0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule --cpu-limit=%d %s 0.03/0.23 % Computer : n189.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 05:25:09 CDT 2018 0.03/0.24 % CPUTime : 0.03/0.24 # Version: 2.2pre001 0.03/0.25 # No SInE strategy applied 0.03/0.25 # Trying AutoSched0 for 151 seconds 8.23/8.42 # AutoSched0-Mode selected heuristic G_E___107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y 8.23/8.42 # and selection function SelectMaxLComplexAvoidPosPred. 8.23/8.42 # 8.23/8.42 # Preprocessing time : 0.032 s 8.23/8.42 # Presaturation interreduction done 8.23/8.42 8.23/8.42 # Proof found! 8.23/8.42 # SZS status Theorem 8.23/8.42 # SZS output start CNFRefutation 8.23/8.42 fof(fact_insert__not__empty, axiom, ![X14, X13, X4]:c_Set_Oinsert(X4,X13,X14)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_insert__not__empty)). 8.23/8.42 fof(fact_insert__image, axiom, ![X6, X24, X14, X19, X4]:(c_Set_Oimage(X4,X24,X6,X14)=c_Set_Oinsert(X24,hAPP(X6,X19),c_Set_Oimage(X4,X24,X6,X14))<=c_member(X4,X19,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_insert__image)). 8.23/8.42 fof(fact_eq__mem, axiom, ![X18, X19, X4]:(X19=X18<=>c_member(X4,X19,c_fequal(X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__mem)). 8.23/8.42 fof(fact_empty__is__image, axiom, ![X14, X6, X24, X4]:(X14=c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool))<=>c_Set_Oimage(X24,X4,X6,X14)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_empty__is__image)). 8.23/8.42 fof(fact_rev__image__eqI, axiom, ![X24, X6, X26, X14, X19, X4]:((X26=hAPP(X6,X19)=>c_member(X24,X26,c_Set_Oimage(X4,X24,X6,X14)))<=c_member(X4,X19,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_rev__image__eqI)). 8.23/8.42 fof(fact_all__not__in__conv, axiom, ![X14, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X14<=>![X23]:~(c_member(X4,X23,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_all__not__in__conv)). 8.23/8.42 fof(fact_Suc__inject, axiom, ![X3, X2]:(hAPP(c_Nat_OSuc,X3)=hAPP(c_Nat_OSuc,X2)=>X3=X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__inject)). 8.23/8.42 fof(fact_gr0__conv__Suc, axiom, ![X8]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)<=>?[X25]:X8=hAPP(c_Nat_OSuc,X25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr0__conv__Suc)). 8.23/8.42 fof(fact_image__iff, axiom, ![X14, X6, X24, X33, X4]:(?[X23]:(c_member(X24,X23,X14)&X33=hAPP(X6,X23))<=>c_member(X4,X33,c_Set_Oimage(X24,X4,X6,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_image__iff)). 8.23/8.42 fof(fact_finite__code, axiom, ![X14, X4]:(class_Finite__Set_Ofinite(X4)=>c_Finite__Set_Ofinite(X4,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_finite__code)). 8.23/8.42 fof(fact_less__iff__Suc__add, axiom, ![X8, X7]:(?[X52]:hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X52))=X8<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__iff__Suc__add)). 8.23/8.42 fof(fact_le__trans, axiom, ![X16, X21, X22]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X16)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X16))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__trans)). 8.23/8.42 fof(fact_Suc__le__mono, axiom, ![X7, X8]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8),hAPP(c_Nat_OSuc,X7))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__le__mono)). 8.23/8.42 fof(fact_card__mono, axiom, ![X14, X27, X4]:((c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X14,X27)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X4,X14),c_Finite__Set_Ocard(X4,X27)))<=c_Finite__Set_Ofinite(X4,X27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_card__mono)). 8.23/8.42 fof(fact_card__UNIV__unit, axiom, c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_card__UNIV__unit)). 8.23/8.42 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)). 8.23/8.42 fof(fact_subset__UNIV, axiom, ![X14, X4]:c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X14,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_subset__UNIV)). 8.23/8.42 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)). 8.23/8.42 fof(fact_gr0I, axiom, ![X15]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr0I)). 8.23/8.42 fof(fact_less__eq__nat_Osimps_I1_J, axiom, ![X15]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I1_J)). 8.23/8.42 fof(fact_card__gt__0__iff, axiom, ![X14, X4]:((c_Finite__Set_Ofinite(X4,X14)&X14!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X4,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_card__gt__0__iff)). 8.23/8.42 fof(fact_card__insert__if, axiom, ![X19, X14, X4]:(c_Finite__Set_Ofinite(X4,X14)=>((c_member(X4,X19,X14)=>c_Finite__Set_Ocard(X4,X14)=c_Finite__Set_Ocard(X4,c_Set_Oinsert(X4,X19,X14)))&(~(c_member(X4,X19,X14))=>c_Finite__Set_Ocard(X4,c_Set_Oinsert(X4,X19,X14))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X4,X14))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_card__insert__if)). 8.23/8.42 fof(fact_finite__insert, axiom, ![X14, X13, X4]:(c_Finite__Set_Ofinite(X4,X14)<=>c_Finite__Set_Ofinite(X4,c_Set_Oinsert(X4,X13,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_finite__insert)). 8.23/8.42 fof(fact_Suc__n__not__le__n, axiom, ![X15]:~(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X15),X15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__n__not__le__n)). 8.23/8.42 fof(fact_add_Ocomm__neutral, axiom, ![X12, X4]:(c_Groups_Oplus__class_Oplus(X4,X12,c_Groups_Ozero__class_Ozero(X4))=X12<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add_Ocomm__neutral)). 8.23/8.42 fof(fact_nat_Osimps_I3_J, axiom, ![X46]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X46), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat_Osimps_I3_J)). 8.23/8.42 fof(fact_gr__implies__not0, axiom, ![X15, X17]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X15)=>X15!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr__implies__not0)). 8.23/8.42 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__add)). 8.23/8.42 fof(c_0_28, plain, ![X1414, X1415, X1416]:c_Set_Oinsert(X1416,X1415,X1414)!=c_Orderings_Obot__class_Obot(tc_fun(X1416,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_insert__not__empty])). 8.23/8.42 fof(c_0_29, plain, ![X691, X692, X693, X694, X695]:(~c_member(X695,X694,X693)|c_Set_Oimage(X695,X692,X691,X693)=c_Set_Oinsert(X692,hAPP(X691,X694),c_Set_Oimage(X695,X692,X691,X693))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__image])])])). 8.23/8.42 fof(c_0_30, plain, ![X506, X507, X508, X506, X507, X508]:((X507!=X506|c_member(X508,X507,c_fequal(X506)))&(~c_member(X508,X507,c_fequal(X506))|X507=X506)), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])])])])). 8.23/8.42 cnf(c_0_31, plain, (c_Set_Oinsert(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_28])). 8.23/8.42 cnf(c_0_32, plain, (c_Set_Oimage(X1,X4,X5,X3)=c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3))|~c_member(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_29])). 8.23/8.42 cnf(c_0_33, plain, (c_member(X3,X1,c_fequal(X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_30])). 8.23/8.42 cnf(c_0_34, plain, (c_Set_Oimage(X1,X2,X3,X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_member(X1,X5,X4)), inference(spm,[status(thm)],[c_0_31, c_0_32])). 8.23/8.42 cnf(c_0_35, plain, (c_member(X1,X2,c_fequal(X2))), inference(er,[status(thm)],[c_0_33])). 8.23/8.42 fof(c_0_36, plain, ![X1604, X1605, X1606, X1607, X1604, X1605, X1606, X1607]:((X1604!=c_Orderings_Obot__class_Obot(tc_fun(X1606,tc_HOL_Obool))|c_Set_Oimage(X1606,X1607,X1605,X1604)=c_Orderings_Obot__class_Obot(tc_fun(X1607,tc_HOL_Obool)))&(c_Set_Oimage(X1606,X1607,X1605,X1604)!=c_Orderings_Obot__class_Obot(tc_fun(X1607,tc_HOL_Obool))|X1604=c_Orderings_Obot__class_Obot(tc_fun(X1606,tc_HOL_Obool)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])])])])). 8.23/8.42 fof(c_0_37, plain, ![X1381, X1382, X1383, X1384, X1385, X1386]:(~c_member(X1386,X1385,X1384)|(X1383!=hAPP(X1382,X1385)|c_member(X1381,X1383,c_Set_Oimage(X1386,X1381,X1382,X1384)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__image__eqI])])])). 8.23/8.42 fof(c_0_38, plain, ![X852, X853, X854, X852, X853]:((c_Orderings_Obot__class_Obot(tc_fun(X853,tc_HOL_Obool))!=X852|~c_member(X853,X854,X852))&(c_member(X853,esk25_2(X852,X853),X852)|c_Orderings_Obot__class_Obot(tc_fun(X853,tc_HOL_Obool))=X852)), 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_all__not__in__conv])])])])])])])). 8.23/8.42 cnf(c_0_39, plain, (c_Set_Oimage(X1,X2,X3,c_fequal(X4))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(spm,[status(thm)],[c_0_34, c_0_35])). 8.23/8.42 cnf(c_0_40, plain, (c_Set_Oimage(X2,X3,X4,X1)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_36])). 8.23/8.42 fof(c_0_41, plain, ![X1089, X1090]:(hAPP(c_Nat_OSuc,X1089)!=hAPP(c_Nat_OSuc,X1090)|X1089=X1090), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])])). 8.23/8.42 fof(c_0_42, plain, ![X357, X357, X359]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X357)|X357=hAPP(c_Nat_OSuc,esk6_1(X357)))&(X357!=hAPP(c_Nat_OSuc,X359)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X357))), 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_gr0__conv__Suc])])])])])])). 8.23/8.42 cnf(c_0_43, plain, (c_member(X6,X4,c_Set_Oimage(X1,X6,X5,X3))|~c_member(X1,X2,X3)|X4!=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_37])). 8.23/8.42 cnf(c_0_44, plain, (c_member(X1,esk25_2(X2,X1),X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2), inference(split_conjunct,[status(thm)],[c_0_38])). 8.23/8.42 cnf(c_0_45, plain, (X2=X3|~c_member(X1,X2,c_fequal(X3))), inference(split_conjunct,[status(thm)],[c_0_30])). 8.23/8.42 cnf(c_0_46, plain, (c_fequal(X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(spm,[status(thm)],[c_0_39, c_0_40])). 8.23/8.42 cnf(c_0_47, plain, (X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_41])). 8.23/8.42 cnf(c_0_48, plain, (X1=hAPP(c_Nat_OSuc,esk6_1(X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_42])). 8.23/8.42 cnf(c_0_49, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|X1!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_42])). 8.23/8.42 fof(c_0_50, plain, ![X1392, X1393, X1394, X1395, X1397, X1396, X1392, X1393, X1394, X1395, X1396]:((~c_member(X1394,X1397,X1392)|X1395!=hAPP(X1393,X1397)|c_member(X1396,X1395,c_Set_Oimage(X1394,X1396,X1393,X1392)))&((c_member(X1394,esk38_4(X1392,X1393,X1394,X1395),X1392)|~c_member(X1396,X1395,c_Set_Oimage(X1394,X1396,X1393,X1392)))&(X1395=hAPP(X1393,esk38_4(X1392,X1393,X1394,X1395))|~c_member(X1396,X1395,c_Set_Oimage(X1394,X1396,X1393,X1392))))), 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_image__iff])])])])])])])). 8.23/8.42 cnf(c_0_51, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_member(X3,X4,c_Set_Oimage(X1,X3,X5,X2))|X4!=hAPP(X5,esk25_2(X2,X1))), inference(spm,[status(thm)],[c_0_43, c_0_44])). 8.23/8.42 cnf(c_0_52, plain, (esk25_2(c_fequal(X1),X2)=X1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_44]), c_0_46])). 8.23/8.42 cnf(c_0_53, plain, (X1=esk6_1(X2)|hAPP(c_Nat_OSuc,X1)!=X2), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])). 8.23/8.42 cnf(c_0_54, plain, (X1=hAPP(X2,esk38_4(X3,X2,X4,X1))|~c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_50])). 8.23/8.42 cnf(c_0_55, plain, (c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_fequal(X5)))|X2!=hAPP(X4,X5)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_46])). 8.23/8.42 cnf(c_0_56, plain, (esk6_1(hAPP(c_Nat_OSuc,X1))=X1), inference(er,[status(thm)],[c_0_53])). 8.23/8.42 cnf(c_0_57, plain, (hAPP(X1,esk38_4(c_fequal(X2),X1,X3,X4))=X4|X4!=hAPP(X1,X2)), inference(spm,[status(thm)],[c_0_54, c_0_55])). 8.23/8.42 fof(c_0_58, plain, ![X176, X177]:(~class_Finite__Set_Ofinite(X177)|c_Finite__Set_Ofinite(X177,X176)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])])). 8.23/8.42 cnf(c_0_59, plain, (esk38_4(c_fequal(X1),c_Nat_OSuc,X2,X3)=esk6_1(X3)|X3!=hAPP(c_Nat_OSuc,X1)), inference(spm,[status(thm)],[c_0_56, c_0_57])). 8.23/8.42 fof(c_0_60, plain, ![X1540, X1541, X1542, X1540, X1541]:((hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1541,X1542))!=X1540|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1541,X1540))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1541,X1540)|hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1541,esk41_2(X1540,X1541)))=X1540)), 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_less__iff__Suc__add])])])])])])). 8.23/8.42 fof(c_0_61, plain, ![X1355, X1356, X1357]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1357,X1356)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1356,X1355)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1357,X1355))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])])). 8.23/8.42 fof(c_0_62, plain, ![X1506, X1507, X1506, X1507]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1507),hAPP(c_Nat_OSuc,X1506))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1507,X1506))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1507,X1506)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1507),hAPP(c_Nat_OSuc,X1506)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])])])])). 8.23/8.42 fof(c_0_63, plain, ![X1492, X1493, X1494]:(~c_Finite__Set_Ofinite(X1494,X1493)|(~c_Orderings_Oord__class_Oless__eq(tc_fun(X1494,tc_HOL_Obool),X1492,X1493)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1494,X1492),c_Finite__Set_Ocard(X1494,X1493)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__mono])])])). 8.23/8.42 cnf(c_0_64, plain, (c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit])). 8.23/8.42 cnf(c_0_65, 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])). 8.23/8.42 fof(c_0_66, plain, ![X275, X276]:c_Orderings_Oord__class_Oless__eq(tc_fun(X276,tc_HOL_Obool),X275,c_Orderings_Otop__class_Otop(tc_fun(X276,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_subset__UNIV])). 8.23/8.42 cnf(c_0_67, plain, (c_Finite__Set_Ofinite(X1,X2)|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_58])). 8.23/8.42 cnf(c_0_68, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite])). 8.23/8.42 cnf(c_0_69, plain, (hAPP(c_Nat_OSuc,esk6_1(X1))=X1|X1!=hAPP(c_Nat_OSuc,X2)), inference(spm,[status(thm)],[c_0_57, c_0_59])). 8.23/8.42 cnf(c_0_70, plain, (hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk41_2(X2,X1)))=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_60])). 8.23/8.42 fof(c_0_71, plain, ![X178]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X178|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X178)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])])). 8.23/8.42 cnf(c_0_72, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_61])). 8.23/8.42 cnf(c_0_73, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62])). 8.23/8.42 cnf(c_0_74, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X1,X2))|~c_Finite__Set_Ofinite(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)), inference(split_conjunct,[status(thm)],[c_0_63])). 8.23/8.42 cnf(c_0_75, plain, (c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_64, c_0_65])). 8.23/8.42 cnf(c_0_76, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_66])). 8.23/8.42 cnf(c_0_77, plain, (c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1)), inference(spm,[status(thm)],[c_0_67, c_0_68])). 8.23/8.42 fof(c_0_78, plain, ![X332]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X332), inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J])). 8.23/8.42 fof(c_0_79, plain, ![X197, X198, X197, X198]:((~c_Finite__Set_Ofinite(X198,X197)|X197=c_Orderings_Obot__class_Obot(tc_fun(X198,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X198,X197)))&((c_Finite__Set_Ofinite(X198,X197)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X198,X197)))&(X197!=c_Orderings_Obot__class_Obot(tc_fun(X198,tc_HOL_Obool))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X198,X197))))), 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_card__gt__0__iff])])])])])). 8.23/8.42 fof(c_0_80, plain, ![X1052, X1053, X1054]:((~c_member(X1054,X1052,X1053)|c_Finite__Set_Ocard(X1054,X1053)=c_Finite__Set_Ocard(X1054,c_Set_Oinsert(X1054,X1052,X1053))|~c_Finite__Set_Ofinite(X1054,X1053))&(c_member(X1054,X1052,X1053)|c_Finite__Set_Ocard(X1054,c_Set_Oinsert(X1054,X1052,X1053))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1054,X1053))|~c_Finite__Set_Ofinite(X1054,X1053))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__if])])])])). 8.23/8.42 fof(c_0_81, plain, ![X918, X919, X920, X918, X919, X920]:((~c_Finite__Set_Ofinite(X920,X918)|c_Finite__Set_Ofinite(X920,c_Set_Oinsert(X920,X919,X918)))&(~c_Finite__Set_Ofinite(X920,c_Set_Oinsert(X920,X919,X918))|c_Finite__Set_Ofinite(X920,X918))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])])])])). 8.23/8.42 fof(c_0_82, plain, ![X551]:~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X551),X551), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n])])). 8.23/8.42 cnf(c_0_83, plain, (hAPP(c_Nat_OSuc,esk6_1(X1))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)), inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70])])). 8.23/8.42 cnf(c_0_84, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_71])). 8.23/8.42 cnf(c_0_85, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), inference(spm,[status(thm)],[c_0_72, c_0_73])). 8.23/8.42 cnf(c_0_86, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_76])]), c_0_77])])). 8.23/8.42 cnf(c_0_87, plain, (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_78])). 8.23/8.42 cnf(c_0_88, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2))|~c_Finite__Set_Ofinite(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_79])). 8.23/8.42 cnf(c_0_89, plain, (c_Finite__Set_Ocard(X1,X3)=c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3))|~c_member(X1,X2,X3)|~c_Finite__Set_Ofinite(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_80])). 8.23/8.42 cnf(c_0_90, plain, (c_Finite__Set_Ofinite(X1,X3)|~c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_81])). 8.23/8.42 cnf(c_0_91, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1)), inference(split_conjunct,[status(thm)],[c_0_82])). 8.23/8.42 cnf(c_0_92, plain, (hAPP(c_Nat_OSuc,esk6_1(X1))=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1), inference(spm,[status(thm)],[c_0_83, c_0_84])). 8.23/8.42 cnf(c_0_93, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),hAPP(c_Nat_OSuc,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_87])])). 8.23/8.42 cnf(c_0_94, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2))|~c_member(X1,X3,X2)|~c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X3,X2))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_31]), c_0_90])). 8.23/8.42 fof(c_0_95, plain, ![X776, X777]:(~class_Groups_Ocomm__monoid__add(X777)|c_Groups_Oplus__class_Oplus(X777,X776,c_Groups_Ozero__class_Ozero(X777))=X776), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add_Ocomm__neutral])])])). 8.23/8.42 cnf(c_0_96, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk6_1(X1))), inference(spm,[status(thm)],[c_0_91, c_0_92])). 8.23/8.42 cnf(c_0_97, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X2),X1)), inference(spm,[status(thm)],[c_0_93, c_0_92])). 8.23/8.42 fof(c_0_98, plain, ![X533]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X533), inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J])). 8.23/8.42 fof(c_0_99, plain, ![X282, X283]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X283,X282)|X282!=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_gr__implies__not0])])])])). 8.23/8.42 cnf(c_0_100, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1))|~c_member(tc_Product__Type_Ounit,X2,X1)), inference(spm,[status(thm)],[c_0_94, c_0_77])). 8.23/8.42 cnf(c_0_101, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_60])). 8.23/8.42 cnf(c_0_102, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_95])). 8.23/8.42 cnf(c_0_103, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add])). 8.23/8.42 cnf(c_0_104, plain, (esk6_1(c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(spm,[status(thm)],[c_0_96, c_0_97])). 8.23/8.42 cnf(c_0_105, plain, (c_member(X1,X2,X3)|c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,X3))|~c_Finite__Set_Ofinite(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_80])). 8.23/8.42 cnf(c_0_106, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_98])). 8.23/8.42 cnf(c_0_107, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_99])). 8.23/8.42 cnf(c_0_108, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(X1)))), inference(spm,[status(thm)],[c_0_100, c_0_35])). 8.23/8.42 cnf(c_0_109, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hAPP(c_Nat_OSuc,X1)!=X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_103])])). 8.23/8.42 cnf(c_0_110, plain, (c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_member(tc_Product__Type_Ounit,X2,X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_56]), c_0_77])]), c_0_106])). 8.23/8.42 cnf(c_0_111, plain, (c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(X1))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(spm,[status(thm)],[c_0_107, c_0_108])). 8.23/8.42 cnf(c_0_112, plain, (hAPP(c_Nat_OSuc,X1)!=X2|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(spm,[status(thm)],[c_0_107, c_0_109])). 8.23/8.42 cnf(c_0_113, plain, (X1=X2), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_110]), c_0_111])). 8.23/8.42 cnf(c_0_114, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_112, c_0_113]), c_0_113]), ['proof']). 8.23/8.42 # SZS output end CNFRefutation 8.23/8.42 # Proof object total steps : 115 8.23/8.42 # Proof object clause steps : 63 8.23/8.42 # Proof object formula steps : 52 8.23/8.42 # Proof object conjectures : 0 8.23/8.42 # Proof object clause conjectures : 0 8.23/8.42 # Proof object formula conjectures : 0 8.23/8.42 # Proof object initial clauses used : 32 8.23/8.42 # Proof object initial formulas used : 28 8.23/8.42 # Proof object generating inferences : 28 8.23/8.42 # Proof object simplifying inferences : 23 8.23/8.42 # Training examples: 0 positive, 0 negative 8.23/8.42 # Parsed axioms : 533 8.23/8.42 # Removed by relevancy pruning/SinE : 0 8.23/8.42 # Initial clauses : 775 8.23/8.42 # Removed in clause preprocessing : 40 8.23/8.42 # Initial clauses in saturation : 735 8.23/8.42 # Processed clauses : 33185 8.23/8.42 # ...of these trivial : 466 8.23/8.42 # ...subsumed : 27105 8.23/8.42 # ...remaining for further processing : 5614 8.23/8.42 # Other redundant clauses eliminated : 4545 8.23/8.42 # Clauses deleted for lack of memory : 0 8.23/8.42 # Backward-subsumed : 2149 8.23/8.42 # Backward-rewritten : 43 8.23/8.42 # Generated clauses : 563001 8.23/8.42 # ...of the previous two non-trivial : 517888 8.23/8.42 # Contextual simplify-reflections : 5074 8.23/8.42 # Paramodulations : 556670 8.23/8.42 # Factorizations : 11 8.23/8.42 # Equation resolutions : 5400 8.23/8.42 # Propositional unsat checks : 0 8.23/8.42 # Propositional check models : 0 8.23/8.42 # Propositional check unsatisfiable : 0 8.23/8.42 # Propositional clauses : 0 8.23/8.42 # Propositional clauses after purity: 0 8.23/8.42 # Propositional unsat core size : 0 8.23/8.42 # Current number of processed clauses : 1917 8.23/8.42 # Positive orientable unit clauses : 245 8.23/8.42 # Positive unorientable unit clauses: 1 8.23/8.42 # Negative unit clauses : 129 8.23/8.42 # Non-unit-clauses : 1542 8.23/8.42 # Current number of unprocessed clauses: 98979 8.23/8.42 # ...number of literals in the above : 359004 8.23/8.42 # Current number of archived formulas : 0 8.23/8.42 # Current number of archived clauses : 3646 8.23/8.42 # Clause-clause subsumption calls (NU) : 3240095 8.23/8.42 # Rec. Clause-clause subsumption calls : 2169859 8.23/8.42 # Non-unit clause-clause subsumptions : 25054 8.23/8.42 # Unit Clause-clause subsumption calls : 46522 8.23/8.42 # Rewrite failures with RHS unbound : 4548 8.23/8.42 # BW rewrite match attempts : 22597 8.23/8.42 # BW rewrite match successes : 4513 8.23/8.42 # Condensation attempts : 0 8.23/8.42 # Condensation successes : 0 8.23/8.42 # Termbank termtop insertions : 9145521 8.23/8.45 8.23/8.45 # ------------------------------------------------- 8.23/8.45 # User time : 7.919 s 8.23/8.45 # System time : 0.294 s 8.23/8.45 # Total time : 8.213 s 8.23/8.45 # Maximum resident set size: 2248 pages 8.23/8.45 EOF