0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.12 % Command : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC 0.11/0.32 % Computer : n025.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1200 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Jul 13 16:09:42 EDT 2021 0.11/0.32 % CPUTime : 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 # Version: 2.6rc1-ho 0.11/0.33 # No SInE strategy applied 0.11/0.33 # Trying AutoSched0 for 59 seconds 59.14/59.52 # AutoSched0-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y 59.14/59.52 # and selection function SelectMaxLComplexAvoidPosPred. 59.14/59.52 # 59.14/59.52 # Preprocessing time : 0.095 s 59.32/59.70 # No success with AutoSched0 59.32/59.70 # Trying AutoSched1 for 26 seconds 85.29/85.77 # AutoSched1-Mode selected heuristic G_E___008_C45_F1_PI_SE_Q4_CS_SP_S4SI 85.29/85.77 # and selection function SelectNewComplexAHPNS. 85.29/85.77 # 85.29/85.77 # Preprocessing time : 0.095 s 85.39/85.90 # No success with AutoSched1 85.39/85.90 # Trying AutoSched2 for 8 seconds 87.95/88.44 # AutoSched2-Mode selected heuristic U_____100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN 87.95/88.44 # and selection function SelectComplexExceptUniqMaxHorn. 87.95/88.44 # 87.95/88.44 # Preprocessing time : 0.095 s 87.95/88.44 # Presaturation interreduction done 87.95/88.44 87.95/88.44 # Proof found! 87.95/88.44 # SZS status Theorem 87.95/88.44 # SZS output start CNFRefutation 87.95/88.44 thf(def_d_not, axiom, (d_not)=(^[X36:$o]:(X36=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_d_not)). 87.95/88.44 thf(def_imp, axiom, (imp)=(^[X34:$o, X35:$o]:(X34=>X35)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_imp)). 87.95/88.44 thf(def_l_ec, axiom, (l_ec)=(^[X38:$o, X39:$o]:(X38=>(X39=>~$true))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_l_ec)). 87.95/88.44 thf(def_all_of, axiom, (all_of)=(^[X3:$i > $o, X2:$i > $o]:![X4:$i]:(X3 @ X4=>X2 @ X4)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_all_of)). 87.95/88.44 thf(def_is_of, axiom, (is_of)=(^[X1:$i, X2:$i > $o]:X2 @ X1), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_is_of)). 87.95/88.44 thf(def_non, axiom, (non)=(^[X1:$i, X2:$i > $o, X4:$i]:(X2 @ X4=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_non)). 87.95/88.44 thf(def_d_and, axiom, (d_and)=(^[X40:$o, X41:$o]:((X40=>(X41=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_d_and)). 87.95/88.44 thf(def_l_some, axiom, (l_some)=(^[X1:$i, X2:$i > $o]:(![X488:$i]:(in @ X488 @ X1=>(X2 @ X488=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_l_some)). 87.95/88.44 thf(def_n_is, axiom, (n_is)=(^[X564:$i, X565:$i]:(X564)=(X565)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_n_is)). 87.95/88.44 thf(def_e_is, axiom, (e_is)=(^[X1:$i, X60:$i, X61:$i]:(X60)=(X61)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_e_is)). 87.95/88.44 thf(def_l_or, axiom, (l_or)=(^[X42:$o, X483:$o]:((X42=>~$true)=>X483)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_l_or)). 87.95/88.44 thf(def_and3, axiom, (and3)=(^[X51:$o, X52:$o, X53:$o]:((X51=>(((X52=>(X53=>~$true))=>~$true)=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_and3)). 87.95/88.44 thf(def_n_some, axiom, (n_some)=(^[X566:$i > $o]:(![X567:$i]:(in @ X567 @ nat=>(X566 @ X567=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_n_some)). 87.95/88.44 thf(def_diffprop, axiom, (diffprop)=(^[X1:$i, X183:$i, X4:$i]:(X1)=(n_pl @ X183 @ X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_diffprop)). 87.95/88.44 thf(def_or3, axiom, (or3)=(^[X48:$o, X49:$o, X50:$o]:((X48=>~$true)=>((X49=>~$true)=>X50))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_or3)). 87.95/88.44 thf(def_ec3, axiom, (ec3)=(^[X54:$o, X55:$o, X56:$o]:(((X54=>(X55=>~$true))=>((((X55=>(X56=>~$true))=>((X56=>(X54=>~$true))=>~$true))=>~$true)=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_ec3)). 87.95/88.44 thf(def_d_29_ii, axiom, (d_29_ii)=(^[X1:$i, X184:$i]:(![X588:$i]:(in @ X588 @ nat=>((X1)=(n_pl @ X184 @ X588)=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_d_29_ii)). 87.95/88.44 thf(def_orec3, axiom, (orec3)=(^[X57:$o, X58:$o, X59:$o]:((((X57=>~$true)=>((X58=>~$true)=>X59))=>((((X57=>(X58=>~$true))=>((((X58=>(X59=>~$true))=>((X59=>(X57=>~$true))=>~$true))=>~$true)=>~$true))=>~$true)=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_orec3)). 87.95/88.44 thf(def_moreis, axiom, (moreis)=(^[X1:$i, X187:$i]:(((![X595:$i]:(in @ X595 @ nat=>((X1)=(n_pl @ X187 @ X595)=>~$true))=>~$true)=>~$true)=>(X1)=(X187))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_moreis)). 87.95/88.44 thf(satz9, axiom, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:all_of @ (^[X233:$i]:in @ X233 @ nat) @ (^[X234:$i]:orec3 @ (n_is @ X1 @ X234) @ (n_some @ (^[X4:$i]:n_is @ X1 @ (n_pl @ X234 @ X4))) @ (n_some @ (^[X4:$i]:n_is @ X234 @ (n_pl @ X1 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz9)). 87.95/88.44 thf(satz26c, conjecture, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:all_of @ (^[X291:$i]:in @ X291 @ nat) @ (^[X292:$i]:(moreis @ X292 @ X1<=d_29_ii @ (ordsucc @ X292) @ X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz26c)). 87.95/88.44 thf(def_iii, axiom, (iii)=(^[X1:$i, X185:$i]:(![X591:$i]:(in @ X591 @ nat=>((X185)=(n_pl @ X1 @ X591)=>~$true))=>~$true)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_iii)). 87.95/88.44 thf(satz10c, axiom, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:all_of @ (^[X235:$i]:in @ X235 @ nat) @ (^[X236:$i]:(moreis @ X1 @ X236=>d_not @ (iii @ X1 @ X236)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz10c)). 87.95/88.44 thf(def_lessis, axiom, (lessis)=(^[X1:$i, X188:$i]:(((![X596:$i]:(in @ X596 @ nat=>((X188)=(n_pl @ X1 @ X596)=>~$true))=>~$true)=>~$true)=>(X1)=(X188))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_lessis)). 87.95/88.44 thf(satz25b, axiom, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:all_of @ (^[X303:$i]:in @ X303 @ nat) @ (^[X304:$i]:(lessis @ (n_pl @ X304 @ n_1) @ X1<=iii @ X304 @ X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz25b)). 87.95/88.44 thf(satz4e, axiom, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:n_is @ (ordsucc @ X1) @ (n_pl @ X1 @ n_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz4e)). 87.95/88.44 thf(suc_p, axiom, all_of @ (^[X1:$i]:in @ X1 @ nat) @ (^[X1:$i]:is_of @ (ordsucc @ X1) @ (^[X144:$i]:in @ X144 @ nat)), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', suc_p)). 87.95/88.44 thf(c_0_27, axiom, (d_not)=(^[X36:$o]:(X36=>~$true)), inference(apply_def,[status(thm)],[def_d_not, def_imp])). 87.95/88.44 thf(c_0_28, axiom, (l_ec)=(^[X38:$o, X39:$o]:(X38=>(X39=>~$true))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_l_ec, def_imp]), c_0_27])). 87.95/88.44 thf(c_0_29, axiom, (all_of)=(^[X3:$i > $o, X2:$i > $o]:![X4:$i]:(X3 @ X4=>X2 @ X4)), inference(apply_def,[status(thm)],[def_all_of, def_is_of])). 87.95/88.44 thf(c_0_30, axiom, (non)=(^[X1:$i, X2:$i > $o, X4:$i]:(X2 @ X4=>~$true)), inference(apply_def,[status(thm)],[def_non, c_0_27])). 87.95/88.44 thf(c_0_31, axiom, (d_and)=(^[X40:$o, X41:$o]:((X40=>(X41=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_d_and, c_0_27]), c_0_28])). 87.95/88.44 thf(c_0_32, axiom, (l_some)=(^[X1:$i, X2:$i > $o]:(![X488:$i]:(in @ X488 @ X1=>(X2 @ X488=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_l_some, c_0_29]), c_0_27]), c_0_30])). 87.95/88.44 thf(c_0_33, axiom, (n_is)=(^[X564:$i, X565:$i]:(X564)=(X565)), inference(apply_def,[status(thm)],[def_n_is, def_e_is])). 87.95/88.44 thf(c_0_34, axiom, (l_or)=(^[X42:$o, X483:$o]:((X42=>~$true)=>X483)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_l_or, def_imp]), c_0_27])). 87.95/88.44 thf(c_0_35, axiom, (and3)=(^[X51:$o, X52:$o, X53:$o]:((X51=>(((X52=>(X53=>~$true))=>~$true)=>~$true))=>~$true)), inference(apply_def,[status(thm)],[def_and3, c_0_31])). 87.95/88.44 thf(c_0_36, axiom, (n_some)=(^[X566:$i > $o]:(![X567:$i]:(in @ X567 @ nat=>(X566 @ X567=>~$true))=>~$true)), inference(apply_def,[status(thm)],[def_n_some, c_0_32])). 87.95/88.44 thf(c_0_37, axiom, (diffprop)=(^[X1:$i, X183:$i, X4:$i]:(X1)=(n_pl @ X183 @ X4)), inference(apply_def,[status(thm)],[def_diffprop, c_0_33])). 87.95/88.44 thf(c_0_38, axiom, (or3)=(^[X48:$o, X49:$o, X50:$o]:((X48=>~$true)=>((X49=>~$true)=>X50))), inference(apply_def,[status(thm)],[def_or3, c_0_34])). 87.95/88.44 thf(c_0_39, axiom, (ec3)=(^[X54:$o, X55:$o, X56:$o]:(((X54=>(X55=>~$true))=>((((X55=>(X56=>~$true))=>((X56=>(X54=>~$true))=>~$true))=>~$true)=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_ec3, c_0_28]), c_0_35])). 87.95/88.44 thf(c_0_40, axiom, (d_29_ii)=(^[X1:$i, X184:$i]:(![X588:$i]:(in @ X588 @ nat=>((X1)=(n_pl @ X184 @ X588)=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_d_29_ii, c_0_36]), c_0_37])). 87.95/88.44 thf(c_0_41, axiom, (orec3)=(^[X57:$o, X58:$o, X59:$o]:((((X57=>~$true)=>((X58=>~$true)=>X59))=>((((X57=>(X58=>~$true))=>((((X58=>(X59=>~$true))=>((X59=>(X57=>~$true))=>~$true))=>~$true)=>~$true))=>~$true)=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_orec3, c_0_31]), c_0_38]), c_0_39])). 87.95/88.44 thf(c_0_42, plain, ![X1392:$i, X1402:$i]:(epred18_2 @ X1402 @ X1392<=>~((((X1392)!=(X1402)=>(![X1403:$i]:(in @ X1403 @ nat=>(X1392)!=(n_pl @ X1402 @ X1403))=>~(![X1404:$i]:(in @ X1404 @ nat=>(X1402)!=(n_pl @ X1392 @ X1404)))))=>(((X1392)=(X1402)=>![X1405:$i]:(in @ X1405 @ nat=>(X1392)!=(n_pl @ X1402 @ X1405)))=>((~(![X1406:$i]:(in @ X1406 @ nat=>(X1392)!=(n_pl @ X1402 @ X1406)))=>![X1407:$i]:(in @ X1407 @ nat=>(X1402)!=(n_pl @ X1392 @ X1407)))=>~((~(![X1408:$i]:(in @ X1408 @ nat=>(X1402)!=(n_pl @ X1392 @ X1408)))=>(X1392)!=(X1402)))))))), introduced(definition)). 87.95/88.44 thf(c_0_43, axiom, (moreis)=(^[X1:$i, X187:$i]:(((![X595:$i]:(in @ X595 @ nat=>((X1)=(n_pl @ X187 @ X595)=>~$true))=>~$true)=>~$true)=>(X1)=(X187))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_moreis, c_0_34]), c_0_33]), c_0_40])). 87.95/88.44 thf(c_0_44, plain, ![X1392:$i]:(in @ X1392 @ nat=>![X1402:$i]:(in @ X1402 @ nat=>epred18_2 @ X1402 @ X1392)), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[satz9, c_0_29]), c_0_41]), c_0_33]), c_0_36])]), c_0_42])). 87.95/88.44 thf(c_0_45, negated_conjecture, ~(![X2116:$i]:(in @ X2116 @ nat=>![X2122:$i]:(in @ X2122 @ nat=>(~(![X2124:$i]:(in @ X2124 @ nat=>(ordsucc @ X2122)!=(n_pl @ X2116 @ X2124)))=>(![X2123:$i]:(in @ X2123 @ nat=>(X2122)!=(n_pl @ X2116 @ X2123))=>(X2122)=(X2116)))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[satz26c]), c_0_29]), c_0_40]), c_0_43])])). 87.95/88.44 thf(c_0_46, axiom, (iii)=(^[X1:$i, X185:$i]:(![X591:$i]:(in @ X591 @ nat=>((X185)=(n_pl @ X1 @ X591)=>~$true))=>~$true)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_iii, c_0_36]), c_0_37])). 87.95/88.44 thf(c_0_47, plain, ![X3157:$i, X3158:$i]:(~in @ X3157 @ nat|(~in @ X3158 @ nat|epred18_2 @ X3158 @ X3157)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])). 87.95/88.44 thf(c_0_48, negated_conjecture, ![X3286:$i]:(in @ esk85_0 @ nat&(in @ esk86_0 @ nat&((in @ esk87_0 @ nat&(ordsucc @ esk86_0)=(n_pl @ esk85_0 @ esk87_0))&((~in @ X3286 @ nat|(esk86_0)!=(n_pl @ esk85_0 @ X3286))&(esk86_0)!=(esk85_0))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])). 87.95/88.44 thf(c_0_49, plain, ![X1418:$i]:(in @ X1418 @ nat=>![X1424:$i]:(in @ X1424 @ nat=>((![X1425:$i]:(in @ X1425 @ nat=>(X1418)!=(n_pl @ X1424 @ X1425))=>(X1418)=(X1424))=>![X1426:$i]:(in @ X1426 @ nat=>(X1424)!=(n_pl @ X1418 @ X1426))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[satz10c, c_0_29]), c_0_27]), c_0_46]), c_0_43])])). 87.95/88.44 thf(c_0_50, axiom, (lessis)=(^[X1:$i, X188:$i]:(((![X596:$i]:(in @ X596 @ nat=>((X188)=(n_pl @ X1 @ X596)=>~$true))=>~$true)=>~$true)=>(X1)=(X188))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_lessis, c_0_34]), c_0_33]), c_0_46])). 87.95/88.44 thf(c_0_51, plain, ![X1392:$i, X1402:$i]:(epred18_2 @ X1402 @ X1392=>~((((X1392)!=(X1402)=>(![X1403:$i]:(in @ X1403 @ nat=>(X1392)!=(n_pl @ X1402 @ X1403))=>~(![X1404:$i]:(in @ X1404 @ nat=>(X1402)!=(n_pl @ X1392 @ X1404)))))=>(((X1392)=(X1402)=>![X1405:$i]:(in @ X1405 @ nat=>(X1392)!=(n_pl @ X1402 @ X1405)))=>((~(![X1406:$i]:(in @ X1406 @ nat=>(X1392)!=(n_pl @ X1402 @ X1406)))=>![X1407:$i]:(in @ X1407 @ nat=>(X1402)!=(n_pl @ X1392 @ X1407)))=>~((~(![X1408:$i]:(in @ X1408 @ nat=>(X1402)!=(n_pl @ X1392 @ X1408)))=>(X1392)!=(X1402)))))))), inference(split_equiv,[status(thm)],[c_0_42])). 87.95/88.44 thf(c_0_52, plain, ![X1:$i, X4:$i]:(epred18_2 @ X4 @ X1|~in @ X1 @ nat|~in @ X4 @ nat), inference(split_conjunct,[status(thm)],[c_0_47])). 87.95/88.44 thf(c_0_53, negated_conjecture, in @ esk85_0 @ nat, inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_54, plain, ![X3159:$i, X3160:$i, X3161:$i, X3162:$i]:((~in @ X3161 @ nat|(X3159)!=(n_pl @ X3160 @ X3161)|(~in @ X3162 @ nat|(X3160)!=(n_pl @ X3159 @ X3162))|~in @ X3160 @ nat|~in @ X3159 @ nat)&((X3159)!=(X3160)|(~in @ X3162 @ nat|(X3160)!=(n_pl @ X3159 @ X3162))|~in @ X3160 @ nat|~in @ X3159 @ nat)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])). 87.95/88.44 thf(c_0_55, plain, ![X2227:$i]:(in @ X2227 @ nat=>![X2233:$i]:(in @ X2233 @ nat=>(~(![X2235:$i]:(in @ X2235 @ nat=>(X2227)!=(n_pl @ X2233 @ X2235)))=>(![X2234:$i]:(in @ X2234 @ nat=>(X2227)!=(n_pl @ (n_pl @ X2233 @ n_1) @ X2234))=>(n_pl @ X2233 @ n_1)=(X2227))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[satz25b, c_0_29]), c_0_46]), c_0_50])])). 87.95/88.44 thf(c_0_56, plain, ![X3517:$i, X3518:$i, X3521:$i, X3522:$i, X3523:$i, X3524:$i]:((((in @ (esk122_2 @ X3517 @ X3518) @ nat|in @ (esk121_2 @ X3517 @ X3518) @ nat|(X3517)=(X3518)|~epred18_2 @ X3518 @ X3517)&((X3518)=(n_pl @ X3517 @ (esk122_2 @ X3517 @ X3518))|in @ (esk121_2 @ X3517 @ X3518) @ nat|(X3517)=(X3518)|~epred18_2 @ X3518 @ X3517))&((in @ (esk122_2 @ X3517 @ X3518) @ nat|(X3517)=(n_pl @ X3518 @ (esk121_2 @ X3517 @ X3518))|(X3517)=(X3518)|~epred18_2 @ X3518 @ X3517)&((X3518)=(n_pl @ X3517 @ (esk122_2 @ X3517 @ X3518))|(X3517)=(n_pl @ X3518 @ (esk121_2 @ X3517 @ X3518))|(X3517)=(X3518)|~epred18_2 @ X3518 @ X3517)))&(((X3517)!=(X3518)|(~in @ X3521 @ nat|(X3517)!=(n_pl @ X3518 @ X3521))|~epred18_2 @ X3518 @ X3517)&((~in @ X3522 @ nat|(X3517)!=(n_pl @ X3518 @ X3522)|(~in @ X3523 @ nat|(X3518)!=(n_pl @ X3517 @ X3523))|~epred18_2 @ X3518 @ X3517)&(~in @ X3524 @ nat|(X3518)!=(n_pl @ X3517 @ X3524)|(X3517)!=(X3518)|~epred18_2 @ X3518 @ X3517)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])])). 87.95/88.44 thf(c_0_57, negated_conjecture, ![X1:$i]:(epred18_2 @ esk85_0 @ X1|~in @ X1 @ nat), inference(spm,[status(thm)],[c_0_52, c_0_53])). 87.95/88.44 thf(c_0_58, negated_conjecture, in @ esk86_0 @ nat, inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_59, plain, ![X2104:$i]:(in @ X2104 @ nat=>(ordsucc @ X2104)=(n_pl @ X2104 @ n_1)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[satz4e, c_0_29]), c_0_33])). 87.95/88.44 thf(c_0_60, plain, ![X5:$i, X4:$i, X1:$i]:((X1)!=(X4)|~in @ X5 @ nat|(X4)!=(n_pl @ X1 @ X5)|~in @ X4 @ nat|~in @ X1 @ nat), inference(split_conjunct,[status(thm)],[c_0_54])). 87.95/88.44 thf(c_0_61, plain, ![X698:$i]:(in @ X698 @ nat=>in @ (ordsucc @ X698) @ nat), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[suc_p, def_is_of]), c_0_29])). 87.95/88.44 thf(c_0_62, plain, ![X1:$i, X6:$i, X5:$i, X4:$i]:(~in @ X1 @ nat|(X4)!=(n_pl @ X5 @ X1)|~in @ X6 @ nat|(X5)!=(n_pl @ X4 @ X6)|~in @ X5 @ nat|~in @ X4 @ nat), inference(split_conjunct,[status(thm)],[c_0_54])). 87.95/88.44 thf(c_0_63, plain, ![X3304:$i, X3305:$i, X3306:$i]:((in @ (esk90_2 @ X3304 @ X3305) @ nat|(n_pl @ X3305 @ n_1)=(X3304)|(~in @ X3306 @ nat|(X3304)!=(n_pl @ X3305 @ X3306))|~in @ X3305 @ nat|~in @ X3304 @ nat)&((X3304)=(n_pl @ (n_pl @ X3305 @ n_1) @ (esk90_2 @ X3304 @ X3305))|(n_pl @ X3305 @ n_1)=(X3304)|(~in @ X3306 @ nat|(X3304)!=(n_pl @ X3305 @ X3306))|~in @ X3305 @ nat|~in @ X3304 @ nat)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])])). 87.95/88.44 thf(c_0_64, plain, ![X1:$i, X4:$i]:((X1)=(n_pl @ X4 @ (esk122_2 @ X4 @ X1))|in @ (esk121_2 @ X4 @ X1) @ nat|(X4)=(X1)|~epred18_2 @ X1 @ X4), inference(split_conjunct,[status(thm)],[c_0_56])). 87.95/88.44 thf(c_0_65, negated_conjecture, epred18_2 @ esk85_0 @ esk86_0, inference(spm,[status(thm)],[c_0_57, c_0_58])). 87.95/88.44 thf(c_0_66, negated_conjecture, (esk86_0)!=(esk85_0), inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_67, plain, ![X1:$i, X4:$i]:((X1)=(n_pl @ X4 @ (esk122_2 @ X4 @ X1))|(X4)=(n_pl @ X1 @ (esk121_2 @ X4 @ X1))|(X4)=(X1)|~epred18_2 @ X1 @ X4), inference(split_conjunct,[status(thm)],[c_0_56])). 87.95/88.44 thf(c_0_68, plain, ![X3282:$i]:(~in @ X3282 @ nat|(ordsucc @ X3282)=(n_pl @ X3282 @ n_1)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])). 87.95/88.44 thf(c_0_69, plain, ![X4:$i, X1:$i]:(in @ (esk122_2 @ X1 @ X4) @ nat|in @ (esk121_2 @ X1 @ X4) @ nat|(X1)=(X4)|~epred18_2 @ X4 @ X1), inference(split_conjunct,[status(thm)],[c_0_56])). 87.95/88.44 thf(c_0_70, plain, ![X4:$i, X1:$i]:(in @ (esk122_2 @ X1 @ X4) @ nat|(X1)=(n_pl @ X4 @ (esk121_2 @ X1 @ X4))|(X1)=(X4)|~epred18_2 @ X4 @ X1), inference(split_conjunct,[status(thm)],[c_0_56])). 87.95/88.44 thf(c_0_71, plain, ![X4:$i, X1:$i]:((n_pl @ X1 @ X4)!=(X1)|~in @ (n_pl @ X1 @ X4) @ nat|~in @ X4 @ nat|~in @ X1 @ nat), inference(er,[status(thm)],[c_0_60])). 87.95/88.44 thf(c_0_72, negated_conjecture, (ordsucc @ esk86_0)=(n_pl @ esk85_0 @ esk87_0), inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_73, negated_conjecture, in @ esk87_0 @ nat, inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_74, plain, ![X2941:$i]:(~in @ X2941 @ nat|in @ (ordsucc @ X2941) @ nat), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])). 87.95/88.44 thf(c_0_75, plain, ![X1:$i, X4:$i, X5:$i]:((n_pl @ (n_pl @ X1 @ X4) @ X5)!=(X1)|~in @ (n_pl @ X1 @ X4) @ nat|~in @ X4 @ nat|~in @ X1 @ nat|~in @ X5 @ nat), inference(er,[status(thm)],[c_0_62])). 87.95/88.44 thf(c_0_76, plain, ![X5:$i, X4:$i, X1:$i]:((X1)=(n_pl @ (n_pl @ X4 @ n_1) @ (esk90_2 @ X1 @ X4))|(n_pl @ X4 @ n_1)=(X1)|~in @ X5 @ nat|(X1)!=(n_pl @ X4 @ X5)|~in @ X4 @ nat|~in @ X1 @ nat), inference(split_conjunct,[status(thm)],[c_0_63])). 87.95/88.44 thf(c_0_77, negated_conjecture, ![X1:$i]:(~in @ X1 @ nat|(esk86_0)!=(n_pl @ esk85_0 @ X1)), inference(split_conjunct,[status(thm)],[c_0_48])). 87.95/88.44 thf(c_0_78, negated_conjecture, ((n_pl @ esk86_0 @ (esk122_2 @ esk86_0 @ esk85_0))=(esk85_0)|in @ (esk121_2 @ esk86_0 @ esk85_0) @ nat), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66])). 87.95/88.44 thf(c_0_79, negated_conjecture, ((n_pl @ esk86_0 @ (esk122_2 @ esk86_0 @ esk85_0))=(esk85_0)|(n_pl @ esk85_0 @ (esk121_2 @ esk86_0 @ esk85_0))=(esk86_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_65]), c_0_66])). 87.95/88.44 thf(c_0_80, plain, ![X1:$i]:((ordsucc @ X1)=(n_pl @ X1 @ n_1)|~in @ X1 @ nat), inference(split_conjunct,[status(thm)],[c_0_68])). 87.95/88.44 thf(c_0_81, negated_conjecture, (in @ (esk122_2 @ esk86_0 @ esk85_0) @ nat|in @ (esk121_2 @ esk86_0 @ esk85_0) @ nat), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_65]), c_0_66])). 87.95/88.44 thf(c_0_82, negated_conjecture, ((n_pl @ esk85_0 @ (esk121_2 @ esk86_0 @ esk85_0))=(esk86_0)|in @ (esk122_2 @ esk86_0 @ esk85_0) @ nat), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_65]), c_0_66])). 87.95/88.44 thf(c_0_83, negated_conjecture, ((ordsucc @ esk86_0)!=(esk85_0)|~in @ (ordsucc @ esk86_0) @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_73]), c_0_53])])). 87.95/88.44 thf(c_0_84, plain, ![X1:$i]:(in @ (ordsucc @ X1) @ nat|~in @ X1 @ nat), inference(split_conjunct,[status(thm)],[c_0_74])). 87.95/88.44 thf(c_0_85, plain, ![X5:$i, X4:$i, X1:$i]:(in @ (esk90_2 @ X1 @ X4) @ nat|(n_pl @ X4 @ n_1)=(X1)|~in @ X5 @ nat|(X1)!=(n_pl @ X4 @ X5)|~in @ X4 @ nat|~in @ X1 @ nat), inference(split_conjunct,[status(thm)],[c_0_63])). 87.95/88.44 thf(c_0_86, negated_conjecture, ![X1:$i]:((n_pl @ (ordsucc @ esk86_0) @ X1)!=(esk85_0)|~in @ (ordsucc @ esk86_0) @ nat|~in @ X1 @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_72]), c_0_73]), c_0_53])])). 87.95/88.44 thf(c_0_87, plain, ![X4:$i, X1:$i]:((n_pl @ (n_pl @ X1 @ n_1) @ (esk90_2 @ (n_pl @ X1 @ X4) @ X1))=(n_pl @ X1 @ X4)|(n_pl @ X1 @ n_1)=(n_pl @ X1 @ X4)|~in @ (n_pl @ X1 @ X4) @ nat|~in @ X4 @ nat|~in @ X1 @ nat), inference(er,[status(thm)],[c_0_76])). 87.95/88.44 thf(c_0_88, negated_conjecture, (n_pl @ esk86_0 @ (esk122_2 @ esk86_0 @ esk85_0))=(esk85_0), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79])). 87.95/88.44 thf(c_0_89, negated_conjecture, (n_pl @ esk86_0 @ n_1)=(ordsucc @ esk86_0), inference(spm,[status(thm)],[c_0_80, c_0_58])). 87.95/88.44 thf(c_0_90, negated_conjecture, in @ (esk122_2 @ esk86_0 @ esk85_0) @ nat, inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_81]), c_0_82])). 87.95/88.44 thf(c_0_91, negated_conjecture, (ordsucc @ esk86_0)!=(esk85_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_58])])). 87.95/88.44 thf(c_0_92, plain, ![X4:$i, X1:$i]:((n_pl @ X1 @ n_1)=(n_pl @ X1 @ X4)|in @ (esk90_2 @ (n_pl @ X1 @ X4) @ X1) @ nat|~in @ (n_pl @ X1 @ X4) @ nat|~in @ X4 @ nat|~in @ X1 @ nat), inference(er,[status(thm)],[c_0_85])). 87.95/88.44 thf(c_0_93, negated_conjecture, ![X1:$i]:((n_pl @ (ordsucc @ esk86_0) @ X1)!=(esk85_0)|~in @ X1 @ nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_84]), c_0_58])])). 87.95/88.44 thf(c_0_94, negated_conjecture, (n_pl @ (ordsucc @ esk86_0) @ (esk90_2 @ esk85_0 @ esk86_0))=(esk85_0), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89]), c_0_89]), c_0_53]), c_0_90]), c_0_58])]), c_0_91])). 87.95/88.44 thf(c_0_95, negated_conjecture, in @ (esk90_2 @ esk85_0 @ esk86_0) @ nat, inference(sr,[status(thm)],[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_92, c_0_88]), c_0_89]), c_0_53]), c_0_90]), c_0_58])]), c_0_91])). 87.95/88.44 thf(c_0_96, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94]), c_0_95])]), ['proof']). 87.95/88.44 # SZS output end CNFRefutation 87.95/88.44 # Proof object total steps : 97 87.95/88.44 # Proof object clause steps : 37 87.95/88.44 # Proof object formula steps : 60 87.95/88.44 # Proof object conjectures : 25 87.95/88.44 # Proof object clause conjectures : 22 87.95/88.44 # Proof object formula conjectures : 3 87.95/88.44 # Proof object initial clauses used : 17 87.95/88.44 # Proof object initial formulas used : 27 87.95/88.44 # Proof object generating inferences : 16 87.95/88.44 # Proof object simplifying inferences : 35 87.95/88.44 # Training examples: 0 positive, 0 negative 87.95/88.44 # Parsed axioms : 408 87.95/88.44 # Removed by relevancy pruning/SinE : 0 87.95/88.44 # Initial clauses : 647 87.95/88.44 # Removed in clause preprocessing : 169 87.95/88.44 # Initial clauses in saturation : 478 87.95/88.44 # Processed clauses : 7003 87.95/88.44 # ...of these trivial : 163 87.95/88.44 # ...subsumed : 2228 87.95/88.44 # ...remaining for further processing : 4612 87.95/88.44 # Other redundant clauses eliminated : 5399 87.95/88.44 # Clauses deleted for lack of memory : 0 87.95/88.44 # Backward-subsumed : 294 87.95/88.44 # Backward-rewritten : 200 87.95/88.44 # Generated clauses : 94849 87.95/88.44 # ...of the previous two non-trivial : 88534 87.95/88.44 # Contextual simplify-reflections : 120 87.95/88.44 # Paramodulations : 76707 87.95/88.44 # Factorizations : 0 87.95/88.44 # NegExts : 251 87.95/88.44 # Equation resolutions : 5406 87.95/88.44 # Propositional unsat checks : 0 87.95/88.44 # Propositional check models : 0 87.95/88.44 # Propositional check unsatisfiable : 0 87.95/88.44 # Propositional clauses : 0 87.95/88.44 # Propositional clauses after purity: 0 87.95/88.44 # Propositional unsat core size : 0 87.95/88.44 # Propositional preprocessing time : 0.000 87.95/88.44 # Propositional encoding time : 0.000 87.95/88.44 # Propositional solver time : 0.000 87.95/88.44 # Success case prop preproc time : 0.000 87.95/88.44 # Success case prop encoding time : 0.000 87.95/88.44 # Success case prop solver time : 0.000 87.95/88.44 # Current number of processed clauses : 3529 87.95/88.44 # Positive orientable unit clauses : 471 87.95/88.44 # Positive unorientable unit clauses: 21 87.95/88.44 # Negative unit clauses : 154 87.95/88.44 # Non-unit-clauses : 2883 87.95/88.44 # Current number of unprocessed clauses: 82193 87.95/88.44 # ...number of literals in the above : 399075 87.95/88.44 # Current number of archived formulas : 0 87.95/88.44 # Current number of archived clauses : 949 87.95/88.44 # Clause-clause subsumption calls (NU) : 1151921 87.95/88.44 # Rec. Clause-clause subsumption calls : 521230 87.95/88.44 # Non-unit clause-clause subsumptions : 1828 87.95/88.44 # Unit Clause-clause subsumption calls : 116984 87.95/88.44 # Rewrite failures with RHS unbound : 146 87.95/88.44 # BW rewrite match attempts : 298 87.95/88.44 # BW rewrite match successes : 141 87.95/88.44 # Condensation attempts : 0 87.95/88.44 # Condensation successes : 0 87.95/88.44 # Termbank termtop insertions : 1991156 87.95/88.45 87.95/88.45 # ------------------------------------------------- 87.95/88.45 # User time : 85.423 s 87.95/88.45 # System time : 2.413 s 87.95/88.45 # Total time : 87.836 s 87.95/88.45 # Maximum resident set size: 2344 pages 87.95/88.45 EOF