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 0.03/0.24 % Computer : n178.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 05:55:10 CDT 2018 0.03/0.24 % CPUTime : 0.06/0.30 openjdk version "1.8.0_144" 0.06/0.31 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.06/0.31 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.42 start to proof:theBenchmark.p 9.69/9.89 % Version : CSE_E---1.0 9.69/9.89 % Problem : theBenchmark.p 9.69/9.89 % Proof found! 9.69/9.89 % SZS status Theorem for theBenchmark.p 9.69/9.89 % SZS output start Proof 9.69/9.89 fof(fact_empty__def, axiom, (![X3]:c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3),hAPP(c_COMBK(tc_HOL_Obool,X3),c_fFalse))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_empty__def)). 9.69/9.89 fof(fact_Collect__def, axiom, (![X38]:![X3]:hAPP(c_Set_OCollect(X3),X38)=X38), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__def)). 9.69/9.89 fof(fact_Collect__neg__eq, axiom, (![X38]:![X3]:hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X38))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_OCollect(X3),X38))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 9.69/9.89 fof(fact_Collect__empty__eq, axiom, (![X38]:![X3]:(![X4]:~(hBOOL(hAPP(X38,X4)))<=>hAPP(c_Set_OCollect(X3),X38)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 9.69/9.89 fof(help_c__COMBK__1, axiom, (![X247]:![X246]:![X96]:![X24]:hAPP(hAPP(c_COMBK(X24,X96),X246),X247)=X246), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__COMBK__1)). 9.69/9.89 fof(fact_double__complement, axiom, (![X22]:![X3]:X22=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X22))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__complement)). 9.69/9.89 fof(fact_UNIV__def, axiom, (![X3]:c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3),hAPP(c_COMBK(tc_HOL_Obool,X3),c_fTrue))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_UNIV__def)). 9.69/9.89 fof(fact_add__eq__self__zero, axiom, (![X30]:![X7]:(X30=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X30)=X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 9.69/9.89 fof(fact_nat__0, axiom, (hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__0)). 9.69/9.89 fof(fact_Pls__def, axiom, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Pls__def)). 9.69/9.89 fof(fact_Suc__not__Zero, axiom, (![X7]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__not__Zero)). 9.69/9.89 fof(help_c__COMBB__1, axiom, (![X14]:![X79]:![X38]:![X15]:![X3]:![X16]:hAPP(X38,hAPP(X79,X14))=hAPP(hAPP(hAPP(c_COMBB(X16,X3,X15),X38),X79),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__COMBB__1)). 9.69/9.89 fof(help_c__fNot__1, axiom, (![X38]:(~(hBOOL(X38))|~(hBOOL(hAPP(c_fNot,X38))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__fNot__1)). 9.69/9.89 fof(fact_Compl__empty__eq, axiom, (![X3]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 9.69/9.89 fof(fact_add__Suc__right, axiom, (![X30]:![X7]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X30))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(c_Nat_OSuc,X30))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Suc__right)). 9.69/9.89 fof(fact_hd_Osimps, axiom, (![X52]:![X31]:![X24]:X31=hAPP(c_List_Ohd(X24),hAPP(hAPP(c_List_Olist_OCons(X24),X31),X52))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_hd_Osimps)). 9.69/9.89 fof(fact_Nat_Oadd__0__right, axiom, (![X7]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X7), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 9.69/9.89 fof(conj_1, hypothesis, (hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_1)). 9.69/9.89 fof(fact_n__not__Suc__n, axiom, (![X30]:X30!=hAPP(c_Nat_OSuc,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_n__not__Suc__n)). 9.69/9.89 fof(c_0_19, plain, (![X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse))), inference(variable_rename,[status(thm)],[fact_empty__def])). 9.69/9.89 fof(c_0_20, plain, (![X39]:![X40]:hAPP(c_Set_OCollect(X40),X39)=X39), inference(variable_rename,[status(thm)],[fact_Collect__def])). 9.69/9.89 fof(c_0_21, plain, (![X39]:![X40]:hAPP(c_Set_OCollect(X40),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X40),c_fNot),X39))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X40,tc_HOL_Obool)),hAPP(c_Set_OCollect(X40),X39))), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 9.69/9.89 fof(c_0_22, plain, (![X39]:![X40]:![X39]:![X40]:![X42]:((hBOOL(hAPP(X39,esk61_1(X39)))|hAPP(c_Set_OCollect(X40),X39)=c_Orderings_Obot__class_Obot(tc_fun(X40,tc_HOL_Obool)))&(hAPP(c_Set_OCollect(X40),X39)!=c_Orderings_Obot__class_Obot(tc_fun(X40,tc_HOL_Obool))|~hBOOL(hAPP(X39,X42))))), 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])])])])])])])). 9.69/9.89 fof(c_0_23, plain, (![X248]:![X249]:![X250]:![X251]:hAPP(hAPP(c_COMBK(X251,X250),X249),X248)=X249), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 9.69/9.89 cnf(c_0_24,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_19])). 9.69/9.89 cnf(c_0_25,plain,(hAPP(c_Set_OCollect(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_20])). 9.69/9.89 fof(c_0_26, plain, (![X23]:![X24]:X23=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24,tc_HOL_Obool)),X23))), inference(variable_rename,[status(thm)],[fact_double__complement])). 9.69/9.89 cnf(c_0_27,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_21])). 9.69/9.89 cnf(c_0_28,plain,(hAPP(c_Set_OCollect(X1),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X2,esk61_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_22])). 9.69/9.89 cnf(c_0_29,plain,(hAPP(hAPP(c_COMBK(X1,X2),X3),X4)=X3), inference(split_conjunct,[status(thm)],[c_0_23])). 9.69/9.89 cnf(c_0_30,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_24, c_0_25])). 9.69/9.89 fof(c_0_31, plain, (![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fTrue))), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 9.69/9.89 fof(c_0_32, plain, (![X31]:![X32]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)!=X32|X31=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)],[inference(fof_simplification,[status(thm)],[fact_add__eq__self__zero])])])])])). 9.69/9.89 cnf(c_0_33,plain,(hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_nat__0])). 9.69/9.89 cnf(c_0_34,plain,(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_Pls__def])). 9.69/9.89 fof(c_0_35, plain, (![X8]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X8)), inference(variable_rename,[status(thm)],[fact_Suc__not__Zero])). 9.69/9.89 fof(c_0_36, plain, (![X80]:![X81]:![X82]:![X83]:![X84]:![X85]:hAPP(X82,hAPP(X81,X80))=hAPP(hAPP(hAPP(c_COMBB(X85,X84,X83),X82),X81),X80)), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 9.69/9.89 cnf(c_0_37,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_26])). 9.69/9.89 cnf(c_0_38,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_27, c_0_25]), c_0_25])). 9.69/9.89 fof(c_0_39, plain, (![X39]:(~hBOOL(X39)|~hBOOL(hAPP(c_fNot,X39)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 9.69/9.89 cnf(c_0_40,plain,(X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk61_1(X1)))), inference(rw,[status(thm)],[c_0_28, c_0_25])). 9.69/9.89 cnf(c_0_41,plain,(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)=c_fFalse), inference(spm,[status(thm)],[c_0_29, c_0_30])). 9.69/9.89 fof(c_0_42, plain, (![X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 9.69/9.89 cnf(c_0_43,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_31])). 9.69/9.89 cnf(c_0_44,plain,(X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_32])). 9.69/9.89 cnf(c_0_45,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Int_OPls)), inference(rw,[status(thm)],[c_0_33, c_0_34])). 9.69/9.89 fof(c_0_46, plain, (![X31]:![X32]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,X31))), inference(variable_rename,[status(thm)],[fact_add__Suc__right])). 9.69/9.89 cnf(c_0_47,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_35])). 9.69/9.89 cnf(c_0_48,plain,(hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(hAPP(c_COMBB(X4,X5,X6),X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_36])). 9.69/9.89 cnf(c_0_49,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_37, c_0_38]), c_0_38])). 9.69/9.89 fof(c_0_50, plain, (![X53]:![X54]:![X55]:X54=hAPP(c_List_Ohd(X55),hAPP(hAPP(c_List_Olist_OCons(X55),X54),X53))), inference(variable_rename,[status(thm)],[fact_hd_Osimps])). 9.69/9.89 cnf(c_0_51,plain,(~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_39])). 9.69/9.89 cnf(c_0_52,plain,(c_fFalse=X1|hBOOL(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_40]), c_0_41]), c_0_29])). 9.69/9.89 cnf(c_0_53,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_42])). 9.69/9.89 cnf(c_0_54,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_43, c_0_25])). 9.69/9.89 cnf(c_0_55,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_44, c_0_45])). 9.69/9.89 cnf(c_0_56,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_46])). 9.69/9.89 cnf(c_0_57,plain,(hAPP(c_Int_Onat,c_Int_OPls)!=hAPP(c_Nat_OSuc,X1)), inference(rw,[status(thm)],[c_0_47, c_0_45])). 9.69/9.89 fof(c_0_58, plain, (![X8]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X8), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 9.69/9.89 cnf(c_0_59,plain,(hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2)))=hAPP(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_48])). 9.69/9.89 cnf(c_0_60,plain,(X1=hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_50])). 9.69/9.89 cnf(c_0_61,plain,(hAPP(c_fNot,X1)=c_fFalse|~hBOOL(X1)), inference(spm,[status(thm)],[c_0_51, c_0_52])). 9.69/9.89 cnf(c_0_62,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_53, c_0_38])). 9.69/9.89 cnf(c_0_63,plain,(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)=c_fTrue), inference(spm,[status(thm)],[c_0_29, c_0_54])). 9.69/9.89 cnf(c_0_64,hypothesis,(hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F))), inference(split_conjunct,[status(thm)],[conj_1])). 9.69/9.89 cnf(c_0_65,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_55, c_0_56]), c_0_57])). 9.69/9.89 cnf(c_0_66,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_58])). 9.69/9.89 fof(c_0_67, plain, (![X31]:X31!=hAPP(c_Nat_OSuc,X31)), inference(variable_rename,[status(thm)],[fact_n__not__Suc__n])). 9.69/9.89 cnf(c_0_68,plain,(hAPP(c_fNot,hAPP(c_fNot,X1))=X1), inference(spm,[status(thm)],[c_0_59, c_0_60])). 9.69/9.89 cnf(c_0_69,plain,(hAPP(c_fNot,X1)=c_fFalse|c_fFalse=X1), inference(spm,[status(thm)],[c_0_61, c_0_52])). 9.69/9.89 cnf(c_0_70,plain,(hAPP(c_fNot,c_fFalse)=c_fTrue), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_62]), c_0_63]), c_0_41])). 9.69/9.89 cnf(c_0_71,hypothesis,(hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F))=c_fFalse), inference(spm,[status(thm)],[c_0_61, c_0_64])). 9.69/9.89 cnf(c_0_72,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_65, c_0_56])). 9.69/9.89 cnf(c_0_73,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_66, c_0_45])). 9.69/9.89 cnf(c_0_74,plain,(X1!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_67])). 9.69/9.89 cnf(c_0_75,plain,(c_fFalse=X1|c_fTrue=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70])). 9.69/9.89 cnf(c_0_76,hypothesis,(hAPP(c_Finite__Set_Ofinite(t_a),v_F)=c_fTrue), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_71]), c_0_70])). 9.69/9.89 cnf(c_0_77,plain,(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))!=X1), inference(spm,[status(thm)],[c_0_72, c_0_73])). 9.69/9.89 cnf(c_0_78,plain,(hAPP(c_Nat_OSuc,X1)=c_fFalse|c_fTrue!=X1), inference(spm,[status(thm)],[c_0_74, c_0_75])). 9.69/9.89 cnf(c_0_79,hypothesis,(hAPP(c_fTrue,v_F)=c_fTrue|c_Finite__Set_Ofinite(t_a)=c_fFalse), inference(spm,[status(thm)],[c_0_76, c_0_75])). 9.69/9.89 cnf(c_0_80,plain,(hAPP(c_Nat_OSuc,c_fFalse)!=X1|c_fTrue!=X1), inference(spm,[status(thm)],[c_0_77, c_0_78])). 9.69/9.89 cnf(c_0_81,hypothesis,(hAPP(c_fTrue,v_F)=c_fTrue|hAPP(c_fFalse,v_F)=c_fTrue), inference(spm,[status(thm)],[c_0_76, c_0_79])). 9.69/9.89 cnf(c_0_82,plain,(c_fTrue!=X1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_75]), c_0_74])). 9.69/9.89 cnf(c_0_83,hypothesis,($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_81, c_0_82]), c_0_82]), ['proof']). 9.69/9.89 % SZS output end Proof 9.69/9.89 % User time : 9.177 s 9.69/9.89 % System time : 0.216 s 9.69/9.89 % Total time : 9.394 s 9.69/9.89 9.80/9.90 EOF