 11.46/11.63 cnf(c_0_26,plain,(hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_20])). 11.46/11.63 cnf(c_0_27,plain,(X1=hAPP(c_Set_OCollect(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_21])). 11.46/11.63 fof(c_0_28, plain, (![X33]:![X34]:X33=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X34,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X34,tc_HOL_Obool)),X33))), inference(variable_rename,[status(thm)],[fact_double__complement])). 11.46/11.63 cnf(c_0_29,plain,(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))), inference(split_conjunct,[status(thm)],[c_0_22])). 11.46/11.63 fof(c_0_30, plain, (![X33]:![X34]:X33=hAPP(c_Set_Ovimage(X34,X34,c_Fun_Oid(X34)),X33)), inference(variable_rename,[status(thm)],[fact_vimage__id])). 11.46/11.63 cnf(c_0_31,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_23])). 11.46/11.63 cnf(c_0_32,plain,(hAPP(c_Set_OCollect(X1),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X2,esk66_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_24])). 11.46/11.63 cnf(c_0_33,plain,(X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_25])). 11.46/11.63 cnf(c_0_34,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_26, c_0_27])). 11.46/11.63 fof(c_0_35, plain, (![X15]:hAPP(c_Set_OCollect(X15),hAPP(c_COMBK(tc_HOL_Obool,X15),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 11.46/11.63 fof(c_0_36, plain, (![X30]:![X31]:(X31!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30)|X30=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])])])). 11.46/11.63 cnf(c_0_37,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J])). 11.46/11.63 cnf(c_0_38,plain,(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_Pls__def])). 11.46/11.63 fof(c_0_39, plain, (![X273]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X273)), inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J])). 11.46/11.63 cnf(c_0_40,plain,(X1=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X1))), inference(split_conjunct,[status(thm)],[c_0_28])). 11.46/11.63 cnf(c_0_41,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_29, c_0_27]), c_0_27])). 11.46/11.63 cnf(c_0_42,plain,(X1=hAPP(c_Set_Ovimage(X2,X2,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_30])). 11.46/11.63 cnf(c_0_43,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_31, c_0_27]), c_0_27])). 11.46/11.63 fof(c_0_44, plain, (![X40]:(~hBOOL(hAPP(c_fNot,X40))|~hBOOL(X40))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 11.46/11.63 cnf(c_0_45,plain,(X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk66_1(X1)))), inference(rw,[status(thm)],[c_0_32, c_0_27])). 11.46/11.63 cnf(c_0_46,plain,(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)=c_fFalse), inference(spm,[status(thm)],[c_0_33, c_0_34])). 11.46/11.63 fof(c_0_47, plain, (![X15]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 11.46/11.63 cnf(c_0_48,plain,(hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_35])). 11.46/11.63 cnf(c_0_49,plain,(X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_36])). 11.46/11.63 cnf(c_0_50,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Int_OPls)), inference(rw,[status(thm)],[c_0_37, c_0_38])). 11.46/11.63 fof(c_0_51, plain, (![X30]:![X31]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30))), inference(variable_rename,[status(thm)],[fact_add__Suc__right])). 11.46/11.63 cnf(c_0_52,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_39])). 11.46/11.63 fof(c_0_53, plain, (![X8]:![X9]:X8=hAPP(c_Fun_Oid(X9),X8)), inference(variable_rename,[status(thm)],[fact_id__apply])). 11.46/11.63 cnf(c_0_54,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_40, c_0_41]), c_0_41])). 11.46/11.63 cnf(c_0_55,plain,(hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2), inference(rw,[status(thm)],[c_0_42, c_0_43])). 11.46/11.63 fof(c_0_56, plain, (![X120]:![X121]:![X122]:![X123]:![X124]:![X125]:hAPP(hAPP(hAPP(c_COMBB(X125,X124,X123),X122),X121),X120)=hAPP(X122,hAPP(X121,X120))), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 11.46/11.63 cnf(c_0_57,plain,(~hBOOL(X1)|~hBOOL(hAPP(c_fNot,X1))), inference(split_conjunct,[status(thm)],[c_0_44])). 11.46/11.63 cnf(c_0_58,plain,(c_fFalse=X1|hBOOL(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_45]), c_0_46]), c_0_33])). 11.46/11.63 cnf(c_0_59,plain,(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_47])). 11.46/11.63 cnf(c_0_60,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_48, c_0_27])). 11.46/11.63 cnf(c_0_61,plain,(X1=hAPP(c_Int_Onat,c_Int_OPls)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=X2), inference(rw,[status(thm)],[c_0_49, c_0_50])). 11.46/11.63 cnf(c_0_62,plain,(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_51])). 11.46/11.63 cnf(c_0_63,plain,(hAPP(c_Int_Onat,c_Int_OPls)!=hAPP(c_Nat_OSuc,X1)), inference(rw,[status(thm)],[c_0_52, c_0_50])). 11.46/11.63 fof(c_0_64, plain, (![X13]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X13), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 11.46/11.63 cnf(c_0_65,plain,(X1=hAPP(c_Fun_Oid(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_53])). 11.46/11.63 cnf(c_0_66,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_54, c_0_55])). 11.46/11.63 cnf(c_0_67,plain,(hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_56])). 11.46/11.63 cnf(c_0_68,plain,(hAPP(c_fNot,X1)=c_fFalse|~hBOOL(X1)), inference(spm,[status(thm)],[c_0_57, c_0_58])). 11.46/11.63 cnf(c_0_69,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_59, c_0_41])). 11.46/11.63 cnf(c_0_70,plain,(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)=c_fTrue), inference(spm,[status(thm)],[c_0_33, c_0_60])). 11.46/11.63 cnf(c_0_71,plain,(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))!=X1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_63])). 11.46/11.63 cnf(c_0_72,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_64])). 11.46/11.63 fof(c_0_73, plain, (![X30]:hAPP(c_Nat_OSuc,X30)!=X30), inference(variable_rename,[status(thm)],[fact_n__not__Suc__n])). 11.46/11.63 cnf(c_0_74,plain,(hAPP(c_fNot,hAPP(c_fNot,X1))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_67])). 11.46/11.63 cnf(c_0_75,plain,(hAPP(c_fNot,X1)=c_fFalse|c_fFalse=X1), inference(spm,[status(thm)],[c_0_68, c_0_58])). 11.46/11.63 cnf(c_0_76,plain,(hAPP(c_fNot,c_fFalse)=c_fTrue), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_69]), c_0_70]), c_0_46])). 11.46/11.63 cnf(c_0_77,plain,(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))!=X1), inference(spm,[status(thm)],[c_0_71, c_0_62])). 11.46/11.63 cnf(c_0_78,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls))=X1), inference(rw,[status(thm)],[c_0_72, c_0_50])). 11.46/11.63 cnf(c_0_79,plain,(hAPP(c_Nat_OSuc,X1)!=X1), inference(split_conjunct,[status(thm)],[c_0_73])). 11.46/11.63 cnf(c_0_80,plain,(c_fFalse=X1|c_fTrue=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_76])). 11.46/11.63 cnf(c_0_81,plain,(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))!=X1), inference(spm,[status(thm)],[c_0_77, c_0_78])). 11.46/11.63 cnf(c_0_82,plain,(hAPP(c_Nat_OSuc,X1)=c_fFalse|c_fTrue!=X1), inference(spm,[status(thm)],[c_0_79, c_0_80])). 11.46/11.63 cnf(c_0_83,plain,(hAPP(c_Nat_OSuc,c_fFalse)!=X1|c_fTrue!=X1), inference(spm,[status(thm)],[c_0_81, c_0_82])). 11.46/11.63 cnf(c_0_84,plain,(c_fTrue!=X1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_80]), c_0_79])). 11.46/11.63 cnf(c_0_85,plain,($false), inference(sr,[status(thm)],[c_0_70, c_0_84]), ['proof']). 11.46/11.63 % SZS output end Proof 11.46/11.63 % User time : 10.860 s 11.46/11.63 % System time : 0.250 s 11.46/11.63 % Total time : 11.110 s 11.46/11.63 11.46/11.63 EOF