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 0.03/0.23 % Computer : n126.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 06:00:09 CDT 2018 0.07/0.23 % CPUTime : 0.07/0.30 openjdk version "1.8.0_144" 0.07/0.30 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.07/0.30 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.15/0.42 start to proof:theBenchmark.p 10.67/10.77 % Version : CSE_E---1.0 10.67/10.77 % Problem : theBenchmark.p 10.67/10.77 % Proof found! 10.67/10.77 % SZS status Theorem for theBenchmark.p 10.67/10.77 % SZS output start Proof 10.67/10.77 fof(fact_nat__0, axiom, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__0)). 10.67/10.77 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)). 10.67/10.77 fof(fact_o__def, axiom, (![X20]:![X52]:![X22]:![X53]:![X9]:![X23]:hAPP(hAPP(c_Fun_Ocomp(X23,X9,X53,X22),X52),X20)=hAPP(X22,hAPP(X52,X20))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_o__def)). 10.67/10.77 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/sandbox/benchmark/theBenchmark.p', fact_empty__def)). 10.67/10.77 fof(fact_Collect__def, axiom, (![X38]:![X9]:hAPP(c_Set_OCollect(X9),X38)=X38), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__def)). 10.67/10.77 fof(fact_One__nat__def, axiom, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_One__nat__def)). 10.67/10.77 fof(fact_int__of__def, axiom, (c_Code__Numeral_Oint__of=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__of__def)). 10.67/10.77 fof(fact_nat__of__of__nat, axiom, (![X6]:hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X6))=X6), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__of__of__nat)). 10.67/10.77 fof(fact_Collect__neg__eq, axiom, (![X38]:![X9]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9),X38))=hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9),c_fNot),X38))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 10.67/10.77 fof(fact_Collect__empty__eq, axiom, (![X38]:![X9]:(hAPP(c_Set_OCollect(X9),X38)=c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))<=>![X33]:~(hBOOL(hAPP(X38,X33))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 10.67/10.77 fof(help_c__COMBK__1, axiom, (![X241]:![X200]:![X9]:![X2]:X200=hAPP(hAPP(c_COMBK(X2,X9),X200),X241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__COMBK__1)). 10.67/10.77 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/sandbox/benchmark/theBenchmark.p', fact_UNIV__def)). 10.67/10.77 fof(fact_negative__zle__0, axiom, (![X6]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_negative__zle__0)). 10.67/10.77 fof(fact_mult__Min, axiom, (![X54]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X54)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__Min)). 10.67/10.77 fof(fact_zmult__eq__1__iff, axiom, (![X46]:![X27]:(((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X46&hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X27)|(c_Groups_Oone__class_Oone(tc_Int_Oint)=X46&X27=c_Groups_Oone__class_Oone(tc_Int_Oint)))<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X46)=c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__eq__1__iff)). 10.67/10.77 fof(fact_number__of__is__id, axiom, (![X54]:X54=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_number__of__is__id)). 10.67/10.77 fof(fact_transfer__int__nat__numerals_I2_J, axiom, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_transfer__int__nat__numerals_I2_J)). 10.67/10.77 fof(fact_not__one__le__zero, axiom, (![X2]:(class_Rings_Olinordered__semidom(X2)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),c_Groups_Ozero__class_Ozero(X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__one__le__zero)). 10.67/10.77 fof(fact_double__complement, axiom, (![X21]:![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)),X21))=X21), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__complement)). 10.67/10.77 fof(fact_sum__case__KK, axiom, (![X20]:![X13]:![X53]:![X9]:![X23]:X13=hAPP(c_Sum__Type_Osum_Osum__case(X23,X9,X53,hAPP(c_COMBK(X9,X23),X13),hAPP(c_COMBK(X9,X53),X13)),X20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sum__case__KK)). 10.67/10.77 fof(fact_Compl__UNIV__eq, axiom, (![X9]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Compl__UNIV__eq)). 10.67/10.77 fof(fact_neg__equal__0__iff__equal, axiom, (![X13]:![X9]:((c_Groups_Ozero__class_Ozero(X9)=X13<=>c_Groups_Ozero__class_Ozero(X9)=hAPP(c_Groups_Ouminus__class_Ouminus(X9),X13))<=class_Groups_Ogroup__add(X9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__equal__0__iff__equal)). 10.67/10.77 fof(fact_zminus__zminus, axiom, (![X47]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X47))=X47), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zminus__zminus)). 10.67/10.77 fof(arity_Int__Oint__Rings_Olinordered__semidom, axiom, (class_Rings_Olinordered__semidom(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semidom)). 10.67/10.77 fof(help_c__COMBB__1, axiom, (![X71]:![X35]:![X38]:![X53]:![X9]:![X23]:hAPP(X38,hAPP(X35,X71))=hAPP(hAPP(hAPP(c_COMBB(X23,X9,X53),X38),X35),X71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__COMBB__1)). 10.67/10.77 fof(help_c__fNot__1, axiom, (![X38]:(~(hBOOL(hAPP(c_fNot,X38)))|~(hBOOL(X38)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__fNot__1)). 10.67/10.77 fof(fact_neg__zminus__int, axiom, (![X6]:hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X6)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__zminus__int)). 10.67/10.77 fof(arity_Int__Oint__Groups_Ogroup__add, axiom, (class_Groups_Ogroup__add(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ogroup__add)). 10.67/10.77 fof(fact_not__neg__0, axiom, (~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__neg__0)). 10.67/10.77 fof(fact_Abs__Integ__cases, axiom, (![X20]:~(![X92]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X92),c_Int_OInteg)))<=X20=hAPP(c_Int_OAbs__Integ,X92)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Abs__Integ__cases)). 10.67/10.77 fof(fact_Nat_Oadd__0__right, axiom, (![X7]:X7=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 10.67/10.77 fof(fact_int__of__code, axiom, (![X54]:((hAPP(c_Code__Numeral_Oint__of,X54)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=X54=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(((hAPP(c_Code__Numeral_Oint__of,X54)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X54),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X54,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))&(hAPP(c_Code__Numeral_Oint__of,X54)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X54),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X54,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=X54!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__of__code)). 10.67/10.77 fof(fact_zero__code__numeral__def, axiom, (hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__code__numeral__def)). 10.67/10.77 fof(fact_nat__of__inverse, axiom, (![X48]:X48=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X48))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__of__inverse)). 10.67/10.77 fof(fact_prod__size__simp, axiom, (![X73]:![X52]:![X22]:![X23]:![X9]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22,hAPP(c_Product__Type_Ofst(X9,X23),X73))),hAPP(X52,hAPP(c_Product__Type_Osnd(X9,X23),X73)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X9,X23,X22,X52,X73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_prod__size__simp)). 10.67/10.77 fof(fact_nat__add__assoc, axiom, (![X54]:![X6]:![X7]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X6)),X54)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X54))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__assoc)). 10.67/10.77 fof(fact_add__Suc__right, axiom, (![X6]:![X7]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(c_Nat_OSuc,X6))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Suc__right)). 10.67/10.77 fof(fact_transfer__int__nat__quantifiers_I2_J, axiom, (![X38]:(?[X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))&hBOOL(hAPP(X38,X33)))<=>?[X33]:hBOOL(hAPP(X38,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I2_J)). 10.67/10.77 fof(fact_zmod__zero, axiom, (![X12]:c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmod__zero)). 10.67/10.77 fof(fact_dvd__0__left, axiom, (![X1]:![X2]:(class_Rings_Ocomm__semiring__1(X2)=>(c_Groups_Ozero__class_Ozero(X2)=X1<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ozero__class_Ozero(X2)),X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_dvd__0__left)). 10.67/10.77 fof(fact_dvd__eq__mod__eq__0, axiom, (![X24]:![X13]:![X9]:(class_Divides_Osemiring__div(X9)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X13),X24))<=>c_Divides_Odiv__class_Omod(X9,X24,X13)=c_Groups_Ozero__class_Ozero(X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_dvd__eq__mod__eq__0)). 10.67/10.77 fof(fact_Bit1__def, axiom, (![X54]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X54)),X54)=c_Int_OBit1(X54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bit1__def)). 10.67/10.77 fof(arity_Int__Oint__Rings_Ocomm__semiring__1, axiom, (class_Rings_Ocomm__semiring__1(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring__1)). 10.67/10.77 fof(arity_Int__Oint__Divides_Osemiring__div, axiom, (class_Divides_Osemiring__div(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Osemiring__div)). 10.67/10.77 fof(fact_equal__neg__zero, axiom, (![X13]:![X9]:((hAPP(c_Groups_Ouminus__class_Ouminus(X9),X13)=X13<=>X13=c_Groups_Ozero__class_Ozero(X9))<=class_Groups_Olinordered__ab__group__add(X9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_equal__neg__zero)). 10.67/10.77 fof(fact_minus__Min, axiom, (c_Int_OBit1(c_Int_OPls)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__Min)). 10.67/10.77 fof(fact_add__Pls__right, axiom, (![X54]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X54),c_Int_OPls)=X54), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Pls__right)). 10.67/10.77 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add, axiom, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__group__add)). 10.67/10.77 fof(fact_rel__simps_I37_J, axiom, (c_Int_OMin!=c_Int_OPls), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_rel__simps_I37_J)). 10.67/10.77 cnf(c_0_49,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_nat__0])). 10.67/10.77 cnf(c_0_50,plain,(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_Pls__def])). 10.67/10.77 fof(c_0_51, plain, (![X54]:![X55]:![X56]:![X57]:![X58]:![X59]:hAPP(hAPP(c_Fun_Ocomp(X59,X58,X57,X56),X55),X54)=hAPP(X56,hAPP(X55,X54))), inference(variable_rename,[status(thm)],[fact_o__def])). 10.67/10.77 fof(c_0_52, plain, (![X10]:c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))=hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse))), inference(variable_rename,[status(thm)],[fact_empty__def])). 10.67/10.77 fof(c_0_53, plain, (![X39]:![X40]:hAPP(c_Set_OCollect(X40),X39)=X39), inference(variable_rename,[status(thm)],[fact_Collect__def])). 10.67/10.77 cnf(c_0_54,plain,(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_One__nat__def])). 10.67/10.77 cnf(c_0_55,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Int_OPls)), inference(rw,[status(thm)],[c_0_49, c_0_50])). 10.67/10.77 cnf(c_0_56,plain,(hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_51])). 10.67/10.77 cnf(c_0_57,plain,(c_Code__Numeral_Oint__of=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)), inference(split_conjunct,[status(thm)],[fact_int__of__def])). 10.67/10.77 fof(c_0_58, plain, (![X7]:hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X7))=X7), inference(variable_rename,[status(thm)],[fact_nat__of__of__nat])). 10.67/10.77 fof(c_0_59, plain, (![X39]:![X40]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X40,tc_HOL_Obool)),hAPP(c_Set_OCollect(X40),X39))=hAPP(c_Set_OCollect(X40),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X40),c_fNot),X39))), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 10.67/10.77 fof(c_0_60, plain, (![X39]:![X40]:![X41]:![X39]:![X40]:((hAPP(c_Set_OCollect(X40),X39)!=c_Orderings_Obot__class_Obot(tc_fun(X40,tc_HOL_Obool))|~hBOOL(hAPP(X39,X41)))&(hBOOL(hAPP(X39,esk79_1(X39)))|hAPP(c_Set_OCollect(X40),X39)=c_Orderings_Obot__class_Obot(tc_fun(X40,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_Collect__empty__eq])])])])])])])). 10.67/10.77 fof(c_0_61, plain, (![X242]:![X243]:![X244]:![X245]:X243=hAPP(hAPP(c_COMBK(X245,X244),X243),X242)), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 10.67/10.77 cnf(c_0_62,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_52])). 10.67/10.77 cnf(c_0_63,plain,(hAPP(c_Set_OCollect(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_53])). 10.67/10.77 fof(c_0_64, plain, (![X10]:c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))=hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue))), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 10.67/10.77 fof(c_0_65, plain, (![X7]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_negative__zle__0])). 10.67/10.77 fof(c_0_66, plain, (![X55]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X55)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X55)), inference(variable_rename,[status(thm)],[fact_mult__Min])). 10.67/10.77 fof(c_0_67, plain, (![X47]:![X48]:![X47]:![X48]:((((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X47|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X48)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)=c_Groups_Oone__class_Oone(tc_Int_Oint))&((c_Groups_Oone__class_Oone(tc_Int_Oint)!=X47|X48!=c_Groups_Oone__class_Oone(tc_Int_Oint))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)=c_Groups_Oone__class_Oone(tc_Int_Oint)))&((((c_Groups_Oone__class_Oone(tc_Int_Oint)=X47|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X47)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)!=c_Groups_Oone__class_Oone(tc_Int_Oint))&((X48=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X47)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)!=c_Groups_Oone__class_Oone(tc_Int_Oint)))&(((c_Groups_Oone__class_Oone(tc_Int_Oint)=X47|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X48)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)!=c_Groups_Oone__class_Oone(tc_Int_Oint))&((X48=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X48)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)!=c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])])])])). 10.67/10.77 fof(c_0_68, plain, (![X55]:X55=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X55)), inference(variable_rename,[status(thm)],[fact_number__of__is__id])). 10.67/10.77 cnf(c_0_69,plain,(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J])). 10.67/10.77 cnf(c_0_70,plain,(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))), inference(rw,[status(thm)],[c_0_54, c_0_55])). 10.67/10.77 cnf(c_0_71,plain,(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Code__Numeral_Onat__of,X1))=hAPP(c_Code__Numeral_Oint__of,X1)), inference(spm,[status(thm)],[c_0_56, c_0_57])). 10.67/10.77 cnf(c_0_72,plain,(hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_58])). 10.67/10.77 fof(c_0_73, plain, (![X3]:(~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Oone__class_Oone(X3)),c_Groups_Ozero__class_Ozero(X3))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__le__zero])])])). 10.67/10.77 fof(c_0_74, plain, (![X22]:![X23]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23,tc_HOL_Obool)),X22))=X22), inference(variable_rename,[status(thm)],[fact_double__complement])). 10.67/10.77 cnf(c_0_75,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_59])). 10.67/10.77 fof(c_0_76, plain, (![X54]:![X55]:![X56]:![X57]:![X58]:X55=hAPP(c_Sum__Type_Osum_Osum__case(X58,X57,X56,hAPP(c_COMBK(X57,X58),X55),hAPP(c_COMBK(X57,X56),X55)),X54)), inference(variable_rename,[status(thm)],[fact_sum__case__KK])). 10.67/10.77 cnf(c_0_77,plain,(hAPP(c_Set_OCollect(X1),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X2,esk79_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_60])). 10.67/10.77 cnf(c_0_78,plain,(X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_61])). 10.67/10.77 cnf(c_0_79,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_62, c_0_63])). 10.67/10.77 fof(c_0_80, plain, (![X10]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq])). 10.67/10.77 cnf(c_0_81,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_64])). 10.67/10.77 fof(c_0_82, plain, (![X14]:![X15]:(((c_Groups_Ozero__class_Ozero(X15)!=X14|c_Groups_Ozero__class_Ozero(X15)=hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14))|~class_Groups_Ogroup__add(X15))&((c_Groups_Ozero__class_Ozero(X15)!=hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)|c_Groups_Ozero__class_Ozero(X15)=X14)|~class_Groups_Ogroup__add(X15)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__equal__0__iff__equal])])])])). 10.67/10.77 fof(c_0_83, plain, (![X48]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X48))=X48), inference(variable_rename,[status(thm)],[fact_zminus__zminus])). 10.67/10.77 cnf(c_0_84,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_65])). 10.67/10.77 cnf(c_0_85,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_66])). 10.67/10.77 cnf(c_0_86,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X1|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X2), inference(split_conjunct,[status(thm)],[c_0_67])). 10.67/10.77 cnf(c_0_87,plain,(X1=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_68])). 10.67/10.77 cnf(c_0_88,plain,(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)))=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_69, c_0_70])). 10.67/10.77 cnf(c_0_89,plain,(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)=hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,X1))), inference(spm,[status(thm)],[c_0_71, c_0_72])). 10.67/10.77 cnf(c_0_90,plain,(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_73])). 10.67/10.77 cnf(c_0_91,plain,(class_Rings_Olinordered__semidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom])). 10.67/10.77 fof(c_0_92, plain, (![X72]:![X73]:![X74]:![X75]:![X76]:![X77]:hAPP(X74,hAPP(X73,X72))=hAPP(hAPP(hAPP(c_COMBB(X77,X76,X75),X74),X73),X72)), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 10.67/10.77 cnf(c_0_93,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_74])). 10.67/10.77 cnf(c_0_94,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_75, c_0_63]), c_0_63])). 10.67/10.77 fof(c_0_95, plain, (![X39]:(~hBOOL(hAPP(c_fNot,X39))|~hBOOL(X39))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 10.67/10.77 cnf(c_0_96,plain,(X1=hAPP(c_Sum__Type_Osum_Osum__case(X2,X3,X4,hAPP(c_COMBK(X3,X2),X1),hAPP(c_COMBK(X3,X4),X1)),X5)), inference(split_conjunct,[status(thm)],[c_0_76])). 10.67/10.77 cnf(c_0_97,plain,(X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk79_1(X1)))), inference(rw,[status(thm)],[c_0_77, c_0_63])). 10.67/10.77 cnf(c_0_98,plain,(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)=c_fFalse), inference(spm,[status(thm)],[c_0_78, c_0_79])). 10.67/10.77 cnf(c_0_99,plain,(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_80])). 10.67/10.77 cnf(c_0_100,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_81, c_0_63])). 10.67/10.77 fof(c_0_101, plain, (![X7]:hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X7)))))), inference(variable_rename,[status(thm)],[fact_neg__zminus__int])). 10.67/10.77 cnf(c_0_102,plain,(c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Ogroup__add(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_82])). 10.67/10.77 cnf(c_0_103,plain,(class_Groups_Ogroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add])). 10.67/10.77 cnf(c_0_104,plain,(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=X1), inference(split_conjunct,[status(thm)],[c_0_83])). 10.67/10.77 fof(c_0_105, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(fof_simplification,[status(thm)],[fact_not__neg__0])). 10.67/10.77 cnf(c_0_106,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85]), c_0_50])). 10.67/10.77 cnf(c_0_107,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin!=X2|c_Int_OMin!=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87]), c_0_87])). 10.67/10.77 cnf(c_0_108,plain,(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))), inference(rw,[status(thm)],[c_0_88, c_0_89])). 10.67/10.77 cnf(c_0_109,plain,(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_50]), c_0_91])])). 10.67/10.77 cnf(c_0_110,plain,(hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(hAPP(c_COMBB(X4,X5,X6),X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_92])). 10.67/10.77 cnf(c_0_111,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_93, c_0_94]), c_0_94])). 10.67/10.77 fof(c_0_112, plain, (![X93]:(X93=hAPP(c_Int_OAbs__Integ,esk497_1(X93))&hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk497_1(X93)),c_Int_OInteg)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases])])])])). 10.67/10.77 cnf(c_0_113,plain,(~hBOOL(X1)|~hBOOL(hAPP(c_fNot,X1))), inference(split_conjunct,[status(thm)],[c_0_95])). 10.67/10.77 cnf(c_0_114,plain,(c_fFalse=X1|hBOOL(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_98]), c_0_96])). 10.67/10.77 cnf(c_0_115,plain,(hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_99, c_0_94])). 10.67/10.77 cnf(c_0_116,plain,(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)=c_fTrue), inference(spm,[status(thm)],[c_0_78, c_0_100])). 10.67/10.77 cnf(c_0_117,plain,(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))))), inference(split_conjunct,[status(thm)],[c_0_101])). 10.67/10.77 cnf(c_0_118,plain,(c_Int_OPls=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)!=c_Int_OPls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_85]), c_0_50]), c_0_50]), c_0_103])])). 10.67/10.77 cnf(c_0_119,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_85]), c_0_85])). 10.67/10.77 cnf(c_0_120,plain,(~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_105])). 10.67/10.77 fof(c_0_121, plain, (![X8]:X8=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 10.67/10.77 fof(c_0_122, plain, (![X55]:![X55]:((X55!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Code__Numeral_Oint__of,X55)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X55,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hAPP(c_Code__Numeral_Oint__of,X55)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|X55=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X55,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hAPP(c_Code__Numeral_Oint__of,X55)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|X55=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), inference(distribute,[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_int__of__code])])])])])])). 10.67/10.77 cnf(c_0_123,plain,(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__def])). 10.67/10.77 cnf(c_0_124,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,X1)))),c_Int_OPls))), inference(rw,[status(thm)],[c_0_106, c_0_89])). 10.67/10.77 cnf(c_0_125,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))|c_Int_OMin!=X2|c_Int_OMin!=X1), inference(rw,[status(thm)],[c_0_107, c_0_108])). 10.67/10.77 cnf(c_0_126,plain,(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))),c_Int_OPls))), inference(rw,[status(thm)],[c_0_109, c_0_108])). 10.67/10.77 fof(c_0_127, plain, (![X49]:X49=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X49))), inference(variable_rename,[status(thm)],[fact_nat__of__inverse])). 10.67/10.77 cnf(c_0_128,plain,(hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2)))=hAPP(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_111]), c_0_110])). 10.67/10.77 cnf(c_0_129,plain,(X1=hAPP(c_Int_OAbs__Integ,esk497_1(X1))), inference(split_conjunct,[status(thm)],[c_0_112])). 10.67/10.77 cnf(c_0_130,plain,(hAPP(c_fNot,X1)=c_fFalse|~hBOOL(X1)), inference(spm,[status(thm)],[c_0_113, c_0_114])). 10.67/10.77 cnf(c_0_131,plain,(hAPP(c_fNot,c_fTrue)=c_fFalse), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_115]), c_0_98]), c_0_116])). 10.67/10.77 cnf(c_0_132,plain,(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))))), inference(rw,[status(thm)],[c_0_117, c_0_85])). 10.67/10.77 cnf(c_0_133,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)=c_Int_OPls|X1!=c_Int_OPls), inference(spm,[status(thm)],[c_0_118, c_0_119])). 10.67/10.77 cnf(c_0_134,plain,(~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls))), inference(rw,[status(thm)],[c_0_120, c_0_50])). 10.67/10.77 fof(c_0_135, plain, (![X74]:![X75]:![X76]:![X77]:![X78]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X76,hAPP(c_Product__Type_Ofst(X78,X77),X74))),hAPP(X75,hAPP(c_Product__Type_Osnd(X78,X77),X74)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X78,X77,X76,X75,X74)), inference(variable_rename,[status(thm)],[fact_prod__size__simp])). 10.67/10.77 fof(c_0_136, plain, (![X55]:![X56]:![X57]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X56)),X55)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X55))), inference(variable_rename,[status(thm)],[fact_nat__add__assoc])). 10.67/10.77 fof(c_0_137, plain, (![X8]:![X9]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),hAPP(c_Nat_OSuc,X8))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X8))), inference(variable_rename,[status(thm)],[fact_add__Suc__right])). 10.67/10.77 cnf(c_0_138,plain,(X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_121])). 10.67/10.77 cnf(c_0_139,plain,(hAPP(c_Code__Numeral_Oint__of,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_122])). 10.67/10.77 cnf(c_0_140,plain,(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Int_Onat,c_Int_OPls))), inference(rw,[status(thm)],[c_0_123, c_0_55])). 10.67/10.77 cnf(c_0_141,plain,(hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,X1))!=c_Int_OMin), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_125]), c_0_126])). 10.67/10.77 cnf(c_0_142,plain,(X1=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1))), inference(split_conjunct,[status(thm)],[c_0_127])). 10.67/10.77 cnf(c_0_143,plain,(hAPP(c_fNot,hAPP(c_fNot,X1))=X1), inference(spm,[status(thm)],[c_0_128, c_0_129])). 10.67/10.77 cnf(c_0_144,plain,(hAPP(c_fNot,X1)=c_fFalse|c_fFalse=X1), inference(spm,[status(thm)],[c_0_130, c_0_114])). 10.67/10.77 cnf(c_0_145,plain,(hAPP(c_fNot,c_fFalse)=c_fTrue), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_116]), c_0_131])). 10.67/10.77 cnf(c_0_146,plain,(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))!=c_Int_OPls), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134])). 10.67/10.77 cnf(c_0_147,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_135])). 10.67/10.77 cnf(c_0_148,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_136])). 10.67/10.77 cnf(c_0_149,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_137])). 10.67/10.77 cnf(c_0_150,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_138, c_0_55])). 10.67/10.77 cnf(c_0_151,plain,(hAPP(c_Code__Numeral_Oint__of,X1)=c_Int_OPls|X1!=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Int_Onat,c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_50]), c_0_140])). 10.67/10.77 cnf(c_0_152,plain,(hAPP(c_Code__Numeral_Oint__of,X1)!=c_Int_OMin), inference(spm,[status(thm)],[c_0_141, c_0_142])). 10.67/10.77 cnf(c_0_153,plain,(c_fFalse=X1|c_fTrue=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_144]), c_0_145])). 10.67/10.77 cnf(c_0_154,plain,(hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,X1)))!=c_Int_OPls), inference(rw,[status(thm)],[c_0_146, c_0_89])). 10.67/10.77 cnf(c_0_155,plain,(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147, c_0_55]), c_0_148]), c_0_149]), c_0_150]), c_0_149])). 10.67/10.77 cnf(c_0_156,plain,(hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Int_Onat,c_Int_OPls)))=c_Int_OPls), inference(er,[status(thm)],[c_0_151])). 10.67/10.77 cnf(c_0_157,plain,(hAPP(c_Code__Numeral_Oint__of,X1)=c_fFalse|c_fTrue!=c_Int_OMin), inference(spm,[status(thm)],[c_0_152, c_0_153])). 10.67/10.77 fof(c_0_158, plain, (![X39]:![X40]:![X39]:![X42]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X40))|~hBOOL(hAPP(X39,X40)))|hBOOL(hAPP(X39,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk37_1(X39)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk38_1(X39)))|~hBOOL(hAPP(X39,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42))))&(hBOOL(hAPP(X39,esk38_1(X39)))|~hBOOL(hAPP(X39,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42))))))), 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_transfer__int__nat__quantifiers_I2_J])])])])])])])). 10.67/10.77 fof(c_0_159, plain, (![X13]:c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_zmod__zero])). 10.67/10.77 cnf(c_0_160,plain,(hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,c_Product__Type_Oprod_Oprod__size(X1,X2,X3,X4,X5)))!=c_Int_OPls), inference(spm,[status(thm)],[c_0_154, c_0_155])). 10.67/10.77 cnf(c_0_161,plain,(c_fFalse=c_Int_OPls|c_fTrue!=c_Int_OMin), inference(spm,[status(thm)],[c_0_156, c_0_157])). 10.67/10.77 fof(c_0_162, plain, (![X3]:![X4]:(~class_Rings_Ocomm__semiring__1(X4)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),c_Groups_Ozero__class_Ozero(X4)),X3))|c_Groups_Ozero__class_Ozero(X4)=X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__0__left])])])). 10.67/10.77 cnf(c_0_163,plain,(hBOOL(hAPP(X1,esk38_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_158])). 10.67/10.77 fof(c_0_164, plain, (![X25]:![X26]:![X27]:(((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X25))|c_Divides_Odiv__class_Omod(X27,X25,X26)=c_Groups_Ozero__class_Ozero(X27))|~class_Divides_Osemiring__div(X27))&((c_Divides_Odiv__class_Omod(X27,X25,X26)!=c_Groups_Ozero__class_Ozero(X27)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X25)))|~class_Divides_Osemiring__div(X27)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])])). 10.67/10.77 cnf(c_0_165,plain,(c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_159])). 10.67/10.77 cnf(c_0_166,plain,(c_fTrue!=c_Int_OMin), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_157]), c_0_161])). 10.67/10.77 fof(c_0_167, plain, (![X55]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X55)),X55)=c_Int_OBit1(X55)), inference(variable_rename,[status(thm)],[fact_Bit1__def])). 10.67/10.77 cnf(c_0_168,plain,(c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_162])). 10.67/10.77 cnf(c_0_169,plain,(class_Rings_Ocomm__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1])). 10.67/10.77 cnf(c_0_170,plain,(hBOOL(hAPP(X1,esk38_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,X2))))), inference(rw,[status(thm)],[c_0_163, c_0_89])). 10.67/10.77 cnf(c_0_171,plain,(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))|~class_Divides_Osemiring__div(X1)|c_Divides_Odiv__class_Omod(X1,X3,X2)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_164])). 10.67/10.77 cnf(c_0_172,plain,(c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X1)=c_Int_OPls), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165, c_0_50]), c_0_50])). 10.67/10.77 cnf(c_0_173,plain,(class_Divides_Osemiring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div])). 10.67/10.77 cnf(c_0_174,plain,(c_fFalse=X1|X1!=c_Int_OMin), inference(spm,[status(thm)],[c_0_166, c_0_153])). 10.67/10.77 fof(c_0_175, plain, (![X14]:![X15]:(((hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)!=X14|X14=c_Groups_Ozero__class_Ozero(X15))|~class_Groups_Olinordered__ab__group__add(X15))&((X14!=c_Groups_Ozero__class_Ozero(X15)|hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)=X14)|~class_Groups_Olinordered__ab__group__add(X15)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equal__neg__zero])])])])). 10.67/10.77 cnf(c_0_176,plain,(c_Int_OBit1(c_Int_OPls)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)), inference(split_conjunct,[status(thm)],[fact_minus__Min])). 10.67/10.77 cnf(c_0_177,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_167])). 10.67/10.77 fof(c_0_178, plain, (![X55]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),c_Int_OPls)=X55), inference(variable_rename,[status(thm)],[fact_add__Pls__right])). 10.67/10.77 cnf(c_0_179,plain,(c_Int_OPls=X1|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Int_OPls),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_50]), c_0_169])])). 10.67/10.77 cnf(c_0_180,plain,(hBOOL(hAPP(X1,esk38_1(X1)))|~hBOOL(hAPP(X1,c_Int_OPls))), inference(spm,[status(thm)],[c_0_170, c_0_156])). 10.67/10.77 cnf(c_0_181,plain,(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Int_OPls))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171, c_0_172]), c_0_50]), c_0_173])])). 10.67/10.77 cnf(c_0_182,plain,(c_fFalse=c_Int_OMin), inference(er,[status(thm)],[c_0_174])). 10.67/10.77 cnf(c_0_183,plain,(X2=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X2), inference(split_conjunct,[status(thm)],[c_0_175])). 10.67/10.77 cnf(c_0_184,plain,(class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add])). 10.67/10.77 cnf(c_0_185,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)), inference(rw,[status(thm)],[c_0_176, c_0_177])). 10.67/10.77 cnf(c_0_186,plain,(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls)=X1), inference(split_conjunct,[status(thm)],[c_0_178])). 10.67/10.77 cnf(c_0_187,plain,(esk38_1(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Int_OPls))=c_Int_OPls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179, c_0_180]), c_0_181])])). 10.67/10.77 cnf(c_0_188,plain,(c_fTrue=X1|c_Int_OMin=X1), inference(rw,[status(thm)],[c_0_153, c_0_182])). 10.67/10.77 cnf(c_0_189,plain,(c_Int_OMin!=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J])). 10.67/10.77 cnf(c_0_190,plain,(X1=c_Int_OPls|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)!=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183, c_0_85]), c_0_50]), c_0_184])])). 10.67/10.77 cnf(c_0_191,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185, c_0_186]), c_0_186]), c_0_85])). 10.67/10.77 cnf(c_0_192,plain,(c_fTrue=c_Int_OPls), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187, c_0_188]), c_0_187]), c_0_189])). 10.67/10.77 cnf(c_0_193,plain,(c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Int_OMin), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_190, c_0_191]), c_0_189])). 10.67/10.77 cnf(c_0_194,plain,(c_Int_OMin=X1|c_Int_OPls=X1), inference(rw,[status(thm)],[c_0_188, c_0_192])). 10.67/10.77 cnf(c_0_195,plain,(hAPP(c_Code__Numeral_Oint__of,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_193, c_0_108])). 10.67/10.77 cnf(c_0_196,plain,($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_194]), c_0_108]), c_0_195]), c_0_154]), ['proof']). 10.67/10.77 % SZS output end Proof 10.67/10.77 % User time : 10.038 s 10.67/10.77 % System time : 0.231 s 10.67/10.77 % Total time : 10.268 s 10.67/10.77 10.73/11.01 EOF