0.00/0.03 % 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 : n117.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 06:00:25 CDT 2018 0.03/0.23 % CPUTime : 0.03/0.30 openjdk version "1.8.0_144" 0.03/0.30 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.03/0.30 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.41 start to proof:theBenchmark.p 1.70/1.86 % Version : CSE_E---1.0 1.70/1.86 % Problem : theBenchmark.p 1.70/1.86 % Proof found! 1.70/1.86 % SZS status Theorem for theBenchmark.p 1.70/1.86 % SZS output start Proof 1.70/1.86 fof(fact_finite, axiom, (![X8]:![X2]:(c_Finite__Set_Ofinite(X2,X8)<=class_Finite__Set_Ofinite(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_finite)). 1.70/1.86 fof(fact_finite__imageD, axiom, (![X8]:![X9]:![X6]:![X2]:(c_Finite__Set_Ofinite(X2,c_Set_Oimage(X6,X2,X9,X8))=>(c_Finite__Set_Ofinite(X6,X8)<=c_Fun_Oinj__on(X6,X2,X9,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_finite__imageD)). 1.70/1.86 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite, axiom, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Finite__Set_Ofinite)). 1.70/1.86 fof(help_c__COMBK__1, axiom, (![X88]:![X67]:![X6]:![X2]:X67=hAPP(hAPP(c_COMBK(X2,X6),X67),X88)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_c__COMBK__1)). 1.70/1.86 fof(fact_inj__on__def, axiom, (![X8]:![X9]:![X6]:![X2]:(![X14]:(hBOOL(hAPP(hAPP(c_member(X2),X14),X8))=>![X78]:(hBOOL(hAPP(hAPP(c_member(X2),X78),X8))=>(X78=X14<=hAPP(X9,X14)=hAPP(X9,X78))))<=>c_Fun_Oinj__on(X2,X6,X9,X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_inj__on__def)). 1.70/1.86 fof(fact_finite__UNIV__inj__surj, axiom, (![X9]:![X2]:(c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=>(c_Fun_Oinj__on(X2,X2,X9,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=>c_Set_Oimage(X2,X2,X9,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_finite__UNIV__inj__surj)). 1.70/1.86 fof(fact_order__less__le, axiom, (![X7]:![X5]:![X2]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X5),X7))<=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,X5),X7))&X5!=X7))<=class_Orderings_Oorder(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__le)). 1.70/1.86 fof(fact_inj__Suc, axiom, (![X48]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_inj__Suc)). 1.70/1.86 fof(fact_add__strict__increasing2, axiom, (![X20]:![X21]:![X22]:![X2]:((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X22))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X21),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X22),X20)))))<=class_Groups_Oordered__comm__monoid__add(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__increasing2)). 1.70/1.86 fof(fact_range__ex1__eq, axiom, (![X12]:![X9]:![X6]:![X2]:(c_Fun_Oinj__on(X2,X6,X9,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=>(?[X14]:(hAPP(X9,X14)=X12&![X79]:(hAPP(X9,X79)=X12=>X14=X79))<=>hBOOL(hAPP(hAPP(c_member(X6),X12),c_Set_Oimage(X2,X6,X9,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_range__ex1__eq)). 1.70/1.86 fof(fact_iso__tuple__UNIV__I, axiom, (![X5]:![X2]:hBOOL(hAPP(hAPP(c_member(X2),X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_iso__tuple__UNIV__I)). 1.70/1.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, axiom, (![X22]:![X2]:(class_Rings_Ocomm__semiring__1(X2)=>X22=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X22),c_Groups_Ozero__class_Ozero(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 1.70/1.86 fof(fact_zero__less__Suc, axiom, (![X26]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__Suc)). 1.70/1.86 fof(fact_less__eq__nat_Osimps_I1_J, axiom, (![X26]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I1_J)). 1.70/1.86 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1, axiom, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__1)). 1.70/1.86 fof(arity_Nat__Onat__Orderings_Oorder, axiom, (class_Orderings_Oorder(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oorder)). 1.70/1.86 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add, axiom, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__comm__monoid__add)). 1.70/1.86 fof(c_0_17, plain, (![X9]:![X10]:(~class_Finite__Set_Ofinite(X10)|c_Finite__Set_Ofinite(X10,X9))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite])])])). 1.70/1.86 fof(c_0_18, plain, (![X10]:![X11]:![X12]:![X13]:(~c_Finite__Set_Ofinite(X13,c_Set_Oimage(X12,X13,X11,X10))|(~c_Fun_Oinj__on(X12,X13,X11,X10)|c_Finite__Set_Ofinite(X12,X10)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageD])])])). 1.70/1.86 cnf(c_0_19,plain,(c_Finite__Set_Ofinite(X1,X2)|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). 1.70/1.86 cnf(c_0_20,plain,(class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite])). 1.70/1.86 fof(c_0_21, plain, (![X89]:![X90]:![X91]:![X92]:X90=hAPP(hAPP(c_COMBK(X92,X91),X90),X89)), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 1.70/1.86 fof(c_0_22, plain, (![X79]:![X80]:![X81]:![X82]:![X79]:![X80]:![X81]:![X82]:![X85]:![X86]:(((hBOOL(hAPP(hAPP(c_member(X82),esk30_4(X79,X80,X81,X82)),X79))|c_Fun_Oinj__on(X82,X81,X80,X79))&((hBOOL(hAPP(hAPP(c_member(X82),esk31_4(X79,X80,X81,X82)),X79))|c_Fun_Oinj__on(X82,X81,X80,X79))&((hAPP(X80,esk30_4(X79,X80,X81,X82))=hAPP(X80,esk31_4(X79,X80,X81,X82))|c_Fun_Oinj__on(X82,X81,X80,X79))&(esk31_4(X79,X80,X81,X82)!=esk30_4(X79,X80,X81,X82)|c_Fun_Oinj__on(X82,X81,X80,X79)))))&(~c_Fun_Oinj__on(X82,X81,X80,X79)|(~hBOOL(hAPP(hAPP(c_member(X82),X85),X79))|(~hBOOL(hAPP(hAPP(c_member(X82),X86),X79))|(hAPP(X80,X85)!=hAPP(X80,X86)|X86=X85)))))), 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)],[inference(fof_simplification,[status(thm)],[fact_inj__on__def])])])])])])])])). 1.70/1.86 cnf(c_0_23,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Fun_Oinj__on(X1,X3,X4,X2)|~c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2))), inference(split_conjunct,[status(thm)],[c_0_18])). 1.70/1.86 cnf(c_0_24,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1)), inference(spm,[status(thm)],[c_0_19, c_0_20])). 1.70/1.86 cnf(c_0_25,plain,(X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_21])). 1.70/1.86 cnf(c_0_26,plain,(c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(X3,esk30_4(X4,X3,X2,X1))=hAPP(X3,esk31_4(X4,X3,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_22])). 1.70/1.86 cnf(c_0_27,plain,(c_Fun_Oinj__on(X1,X2,X3,X4)|esk31_4(X4,X3,X2,X1)!=esk30_4(X4,X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_22])). 1.70/1.86 fof(c_0_28, plain, (![X10]:![X11]:(~c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))|(~c_Fun_Oinj__on(X11,X11,X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))|c_Set_Oimage(X11,X11,X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])])). 1.70/1.86 cnf(c_0_29,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2)), inference(spm,[status(thm)],[c_0_23, c_0_24])). 1.70/1.86 cnf(c_0_30,plain,(c_Fun_Oinj__on(X1,X2,c_COMBK(X3,X4),X5)), inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_25]), c_0_27])). 1.70/1.86 fof(c_0_31, plain, (![X8]:![X9]:![X10]:((((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X9),X8))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X8)))|~class_Orderings_Oorder(X10))&((X9!=X8|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X8)))|~class_Orderings_Oorder(X10)))&(((~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X9),X8))|X9=X8)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X8)))|~class_Orderings_Oorder(X10)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le])])])])). 1.70/1.86 cnf(c_0_32,plain,(c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_28])). 1.70/1.86 cnf(c_0_33,plain,(c_Finite__Set_Ofinite(X1,X2)), inference(spm,[status(thm)],[c_0_29, c_0_30])). 1.70/1.86 fof(c_0_34, plain, (![X49]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X49)), inference(variable_rename,[status(thm)],[fact_inj__Suc])). 1.70/1.86 cnf(c_0_35,plain,(~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_31])). 1.70/1.86 fof(c_0_36, plain, (![X23]:![X24]:![X25]:![X26]:(~class_Groups_Oordered__comm__monoid__add(X26)|(~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26)),X25))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26),X24),X23))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing2])])])). 1.70/1.86 fof(c_0_37, plain, (![X80]:![X81]:![X82]:![X83]:![X84]:![X87]:(((((hAPP(X81,esk38_5(X80,X81,X82,X83,X84))=X80|hAPP(X81,X84)!=X80)|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))&(((X84!=esk38_5(X80,X81,X82,X83,X84)|hAPP(X81,X84)!=X80)|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))&(((hAPP(X81,esk39_4(X80,X81,X82,X83))=X80|~hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))&(((hAPP(X81,X87)!=X80|esk39_4(X80,X81,X82,X83)=X87)|~hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))), 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_range__ex1__eq])])])])])])])). 1.70/1.86 cnf(c_0_38,plain,(c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])). 1.70/1.86 cnf(c_0_39,plain,(c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_34])). 1.70/1.86 fof(c_0_40, plain, (![X6]:![X7]:hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I])). 1.70/1.86 cnf(c_0_41,plain,(~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_35])). 1.70/1.86 cnf(c_0_42,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_36])). 1.70/1.86 fof(c_0_43, plain, (![X23]:![X24]:(~class_Rings_Ocomm__semiring__1(X24)|X23=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24),X23),c_Groups_Ozero__class_Ozero(X24)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])). 1.70/1.86 fof(c_0_44, plain, (![X27]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X27)))), inference(variable_rename,[status(thm)],[fact_zero__less__Suc])). 1.70/1.86 cnf(c_0_45,plain,(hAPP(X3,esk39_4(X4,X3,X2,X1))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_37])). 1.70/1.86 cnf(c_0_46,plain,(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(spm,[status(thm)],[c_0_38, c_0_39])). 1.70/1.86 cnf(c_0_47,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_40])). 1.70/1.86 cnf(c_0_48,plain,(~class_Orderings_Oorder(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))), inference(spm,[status(thm)],[c_0_41, c_0_42])). 1.70/1.86 cnf(c_0_49,plain,(X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),c_Groups_Ozero__class_Ozero(X2))|~class_Rings_Ocomm__semiring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_43])). 1.70/1.86 cnf(c_0_50,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_44])). 1.70/1.86 cnf(c_0_51,plain,(hAPP(c_Nat_OSuc,esk39_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_39]), c_0_47])])). 1.70/1.86 fof(c_0_52, plain, (![X27]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))), inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J])). 1.70/1.86 cnf(c_0_53,plain,(~class_Rings_Ocomm__semiring__1(X1)|~class_Orderings_Oorder(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))), inference(spm,[status(thm)],[c_0_48, c_0_49])). 1.70/1.86 cnf(c_0_54,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(spm,[status(thm)],[c_0_50, c_0_51])). 1.70/1.86 cnf(c_0_55,plain,(class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1])). 1.70/1.86 cnf(c_0_56,plain,(class_Orderings_Oorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder])). 1.70/1.86 cnf(c_0_57,plain,(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add])). 1.70/1.86 cnf(c_0_58,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_52])). 1.70/1.86 cnf(c_0_59,plain,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58])]), ['proof']). 1.70/1.86 % SZS output end Proof 1.70/1.86 % User time : 1.318 s 1.70/1.86 % System time : 0.049 s 1.70/1.86 % Total time : 1.367 s 1.70/1.86 1.78/1.87 EOF