0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.33 Computer : n007.cluster.edu 0.12/0.33 Model : x86_64 x86_64 0.12/0.33 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 RAMPerCPU : 8042.1875MB 0.12/0.33 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % DateTime : Tue Aug 9 04:05:57 EDT 2022 0.12/0.33 % CPUTime : 154.16/118.84 % SZS status Theorem 154.16/118.84 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 154.16/118.84 % Inferences: 169 154.16/118.84 % SZS output start Proof 154.16/118.84 thf(conj_2,conjecture,((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs))). 154.16/118.84 thf(h0,negated_conjecture,(~(((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs)))),inference(assume_negation,[status(cth)],[conj_2])). 154.16/118.84 fof(ax1258, axiom, (~(p404)|p405), file('', ax1258)). 154.16/118.84 fof(ax359, axiom, (~(p106)|~(p1286)), file('', ax359)). 154.16/118.84 fof(ax1257, axiom, (~(p405)|p406), file('', ax1257)). 154.16/118.84 fof(ax1259, axiom, p404, file('', ax1259)). 154.16/118.84 tff(nax1286, axiom, (p1286<=![X2:list_a]:~((fsize_size_list_a @ X2)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk))), file('', nax1286)). 154.16/118.84 fof(ax1558, axiom, p106, file('', ax1558)). 154.16/118.84 fof(ax1256, axiom, (~(p406)|~(p25)|p403), file('', ax1256)). 154.16/118.84 fof(ax655, axiom, (~(p76)|p1000), file('', ax655)). 154.16/118.84 tff(nax37, axiom, (p37<=(fk)=(fzero_zero_nat)), file('', nax37)). 154.16/118.84 fof(ax1627, axiom, ~(p37), file('', ax1627)). 154.16/118.84 fof(ax1522, axiom, (~(p4)|p142), file('', ax1522)). 154.16/118.84 fof(ax1532, axiom, (~(p3)|p132), file('', ax1532)). 154.16/118.84 tff(pax403, axiom, (p403=>(fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)), file('', pax403)). 154.16/118.84 fof(ax1639, axiom, p25, file('', ax1639)). 154.16/118.84 tff(pax1000, axiom, (p1000=>![X3:nat]:(~((fk)=(fzero_zero_nat))=>(fdivide_divide_nat @ (ftimes_times_nat @ X3 @ fk) @ fk)=(X3))), file('', pax1000)). 154.16/118.84 fof(ax1588, axiom, p76, file('', ax1588)). 154.16/118.84 tff(pax9, axiom, (p9=>![X80:nat]:(ftimes_times_nat @ fzero_zero_nat @ X80)=(fzero_zero_nat)), file('', pax9)). 154.16/118.84 fof(ax10, axiom, (~(p142)|p1640), file('', ax10)). 154.16/118.84 fof(ax1660, axiom, p4, file('', ax1660)). 154.16/118.84 fof(ax1175, axiom, (~(p35)|p486), file('', ax1175)). 154.16/118.84 fof(ax109, axiom, (~(p132)|p1539), file('', ax109)). 154.16/118.84 fof(ax1661, axiom, p3, file('', ax1661)). 154.16/118.84 tff(pax1537, axiom, (p1537=>(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)=(fzero_zero_nat)), file('', pax1537)). 154.16/118.84 tff(nax1537, axiom, (p1537<=(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)=(fzero_zero_nat)), file('', nax1537)). 154.16/118.84 tff(pax1536, axiom, (p1536=>(fsize_size_list_a @ fxs)=(fzero_zero_nat)), file('', pax1536)). 154.16/118.84 fof(ax1655, axiom, p9, file('', ax1655)). 154.16/118.84 tff(pax1640, axiom, (p1640=>(ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)=>~((fzero_zero_nat)=(fsuc @ fn)))), file('', pax1640)). 154.16/118.84 tff(pax486, axiom, (p486=>ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)), file('', pax486)). 154.16/118.84 fof(ax1629, axiom, p35, file('', ax1629)). 154.16/118.84 fof(ax1525, axiom, (~(p4)|p139), file('', ax1525)). 154.16/118.84 tff(pax1539, axiom, (p1539=>(~((fsize_size_list_a @ fxs)=(fzero_zero_nat))=>(~((fk)=(fzero_zero_nat))=>~((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)=(fzero_zero_nat))))), file('', pax1539)). 154.16/118.84 fof(ax588, axiom, (~(p83)|p1066), file('', ax588)). 154.16/118.84 fof(ax37, axiom, (~(p139)|p1613), file('', ax37)). 154.16/118.84 fof(ax1003, axiom, (~(p54)|p652), file('', ax1003)). 154.16/118.84 fof(ax1039, axiom, (~(p50)|p616), file('', ax1039)). 154.16/118.84 fof(ax389, axiom, (~(p1066)|p1256), file('', ax389)). 154.16/118.84 fof(ax1581, axiom, p83, file('', ax1581)). 154.16/118.84 tff(nax103, axiom, (p103<=ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)), file('', nax103)). 154.16/118.84 fof(ax1561, axiom, ~(p103), file('', ax1561)). 154.16/118.84 tff(pax1613, axiom, (p1613=>(ford_less_nat @ fn @ (fsuc @ fn)=>~((fn)=(fsuc @ fn)))), file('', pax1613)). 154.16/118.84 tff(pax23, axiom, (p23=>![X76:nat]:ford_less_nat @ X76 @ (fsuc @ X76)), file('', pax23)). 154.16/118.84 tff(pax652, axiom, (p652=>(ford_less_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)=>~(![X43:nat]:~((fsize_size_list_a @ fxs)=(fsuc @ X43))))), file('', pax652)). 154.16/118.84 fof(ax1610, axiom, p54, file('', ax1610)). 154.16/118.84 tff(pax43, axiom, (p43=>![X72:nat]:(~((X72)=(fzero_zero_nat))=>ford_less_nat @ fzero_zero_nat @ X72)), file('', pax43)). 154.16/118.84 tff(pax616, axiom, (p616=>![X43:nat]:(~((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ X43)=(fzero_zero_nat))=>~((~((X43)=(fzero_zero_nat))=>(fsize_size_list_a @ fxs)=(fzero_zero_nat))))), file('', pax616)). 154.16/118.84 fof(ax1614, axiom, p50, file('', ax1614)). 154.16/118.84 tff(nax1536, axiom, (p1536<=(fsize_size_list_a @ fxs)=(fzero_zero_nat)), file('', nax1536)). 154.16/118.84 tff(pax1256, axiom, (p1256=>(~((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk))=>(~(ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk))=>ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)))), file('', pax1256)). 154.16/118.84 tff(pax1245, axiom, (p1245=>(~(ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs))=>(ftimes_times_nat @ fn @ fk)=(fsize_size_list_a @ fxs))), file('', pax1245)). 154.16/118.84 fof(ax1641, axiom, p23, file('', ax1641)). 154.16/118.84 fof(ax1621, axiom, p43, file('', ax1621)). 154.16/118.84 tff(nax1255, axiom, (p1255<=(~(ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk))=>ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs))), file('', nax1255)). 154.16/118.84 tff(pax1255, axiom, (p1255=>(~(ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk))=>ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs))), file('', pax1255)). 154.16/118.84 tff(nax1245, axiom, (p1245<=(~(ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs))=>(ftimes_times_nat @ fn @ fk)=(fsize_size_list_a @ fxs))), file('', nax1245)). 154.16/118.84 tff(pax8, axiom, (p8=>![X80:nat, X81:nat, X63:nat]:(ford_less_nat @ X80 @ (ftimes_times_nat @ X81 @ X63)=>ford_less_nat @ (fdivide_divide_nat @ X80 @ X63) @ X81)), file('', pax8)). 154.16/118.84 tff(pax101, axiom, (p101=>![X59:nat]:~(ford_less_nat @ X59 @ X59)), file('', pax101)). 154.16/118.84 tff(pax61, axiom, (p61=>![X69:nat, X67:nat]:(ford_less_nat @ X69 @ X67=>ford_less_nat @ X69 @ (fsuc @ X67))), file('', pax61)). 154.16/118.84 fof(ax1656, axiom, p8, file('', ax1656)). 154.16/118.84 fof(ax1563, axiom, p101, file('', ax1563)). 154.16/118.84 fof(ax1603, axiom, p61, file('', ax1603)). 154.16/118.84 fof(c_0_60, plain, (~p404|p405), inference(fof_simplification,[status(thm)],[ax1258])). 154.16/118.84 fof(c_0_61, plain, (~p106|~p1286), inference(fof_simplification,[status(thm)],[ax359])). 154.16/118.84 fof(c_0_62, plain, (~p405|p406), inference(fof_simplification,[status(thm)],[ax1257])). 154.16/118.84 thf(c_0_63, plain, (p405|~p404), inference(split_conjunct,[status(thm)],[c_0_60])). 154.16/118.84 thf(c_0_64, plain, (p404), inference(split_conjunct,[status(thm)],[ax1259])). 154.16/118.84 tff(c_0_65, plain, ((fsize_size_list_a @ esk83_0)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|p1286), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1286])])])])). 154.16/118.84 thf(c_0_66, plain, (~p106|~p1286), inference(split_conjunct,[status(thm)],[c_0_61])). 154.16/118.84 thf(c_0_67, plain, (p106), inference(split_conjunct,[status(thm)],[ax1558])). 154.16/118.84 fof(c_0_68, plain, (~p406|~p25|p403), inference(fof_simplification,[status(thm)],[ax1256])). 154.16/118.84 thf(c_0_69, plain, (p406|~p405), inference(split_conjunct,[status(thm)],[c_0_62])). 154.16/118.84 thf(c_0_70, plain, (p405), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])). 154.16/118.84 fof(c_0_71, plain, (~p76|p1000), inference(fof_simplification,[status(thm)],[ax655])). 154.16/118.84 tff(c_0_72, plain, ((fk)!=(fzero_zero_nat)|p37), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax37])])). 154.16/118.84 fof(c_0_73, plain, ~p37, inference(fof_simplification,[status(thm)],[ax1627])). 154.16/118.84 fof(c_0_74, plain, (~p4|p142), inference(fof_simplification,[status(thm)],[ax1522])). 154.16/118.84 fof(c_0_75, plain, (~p3|p132), inference(fof_simplification,[status(thm)],[ax1532])). 154.16/118.84 tff(c_0_76, plain, (~p403|(fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)), inference(fof_nnf,[status(thm)],[pax403])). 154.16/118.84 thf(c_0_77, plain, ((fsize_size_list_a @ esk83_0)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|p1286), inference(split_conjunct,[status(thm)],[c_0_65])). 154.16/118.84 thf(c_0_78, plain, (~p1286), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67])])). 154.16/118.84 thf(c_0_79, plain, (p403|~p406|~p25), inference(split_conjunct,[status(thm)],[c_0_68])). 154.16/118.84 thf(c_0_80, plain, (p25), inference(split_conjunct,[status(thm)],[ax1639])). 154.16/118.84 thf(c_0_81, plain, (p406), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])). 154.16/118.84 tff(c_0_82, plain, ![X560:nat]:(~p1000|((fk)=(fzero_zero_nat)|(fdivide_divide_nat @ (ftimes_times_nat @ X560 @ fk) @ fk)=(X560))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1000])])])])). 154.16/118.84 thf(c_0_83, plain, (p1000|~p76), inference(split_conjunct,[status(thm)],[c_0_71])). 154.16/118.84 thf(c_0_84, plain, (p76), inference(split_conjunct,[status(thm)],[ax1588])). 154.16/118.84 thf(c_0_85, plain, (p37|(fk)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_72])). 154.16/118.84 thf(c_0_86, plain, (~p37), inference(split_conjunct,[status(thm)],[c_0_73])). 154.16/118.84 tff(c_0_87, plain, ![X3813:nat]:(~p9|(ftimes_times_nat @ fzero_zero_nat @ X3813)=(fzero_zero_nat)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])])). 154.16/118.84 fof(c_0_88, plain, (~p142|p1640), inference(fof_simplification,[status(thm)],[ax10])). 154.16/118.84 thf(c_0_89, plain, (p142|~p4), inference(split_conjunct,[status(thm)],[c_0_74])). 154.16/118.84 thf(c_0_90, plain, (p4), inference(split_conjunct,[status(thm)],[ax1660])). 154.16/118.84 fof(c_0_91, plain, (~p35|p486), inference(fof_simplification,[status(thm)],[ax1175])). 154.16/118.84 fof(c_0_92, plain, (~p132|p1539), inference(fof_simplification,[status(thm)],[ax109])). 154.16/118.84 thf(c_0_93, plain, (p132|~p3), inference(split_conjunct,[status(thm)],[c_0_75])). 154.16/118.84 thf(c_0_94, plain, (p3), inference(split_conjunct,[status(thm)],[ax1661])). 154.16/118.84 thf(c_0_95, plain, ((fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|~p403), inference(split_conjunct,[status(thm)],[c_0_76])). 154.16/118.84 thf(c_0_96, plain, (fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)=(fsize_size_list_a @ esk83_0), inference(sr,[status(thm)],[c_0_77, c_0_78])). 154.16/118.84 thf(c_0_97, plain, (p403), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80]), c_0_81])])). 154.16/118.84 thf(c_0_98, plain, ![X1:nat]:((fk)=(fzero_zero_nat)|(fdivide_divide_nat @ (ftimes_times_nat @ X1 @ fk) @ fk)=(X1)|~p1000), inference(split_conjunct,[status(thm)],[c_0_82])). 154.16/118.84 thf(c_0_99, plain, (p1000), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])). 154.16/118.84 thf(c_0_100, plain, (fk)!=(fzero_zero_nat), inference(sr,[status(thm)],[c_0_85, c_0_86])). 154.16/118.84 tff(c_0_101, plain, (~p1537|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)=(fzero_zero_nat)), inference(fof_nnf,[status(thm)],[pax1537])). 154.16/118.84 tff(c_0_102, plain, ((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)!=(fzero_zero_nat)|p1537), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1537])])). 154.16/118.84 tff(c_0_103, plain, (~p1536|(fsize_size_list_a @ fxs)=(fzero_zero_nat)), inference(fof_nnf,[status(thm)],[pax1536])). 154.16/118.84 thf(c_0_104, plain, ![X1:nat]:((ftimes_times_nat @ fzero_zero_nat @ X1)=(fzero_zero_nat)|~p9), inference(split_conjunct,[status(thm)],[c_0_87])). 154.16/118.84 thf(c_0_105, plain, (p9), inference(split_conjunct,[status(thm)],[ax1655])). 154.16/118.84 tff(c_0_106, plain, (~p1640|(~ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)|(fzero_zero_nat)!=(fsuc @ fn))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1640])])). 154.16/118.84 thf(c_0_107, plain, (p1640|~p142), inference(split_conjunct,[status(thm)],[c_0_88])). 154.16/118.84 thf(c_0_108, plain, (p142), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])). 154.16/118.84 tff(c_0_109, plain, (~p486|ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)), inference(fof_nnf,[status(thm)],[pax486])). 154.16/118.84 thf(c_0_110, plain, (p486|~p35), inference(split_conjunct,[status(thm)],[c_0_91])). 154.16/118.84 thf(c_0_111, plain, (p35), inference(split_conjunct,[status(thm)],[ax1629])). 154.16/118.84 fof(c_0_112, plain, (~p4|p139), inference(fof_simplification,[status(thm)],[ax1525])). 154.16/118.84 tff(c_0_113, plain, (~p1539|((fsize_size_list_a @ fxs)=(fzero_zero_nat)|((fk)=(fzero_zero_nat)|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)!=(fzero_zero_nat)))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1539])])). 154.16/118.84 thf(c_0_114, plain, (p1539|~p132), inference(split_conjunct,[status(thm)],[c_0_92])). 154.16/118.84 thf(c_0_115, plain, (p132), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93, c_0_94])])). 154.16/118.84 thf(c_0_116, plain, (fsize_size_list_a @ esk83_0)=(fsuc @ fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95, c_0_96]), c_0_97])])). 154.16/118.84 thf(c_0_117, plain, ![X1:nat]:(fdivide_divide_nat @ (ftimes_times_nat @ X1 @ fk) @ fk)=(X1), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98, c_0_99])]), c_0_100])). 154.16/118.84 thf(c_0_118, plain, ((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)=(fzero_zero_nat)|~p1537), inference(split_conjunct,[status(thm)],[c_0_101])). 154.16/118.84 thf(c_0_119, plain, (p1537|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_102])). 154.16/118.84 thf(c_0_120, plain, ((fsize_size_list_a @ fxs)=(fzero_zero_nat)|~p1536), inference(split_conjunct,[status(thm)],[c_0_103])). 154.16/118.84 thf(c_0_121, plain, ![X1:nat]:(ftimes_times_nat @ fzero_zero_nat @ X1)=(fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105])])). 154.16/118.84 thf(c_0_122, plain, (~p1640|~ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)|(fzero_zero_nat)!=(fsuc @ fn)), inference(split_conjunct,[status(thm)],[c_0_106])). 154.16/118.84 thf(c_0_123, plain, (p1640), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_108])])). 154.16/118.84 thf(c_0_124, plain, (ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)|~p486), inference(split_conjunct,[status(thm)],[c_0_109])). 154.16/118.84 thf(c_0_125, plain, (p486), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110, c_0_111])])). 154.16/118.84 fof(c_0_126, plain, (~p83|p1066), inference(fof_simplification,[status(thm)],[ax588])). 154.16/118.84 fof(c_0_127, plain, (~p139|p1613), inference(fof_simplification,[status(thm)],[ax37])). 154.16/118.84 thf(c_0_128, plain, (p139|~p4), inference(split_conjunct,[status(thm)],[c_0_112])). 154.16/118.84 fof(c_0_129, plain, (~p54|p652), inference(fof_simplification,[status(thm)],[ax1003])). 154.16/118.84 fof(c_0_130, plain, (~p50|p616), inference(fof_simplification,[status(thm)],[ax1039])). 154.16/118.84 thf(c_0_131, plain, ((fsize_size_list_a @ fxs)=(fzero_zero_nat)|(fk)=(fzero_zero_nat)|~p1539|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_113])). 154.16/118.84 thf(c_0_132, plain, (p1539), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_115])])). 154.16/118.84 thf(c_0_133, plain, (fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)=(fsuc @ fn), inference(rw,[status(thm)],[c_0_96, c_0_116])). 154.16/118.84 thf(c_0_134, plain, ((fsize_size_list_a @ fxs)=(fdivide_divide_nat @ fzero_zero_nat @ fk)|~p1537), inference(spm,[status(thm)],[c_0_117, c_0_118])). 154.16/118.84 thf(c_0_135, plain, (p1537|~p1536), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120]), c_0_121])])). 154.16/118.84 thf(c_0_136, plain, ((fsuc @ fn)!=(fzero_zero_nat)|~ford_less_nat @ fzero_zero_nat @ (fsuc @ fn)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122, c_0_123])])). 154.16/118.84 thf(c_0_137, plain, ford_less_nat @ fzero_zero_nat @ (fsuc @ fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124, c_0_125])])). 154.16/118.84 fof(c_0_138, plain, (~p1066|p1256), inference(fof_simplification,[status(thm)],[ax389])). 154.16/118.84 thf(c_0_139, plain, (p1066|~p83), inference(split_conjunct,[status(thm)],[c_0_126])). 154.16/118.84 thf(c_0_140, plain, (p83), inference(split_conjunct,[status(thm)],[ax1581])). 154.16/118.84 tff(c_0_141, plain, (~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|p103), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax103])])). 154.16/118.84 fof(c_0_142, plain, ~p103, inference(fof_simplification,[status(thm)],[ax1561])). 154.16/118.84 tff(c_0_143, plain, (~p1613|(~ford_less_nat @ fn @ (fsuc @ fn)|(fn)!=(fsuc @ fn))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1613])])). 154.16/118.84 thf(c_0_144, plain, (p1613|~p139), inference(split_conjunct,[status(thm)],[c_0_127])). 154.16/118.84 thf(c_0_145, plain, (p139), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128, c_0_90])])). 154.16/118.84 tff(c_0_146, plain, ![X3777:nat]:(~p23|ford_less_nat @ X3777 @ (fsuc @ X3777)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax23])])])). 154.16/118.84 tff(c_0_147, plain, (~p652|(~ford_less_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)|(fsize_size_list_a @ fxs)=(fsuc @ esk1084_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax652])])])])). 154.16/118.84 thf(c_0_148, plain, (p652|~p54), inference(split_conjunct,[status(thm)],[c_0_129])). 154.16/118.84 thf(c_0_149, plain, (p54), inference(split_conjunct,[status(thm)],[ax1610])). 154.16/118.84 tff(c_0_150, plain, ![X3719:nat]:(~p43|((X3719)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X3719)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax43])])])])). 154.16/118.84 tff(c_0_151, plain, ![X2324:nat]:(((X2324)!=(fzero_zero_nat)|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ X2324)=(fzero_zero_nat)|~p616)&((fsize_size_list_a @ fxs)!=(fzero_zero_nat)|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ X2324)=(fzero_zero_nat)|~p616)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax616])])])])])). 154.16/118.84 thf(c_0_152, plain, (p616|~p50), inference(split_conjunct,[status(thm)],[c_0_130])). 154.16/118.84 thf(c_0_153, plain, (p50), inference(split_conjunct,[status(thm)],[ax1614])). 154.16/118.84 tff(c_0_154, plain, ((fsize_size_list_a @ fxs)!=(fzero_zero_nat)|p1536), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1536])])). 154.16/118.84 thf(c_0_155, plain, ((fsize_size_list_a @ fxs)=(fzero_zero_nat)|(ftimes_times_nat @ (fsize_size_list_a @ fxs) @ fk)!=(fzero_zero_nat)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131, c_0_132])]), c_0_100])). 154.16/118.84 thf(c_0_156, plain, ((fdivide_divide_nat @ fzero_zero_nat @ fk)=(fsuc @ fn)|~p1536), inference(spm,[status(thm)],[c_0_133, c_0_120])). 154.16/118.84 thf(c_0_157, plain, ((fdivide_divide_nat @ fzero_zero_nat @ fk)=(fzero_zero_nat)|~p1536), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_134]), c_0_135])). 154.16/118.84 thf(c_0_158, plain, (fsuc @ fn)!=(fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136, c_0_137])])). 154.16/118.84 tff(c_0_159, plain, (~p1256|((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk)|(ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1256])])). 154.16/118.84 thf(c_0_160, plain, (p1256|~p1066), inference(split_conjunct,[status(thm)],[c_0_138])). 154.16/118.84 thf(c_0_161, plain, (p1066), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_140])])). 154.16/118.84 thf(c_0_162, plain, (p103|~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)), inference(split_conjunct,[status(thm)],[c_0_141])). 154.16/118.84 thf(c_0_163, plain, (~p103), inference(split_conjunct,[status(thm)],[c_0_142])). 154.16/118.84 tff(c_0_164, plain, (~p1245|(ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|(ftimes_times_nat @ fn @ fk)=(fsize_size_list_a @ fxs))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1245])])). 154.16/118.84 thf(c_0_165, plain, (~p1613|~ford_less_nat @ fn @ (fsuc @ fn)|(fn)!=(fsuc @ fn)), inference(split_conjunct,[status(thm)],[c_0_143])). 154.16/118.84 thf(c_0_166, plain, (p1613), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144, c_0_145])])). 154.16/118.84 thf(c_0_167, plain, ![X1:nat]:(ford_less_nat @ X1 @ (fsuc @ X1)|~p23), inference(split_conjunct,[status(thm)],[c_0_146])). 154.16/118.84 thf(c_0_168, plain, (p23), inference(split_conjunct,[status(thm)],[ax1641])). 154.16/118.84 thf(c_0_169, plain, ((fsize_size_list_a @ fxs)=(fsuc @ esk1084_0)|~p652|~ford_less_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)), inference(split_conjunct,[status(thm)],[c_0_147])). 154.16/118.84 thf(c_0_170, plain, (p652), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148, c_0_149])])). 154.16/118.84 thf(c_0_171, plain, ![X1:nat]:((X1)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X1|~p43), inference(split_conjunct,[status(thm)],[c_0_150])). 154.16/118.84 thf(c_0_172, plain, (p43), inference(split_conjunct,[status(thm)],[ax1621])). 154.16/118.84 thf(c_0_173, plain, ![X1:nat]:((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ X1)=(fzero_zero_nat)|(fsize_size_list_a @ fxs)!=(fzero_zero_nat)|~p616), inference(split_conjunct,[status(thm)],[c_0_151])). 154.16/118.84 thf(c_0_174, plain, (p616), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152, c_0_153])])). 154.16/118.84 thf(c_0_175, plain, (p1536|(fsize_size_list_a @ fxs)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_154])). 154.16/118.84 thf(c_0_176, plain, ((fsize_size_list_a @ fxs)=(fzero_zero_nat)|~p1537), inference(spm,[status(thm)],[c_0_155, c_0_118])). 154.16/118.84 thf(c_0_177, plain, (~p1536), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_157]), c_0_158])). 154.16/118.84 tff(c_0_178, plain, ((~ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|p1255)&(~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|p1255)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1255])])])). 154.16/118.84 thf(c_0_179, plain, ((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk)|ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|~p1256), inference(split_conjunct,[status(thm)],[c_0_159])). 154.16/118.84 thf(c_0_180, plain, (p1256), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160, c_0_161])])). 154.16/118.84 thf(c_0_181, plain, ~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs), inference(sr,[status(thm)],[c_0_162, c_0_163])). 154.16/118.84 thf(c_0_182, plain, (ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|(ftimes_times_nat @ fn @ fk)=(fsize_size_list_a @ fxs)|~p1245), inference(split_conjunct,[status(thm)],[c_0_164])). 154.16/118.84 thf(c_0_183, plain, ((fsuc @ fn)!=(fn)|~ford_less_nat @ fn @ (fsuc @ fn)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165, c_0_166])])). 154.16/118.84 thf(c_0_184, plain, ![X1:nat]:ford_less_nat @ X1 @ (fsuc @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167, c_0_168])])). 154.16/118.84 thf(c_0_185, plain, ((fsize_size_list_a @ fxs)=(fsuc @ esk1084_0)|~ford_less_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169, c_0_170])])). 154.16/118.84 thf(c_0_186, plain, ![X1:nat]:((X1)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171, c_0_172])])). 154.16/118.84 thf(c_0_187, plain, ![X1:nat]:((ftimes_times_nat @ (fsize_size_list_a @ fxs) @ X1)=(fzero_zero_nat)|(fsize_size_list_a @ fxs)!=(fzero_zero_nat)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173, c_0_174])])). 154.16/118.84 thf(c_0_188, plain, (~p1537), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_177])). 154.16/118.84 tff(c_0_189, plain, (~p1255|(ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1255])])). 154.16/118.84 tff(c_0_190, plain, ((~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|p1245)&((ftimes_times_nat @ fn @ fk)!=(fsize_size_list_a @ fxs)|p1245)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1245])])])). 154.16/118.84 thf(c_0_191, plain, (p1255|~ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)), inference(split_conjunct,[status(thm)],[c_0_178])). 154.16/118.84 thf(c_0_192, plain, ((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk)|ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179, c_0_180])]), c_0_181])). 154.16/118.84 thf(c_0_193, plain, ((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk)|~p1245), inference(sr,[status(thm)],[c_0_182, c_0_181])). 154.16/118.84 thf(c_0_194, plain, (fsuc @ fn)!=(fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183, c_0_184])])). 154.16/118.84 tff(c_0_195, plain, ![X3815:nat, X3816:nat, X3817:nat]:(~p8|(~ford_less_nat @ X3815 @ (ftimes_times_nat @ X3816 @ X3817)|ford_less_nat @ (fdivide_divide_nat @ X3815 @ X3817) @ X3816)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])). 154.16/118.84 thf(c_0_196, plain, ((fsize_size_list_a @ fxs)=(fsuc @ esk1084_0)|(fsize_size_list_a @ fxs)=(fzero_zero_nat)), inference(spm,[status(thm)],[c_0_185, c_0_186])). 154.16/118.84 thf(c_0_197, plain, (fsize_size_list_a @ fxs)!=(fzero_zero_nat), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_187]), c_0_188])). 154.16/118.84 tff(c_0_198, plain, ![X3605:nat]:(~p101|~ford_less_nat @ X3605 @ X3605), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax101])])])])). 154.16/118.84 tff(c_0_199, plain, ![X3681:nat, X3682:nat]:(~p61|(~ford_less_nat @ X3681 @ X3682|ford_less_nat @ X3681 @ (fsuc @ X3682))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax61])])])). 154.16/118.84 thf(c_0_200, plain, (ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|~p1255), inference(split_conjunct,[status(thm)],[c_0_189])). 154.16/118.84 thf(c_0_201, plain, (p1245|(ftimes_times_nat @ fn @ fk)!=(fsize_size_list_a @ fxs)), inference(split_conjunct,[status(thm)],[c_0_190])). 154.16/118.84 thf(c_0_202, plain, ((fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk)|p1255), inference(spm,[status(thm)],[c_0_191, c_0_192])). 154.16/118.84 thf(c_0_203, plain, (~p1245), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_193]), c_0_117]), c_0_194])). 154.16/118.84 thf(c_0_204, plain, ![X4:nat, X3:nat, X1:nat]:(ford_less_nat @ (fdivide_divide_nat @ X1 @ X4) @ X3|~p8|~ford_less_nat @ X1 @ (ftimes_times_nat @ X3 @ X4)), inference(split_conjunct,[status(thm)],[c_0_195])). 154.16/118.84 thf(c_0_205, plain, (p8), inference(split_conjunct,[status(thm)],[ax1656])). 154.16/118.84 thf(c_0_206, plain, (fsize_size_list_a @ fxs)=(fsuc @ esk1084_0), inference(sr,[status(thm)],[c_0_196, c_0_197])). 154.16/118.84 thf(c_0_207, plain, ![X1:nat]:(~p101|~ford_less_nat @ X1 @ X1), inference(split_conjunct,[status(thm)],[c_0_198])). 154.16/118.84 thf(c_0_208, plain, (p101), inference(split_conjunct,[status(thm)],[ax1563])). 154.16/118.84 thf(c_0_209, plain, ![X3:nat, X1:nat]:(ford_less_nat @ X1 @ (fsuc @ X3)|~p61|~ford_less_nat @ X1 @ X3), inference(split_conjunct,[status(thm)],[c_0_199])). 154.16/118.84 thf(c_0_210, plain, (p61), inference(split_conjunct,[status(thm)],[ax1603])). 154.16/118.84 thf(c_0_211, plain, (ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk)|~p1255), inference(sr,[status(thm)],[c_0_200, c_0_181])). 154.16/118.84 thf(c_0_212, plain, (p1255), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_202]), c_0_203])). 154.16/118.84 thf(c_0_213, plain, ![X4:nat, X3:nat, X1:nat]:(ford_less_nat @ (fdivide_divide_nat @ X1 @ X3) @ X4|~ford_less_nat @ X1 @ (ftimes_times_nat @ X4 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_204, c_0_205])])). 154.16/118.84 thf(c_0_214, plain, (fdivide_divide_nat @ (fsuc @ esk1084_0) @ fk)=(fsuc @ fn), inference(rw,[status(thm)],[c_0_133, c_0_206])). 154.16/118.84 thf(c_0_215, plain, ![X1:nat]:~ford_less_nat @ X1 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207, c_0_208])])). 154.16/118.84 thf(c_0_216, plain, ![X3:nat, X1:nat]:(ford_less_nat @ X1 @ (fsuc @ X3)|~ford_less_nat @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209, c_0_210])])). 154.16/118.84 thf(c_0_217, plain, ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211, c_0_212])])). 154.16/118.84 thf(c_0_218, plain, ![X1:nat]:(ford_less_nat @ (fsuc @ fn) @ X1|~ford_less_nat @ (fsuc @ esk1084_0) @ (ftimes_times_nat @ X1 @ fk)), inference(spm,[status(thm)],[c_0_213, c_0_214])). 154.16/118.84 thf(c_0_219, plain, ![X1:nat]:~ford_less_nat @ (fsuc @ X1) @ X1, inference(spm,[status(thm)],[c_0_215, c_0_216])). 154.16/118.84 thf(c_0_220, plain, ford_less_nat @ (fsuc @ esk1084_0) @ (ftimes_times_nat @ fn @ fk), inference(rw,[status(thm)],[c_0_217, c_0_206])). 154.16/118.84 thf(c_0_221, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_218, c_0_219, c_0_220]), ['proof']). 154.16/118.84 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])). 154.16/118.84 thf(0,theorem,((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])). 154.16/118.84 % SZS output end Proof 154.16/118.84 EOF