0.07/0.12 % Problem : SLH0230^1 : TPTP v8.2.0. Released v8.2.0. 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.13/0.34 Computer : n023.cluster.edu 0.13/0.34 Model : x86_64 x86_64 0.13/0.34 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 RAMPerCPU : 8042.1875MB 0.13/0.34 OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 30 0.13/0.34 % DateTime : Mon Jul 3 04:14:51 EDT 2023 0.13/0.34 % CPUTime : 2.82/3.06 % SZS status Theorem 2.82/3.06 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 2.82/3.06 % Inferences: 2 2.82/3.06 % SZS output start Proof 2.82/3.06 thf(ty_set_complex, type, set_complex : $tType). 2.82/3.06 thf(ty_complex, type, complex : $tType). 2.82/3.06 thf(ty_real, type, real : $tType). 2.82/3.06 thf(ty_zero_zero_real, type, zero_zero_real : real). 2.82/3.06 thf(ty_real_V1022390504157884413omplex, type, real_V1022390504157884413omplex : (complex>real)). 2.82/3.06 thf(ty_zero_zero_complex, type, zero_zero_complex : complex). 2.82/3.06 thf(ty_eigen__0, type, eigen__0 : (complex>real)). 2.82/3.06 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)). 2.82/3.06 thf(ty_comple7700996537433184370hic_on, type, comple7700996537433184370hic_on : ((complex>complex)>set_complex>$o)). 2.82/3.06 thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)). 2.82/3.06 thf(ty_one_one_complex, type, one_one_complex : complex). 2.82/3.06 thf(ty_one_one_real, type, one_one_real : real). 2.82/3.06 thf(ty_deriv_complex, type, deriv_complex : ((complex>complex)>complex>complex)). 2.82/3.06 thf(ty_elemen7827680097914048924omplex, type, elemen7827680097914048924omplex : (complex>real>set_complex)). 2.82/3.06 thf(conj_0,conjecture,((comple7700996537433184370hic_on @ cotang8298477626502807258omplex) @ a)). 2.82/3.06 thf(h0,negated_conjecture,(~(((comple7700996537433184370hic_on @ cotang8298477626502807258omplex) @ a))),inference(assume_negation,[status(cth)],[conj_0])). 2.82/3.06 thf(h1,assumption,(~(((![X1:complex]:((ord_less_real @ zero_zero_real) @ (eigen__0 @ X1))) => (~((![X1:complex>complex]:(((comple7700996537433184370hic_on @ X1) @ ((elemen7827680097914048924omplex @ zero_zero_complex) @ (eigen__0 @ (X1 @ zero_zero_complex)))) => ((![X2:complex]:(((ord_less_eq_real @ (real_V1022390504157884413omplex @ X2)) @ (eigen__0 @ (X1 @ zero_zero_complex))) => (~(((~(((X1 @ X2) = zero_zero_complex))) => ((X1 @ X2) = one_one_complex)))))) => ((ord_less_real @ (real_V1022390504157884413omplex @ ((deriv_complex @ X1) @ zero_zero_complex))) @ one_one_real))))))))),introduced(assumption,[])). 2.82/3.06 thf(h2,assumption,(![X1:complex]:((ord_less_real @ zero_zero_real) @ (eigen__0 @ X1))),introduced(assumption,[])). 2.82/3.06 thf(h3,assumption,(![X1:complex>complex]:(((comple7700996537433184370hic_on @ X1) @ ((elemen7827680097914048924omplex @ zero_zero_complex) @ (eigen__0 @ (X1 @ zero_zero_complex)))) => ((![X2:complex]:(((ord_less_eq_real @ (real_V1022390504157884413omplex @ X2)) @ (eigen__0 @ (X1 @ zero_zero_complex))) => (~(((~(((X1 @ X2) = zero_zero_complex))) => ((X1 @ X2) = one_one_complex)))))) => ((ord_less_real @ (real_V1022390504157884413omplex @ ((deriv_complex @ X1) @ zero_zero_complex))) @ one_one_real)))),introduced(assumption,[])). 2.82/3.06 tff(pax7, axiom, (p7=>![X101:complex > complex, X114:set_complex, X133:set_complex]:(fcomple7700996537433184370hic_on @ X101 @ X114=>(ford_le211207098394363844omplex @ X133 @ X114=>fcomple7700996537433184370hic_on @ X101 @ X133))), file('', pax7)). 2.82/3.06 tff(pax2, axiom, (p2=>ford_le211207098394363844omplex @ fa @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))), file('', pax2)). 2.82/3.06 fof(ax48, axiom, p7, file('', ax48)). 2.82/3.06 fof(ax53, axiom, p2, file('', ax53)). 2.82/3.06 tff(pax1, axiom, (p1=>fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))), file('', pax1)). 2.82/3.06 tff(nax55, axiom, (p55<=fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ fa), file('', nax55)). 2.82/3.06 fof(ax0, axiom, ~(p55), file('', ax0)). 2.82/3.06 fof(ax54, axiom, p1, file('', ax54)). 2.82/3.06 tff(c_0_8, plain, ![X574:complex > complex, X575:set_complex, X576:set_complex]:(~p7|(~fcomple7700996537433184370hic_on @ X574 @ X575|(~ford_le211207098394363844omplex @ X576 @ X575|fcomple7700996537433184370hic_on @ X574 @ X576))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])])). 2.82/3.06 tff(c_0_9, plain, (~p2|ford_le211207098394363844omplex @ fa @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))), inference(fof_nnf,[status(thm)],[pax2])). 2.82/3.06 thf(c_0_10, plain, ![X2:complex > complex, X13:set_complex, X17:set_complex]:(fcomple7700996537433184370hic_on @ X2 @ X17|~p7|~fcomple7700996537433184370hic_on @ X2 @ X13|~ford_le211207098394363844omplex @ X17 @ X13), inference(split_conjunct,[status(thm)],[c_0_8])). 2.82/3.06 thf(c_0_11, plain, (p7), inference(split_conjunct,[status(thm)],[ax48])). 2.82/3.06 thf(c_0_12, plain, (ford_le211207098394363844omplex @ fa @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))|~p2), inference(split_conjunct,[status(thm)],[c_0_9])). 2.82/3.06 thf(c_0_13, plain, (p2), inference(split_conjunct,[status(thm)],[ax53])). 2.82/3.06 tff(c_0_14, plain, (~p1|fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))), inference(fof_nnf,[status(thm)],[pax1])). 2.82/3.06 tff(c_0_15, plain, (~fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ fa|p55), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax55])])). 2.82/3.06 fof(c_0_16, plain, ~p55, inference(fof_simplification,[status(thm)],[ax0])). 2.82/3.06 thf(c_0_17, plain, ![X17:set_complex, X13:set_complex, X2:complex > complex]:(fcomple7700996537433184370hic_on @ X2 @ X13|~ford_le211207098394363844omplex @ X13 @ X17|~fcomple7700996537433184370hic_on @ X2 @ X17), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])). 2.82/3.06 thf(c_0_18, plain, ford_le211207098394363844omplex @ fa @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])). 2.82/3.06 thf(c_0_19, plain, (fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))|~p1), inference(split_conjunct,[status(thm)],[c_0_14])). 2.82/3.06 thf(c_0_20, plain, (p1), inference(split_conjunct,[status(thm)],[ax54])). 2.82/3.06 thf(c_0_21, plain, (p55|~fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ fa), inference(split_conjunct,[status(thm)],[c_0_15])). 2.82/3.06 thf(c_0_22, plain, (~p55), inference(split_conjunct,[status(thm)],[c_0_16])). 2.82/3.06 thf(c_0_23, plain, ![X2:complex > complex]:(fcomple7700996537433184370hic_on @ X2 @ fa|~fcomple7700996537433184370hic_on @ X2 @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex)))), inference(spm,[status(thm)],[c_0_17, c_0_18])). 2.82/3.06 thf(c_0_24, plain, fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ (fuminus8566677241136511917omplex @ (fminus_811609699411566653omplex @ fring_1_Ints_complex @ (finsert_complex @ fzero_zero_complex @ fbot_bot_set_complex))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])). 2.82/3.06 thf(c_0_25, plain, ~fcomple7700996537433184370hic_on @ fcotang8298477626502807258omplex @ fa, inference(sr,[status(thm)],[c_0_21, c_0_22])). 2.82/3.06 thf(c_0_26, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25]), ['proof']). 2.82/3.06 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h2,h3,h1,h0])],[])). 2.82/3.06 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,1,h2,h3])). 2.82/3.06 thf(fact_1273_Landau__Picard,axiom,(~((![X1:complex>real]:((![X2:complex]:((ord_less_real @ zero_zero_real) @ (X1 @ X2))) => (~((![X2:complex>complex]:(((comple7700996537433184370hic_on @ X2) @ ((elemen7827680097914048924omplex @ zero_zero_complex) @ (X1 @ (X2 @ zero_zero_complex)))) => ((![X3:complex]:(((ord_less_eq_real @ (real_V1022390504157884413omplex @ X3)) @ (X1 @ (X2 @ zero_zero_complex))) => (~(((~(((X2 @ X3) = zero_zero_complex))) => ((X2 @ X3) = one_one_complex)))))) => ((ord_less_real @ (real_V1022390504157884413omplex @ ((deriv_complex @ X2) @ zero_zero_complex))) @ one_one_real))))))))))). 2.82/3.06 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_1273_Landau__Picard,2,h1])). 2.82/3.06 thf(0,theorem,((comple7700996537433184370hic_on @ cotang8298477626502807258omplex) @ a),inference(contra,[status(thm),contra(discharge,[h0])],[3,h0])). 2.82/3.06 % SZS output end Proof 2.82/3.06 EOF