0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.32 Computer : n005.cluster.edu 0.12/0.32 Model : x86_64 x86_64 0.12/0.32 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 RAMPerCPU : 8042.1875MB 0.12/0.32 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % DateTime : Tue Aug 9 07:01:04 EDT 2022 0.12/0.32 % CPUTime : 119.74/119.29 % SZS status Theorem 119.74/119.29 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 119.74/119.29 % Inferences: 1 119.74/119.29 % SZS output start Proof 119.74/119.29 thf(ty_num, type, num : $tType). 119.74/119.29 thf(ty_real, type, real : $tType). 119.74/119.29 thf(ty_zero_zero_real, type, zero_zero_real : real). 119.74/119.29 thf(ty_eigen__0, type, eigen__0 : real). 119.74/119.29 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)). 119.74/119.29 thf(ty_bit0, type, bit0 : (num>num)). 119.74/119.29 thf(ty_cos_real, type, cos_real : (real>real)). 119.74/119.29 thf(ty_one, type, one : num). 119.74/119.29 thf(ty_numeral_numeral_real, type, numeral_numeral_real : (num>real)). 119.74/119.29 thf(conj_0,conjecture,((ord_less_eq_real @ (semiri5074537144036343181t_real @ (vEBT_V8646137997579335489_i_l_d @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ ((times_times_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_VEBT_cnt @ (vEBT_vebt_buildup @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one)))))))))). 119.74/119.29 thf(h0,negated_conjecture,(~(((ord_less_eq_real @ (semiri5074537144036343181t_real @ (vEBT_V8646137997579335489_i_l_d @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ ((times_times_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_VEBT_cnt @ (vEBT_vebt_buildup @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(assume_negation,[status(cth)],[conj_0])). 119.74/119.29 thf(h1,assumption,(~(((~(((~(((![X1:real]:((~(((~((((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X1)))))) => (X1 = eigen__0))) => (~(((cos_real @ eigen__0) = zero_zero_real)))))) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (~(((ord_less_eq_real @ zero_zero_real) @ eigen__0)))))),introduced(assumption,[])). 119.74/119.29 thf(h2,assumption,(~(((~(((![X1:real]:((~(((~((((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X1)))))) => (X1 = eigen__0))) => (~(((cos_real @ eigen__0) = zero_zero_real)))))) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))),introduced(assumption,[])). 119.74/119.29 thf(h3,assumption,((ord_less_eq_real @ zero_zero_real) @ eigen__0),introduced(assumption,[])). 119.74/119.29 thf(h4,assumption,(~(((![X1:real]:((~(((~((((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X1)))))) => (X1 = eigen__0))) => (~(((cos_real @ eigen__0) = zero_zero_real)))))),introduced(assumption,[])). 119.74/119.29 thf(h5,assumption,((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one))),introduced(assumption,[])). 119.74/119.29 thf(h6,assumption,(![X1:real]:((~(((~((((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X1)))))) => (X1 = eigen__0))),introduced(assumption,[])). 119.74/119.29 thf(h7,assumption,((cos_real @ eigen__0) = zero_zero_real),introduced(assumption,[])). 119.74/119.29 tff(pax1421, axiom, (p1421=>(fsuc @ fone_one_nat)=(fnumeral_numeral_nat @ (fbit0 @ fone))), file('', pax1421)). 119.74/119.29 tff(pax1027, axiom, (p1027=>![X328:nat]:(fdivide_divide_nat @ (fsuc @ (fsuc @ X328)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(fsuc @ (fdivide_divide_nat @ X328 @ (fnumeral_numeral_nat @ (fbit0 @ fone))))), file('', pax1027)). 119.74/119.29 fof(ax47, axiom, p1421, file('', ax47)). 119.74/119.29 tff(nax1260, axiom, (p1260<=fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva))), file('', nax1260)). 119.74/119.29 fof(ax208, axiom, ~(p1260), file('', ax208)). 119.74/119.29 tff(pax71, axiom, (p71=>![X1095:real, X1098:real, X1093:real]:(ftimes_times_real @ X1095 @ (ftimes_times_real @ X1098 @ X1093))=(ftimes_times_real @ X1098 @ (ftimes_times_real @ X1095 @ X1093))), file('', pax71)). 119.74/119.29 tff(pax929, axiom, (p929=>![X400:real]:(ftimes_times_real @ X400 @ fone_one_real)=(X400)), file('', pax929)). 119.74/119.29 tff(pax96, axiom, (p96=>![X1086:nat]:(~(fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva)))=>((X1086)=(fdivide_divide_nat @ (fsuc @ (fsuc @ fva)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=>ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ X1086))) @ (ftimes_times_real @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ X1086))) @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))))))), file('', pax96)). 119.74/119.29 fof(ax441, axiom, p1027, file('', ax441)). 119.74/119.29 fof(ax1397, axiom, p71, file('', ax1397)). 119.74/119.29 fof(ax539, axiom, p929, file('', ax539)). 119.74/119.29 fof(ax1372, axiom, p96, file('', ax1372)). 119.74/119.29 tff(nax967, axiom, (p967<=ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (ftimes_times_real @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))) @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))))), file('', nax967)). 119.74/119.29 fof(ax501, axiom, ~(p967), file('', ax501)). 119.74/119.29 tff(c_0_14, plain, (~p1421|(fsuc @ fone_one_nat)=(fnumeral_numeral_nat @ (fbit0 @ fone))), inference(fof_nnf,[status(thm)],[pax1421])). 119.74/119.29 tff(c_0_15, plain, ![X2313:nat]:(~p1027|(fdivide_divide_nat @ (fsuc @ (fsuc @ X2313)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(fsuc @ (fdivide_divide_nat @ X2313 @ (fnumeral_numeral_nat @ (fbit0 @ fone))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1027])])])). 119.74/119.29 thf(c_0_16, plain, ((fsuc @ fone_one_nat)=(fnumeral_numeral_nat @ (fbit0 @ fone))|~p1421), inference(split_conjunct,[status(thm)],[c_0_14])). 119.74/119.29 thf(c_0_17, plain, (p1421), inference(split_conjunct,[status(thm)],[ax47])). 119.74/119.29 tff(c_0_18, plain, (~fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva))|p1260), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1260])])). 119.74/119.29 fof(c_0_19, plain, ~p1260, inference(fof_simplification,[status(thm)],[ax208])). 119.74/119.29 tff(c_0_20, plain, ![X4931:real, X4932:real, X4933:real]:(~p71|(ftimes_times_real @ X4931 @ (ftimes_times_real @ X4932 @ X4933))=(ftimes_times_real @ X4932 @ (ftimes_times_real @ X4931 @ X4933))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax71])])])). 119.74/119.29 tff(c_0_21, plain, ![X2551:real]:(~p929|(ftimes_times_real @ X2551 @ fone_one_real)=(X2551)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax929])])])). 119.74/119.29 tff(c_0_22, plain, ![X4881:nat]:(~p96|(fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva))|((X4881)!=(fdivide_divide_nat @ (fsuc @ (fsuc @ fva)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))|ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ X4881))) @ (ftimes_times_real @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ X4881))) @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax96])])])])). 119.74/119.29 thf(c_0_23, plain, ![X2:nat]:((fdivide_divide_nat @ (fsuc @ (fsuc @ X2)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(fsuc @ (fdivide_divide_nat @ X2 @ (fnumeral_numeral_nat @ (fbit0 @ fone))))|~p1027), inference(split_conjunct,[status(thm)],[c_0_15])). 119.74/119.29 thf(c_0_24, plain, (fnumeral_numeral_nat @ (fbit0 @ fone))=(fsuc @ fone_one_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])). 119.74/119.29 thf(c_0_25, plain, (p1027), inference(split_conjunct,[status(thm)],[ax441])). 119.74/119.29 thf(c_0_26, plain, (p1260|~fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva))), inference(split_conjunct,[status(thm)],[c_0_18])). 119.74/119.29 thf(c_0_27, plain, (~p1260), inference(split_conjunct,[status(thm)],[c_0_19])). 119.74/119.29 thf(c_0_28, plain, ![X5:real, X4:real, X1:real]:((ftimes_times_real @ X1 @ (ftimes_times_real @ X4 @ X5))=(ftimes_times_real @ X4 @ (ftimes_times_real @ X1 @ X5))|~p71), inference(split_conjunct,[status(thm)],[c_0_20])). 119.74/119.29 thf(c_0_29, plain, (p71), inference(split_conjunct,[status(thm)],[ax1397])). 119.74/119.29 thf(c_0_30, plain, ![X1:real]:((ftimes_times_real @ X1 @ fone_one_real)=(X1)|~p929), inference(split_conjunct,[status(thm)],[c_0_21])). 119.74/119.29 thf(c_0_31, plain, (p929), inference(split_conjunct,[status(thm)],[ax539])). 119.74/119.29 thf(c_0_32, plain, ![X2:nat]:(fdvd_dvd_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fsuc @ (fsuc @ fva))|ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ X2))) @ (ftimes_times_real @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ X2))) @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))))|~p96|(X2)!=(fdivide_divide_nat @ (fsuc @ (fsuc @ fva)) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))), inference(split_conjunct,[status(thm)],[c_0_22])). 119.74/119.29 thf(c_0_33, plain, ![X2:nat]:(fdivide_divide_nat @ (fsuc @ (fsuc @ X2)) @ (fsuc @ fone_one_nat))=(fsuc @ (fdivide_divide_nat @ X2 @ (fsuc @ fone_one_nat))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24]), c_0_24]), c_0_25])])). 119.74/119.29 thf(c_0_34, plain, (p96), inference(split_conjunct,[status(thm)],[ax1372])). 119.74/119.29 thf(c_0_35, plain, ~fdvd_dvd_nat @ (fsuc @ fone_one_nat) @ (fsuc @ (fsuc @ fva)), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_24]), c_0_27])). 119.74/119.29 thf(c_0_36, plain, ![X5:real, X4:real, X1:real]:(ftimes_times_real @ X1 @ (ftimes_times_real @ X4 @ X5))=(ftimes_times_real @ X4 @ (ftimes_times_real @ X1 @ X5)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])). 119.74/119.29 thf(c_0_37, plain, ![X1:real]:(ftimes_times_real @ X1 @ fone_one_real)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])). 119.74/119.29 tff(c_0_38, plain, (~ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (ftimes_times_real @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))) @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))))|p967), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax967])])). 119.74/119.29 fof(c_0_39, plain, ~p967, inference(fof_simplification,[status(thm)],[ax501])). 119.74/119.29 thf(c_0_40, plain, ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat)))))) @ (ftimes_times_real @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat)))))) @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone))))), inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_24]), c_0_24]), c_0_33]), c_0_34])]), c_0_35])])). 119.74/119.29 thf(c_0_41, plain, ![X4:real, X1:real]:(ftimes_times_real @ X1 @ X4)=(ftimes_times_real @ X4 @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_37])). 119.74/119.29 thf(c_0_42, plain, (p967|~ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (ftimes_times_real @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))) @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))))), inference(split_conjunct,[status(thm)],[c_0_38])). 119.74/119.29 thf(c_0_43, plain, (~p967), inference(split_conjunct,[status(thm)],[c_0_39])). 119.74/119.29 thf(c_0_44, plain, ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat)))))) @ (ftimes_times_real @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))) @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat))))))), inference(rw,[status(thm)],[c_0_40, c_0_41])). 119.74/119.29 thf(c_0_45, plain, ~ford_less_eq_real @ (fsemiri5074537144036343181t_real @ (fvEBT_V8646137997579335489_i_l_d @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat)))))) @ (ftimes_times_real @ (fnumeral_numeral_real @ (fbit1 @ (fbit0 @ (fbit1 @ fone)))) @ (fvEBT_VEBT_cnt @ (fvEBT_vebt_buildup @ (fsuc @ (fsuc @ (fdivide_divide_nat @ fva @ (fsuc @ fone_one_nat))))))), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_24]), c_0_24]), c_0_43])). 119.74/119.29 thf(c_0_46, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_44, c_0_45]), ['proof']). 119.74/119.29 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0])],[])). 119.74/119.29 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,1,h6,h7])). 119.74/119.29 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,2,h4,h5])). 119.74/119.29 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,3,h2,h3])). 119.74/119.29 thf(fact_7034_cos__is__zero,axiom,(~((![X1:real]:((~(((~(((![X2:real]:((~(((~((((ord_less_eq_real @ X2) @ (numeral_numeral_real @ (bit0 @ one))) => (~(((cos_real @ X2) = zero_zero_real)))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X2)))))) => (X2 = X1))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (~(((ord_less_eq_real @ zero_zero_real) @ X1)))))))). 119.74/119.29 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_7034_cos__is__zero,4,h1])). 119.74/119.29 thf(0,theorem,((ord_less_eq_real @ (semiri5074537144036343181t_real @ (vEBT_V8646137997579335489_i_l_d @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ ((times_times_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_VEBT_cnt @ (vEBT_vebt_buildup @ (suc @ (suc @ ((divide_divide_nat @ va) @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])). 119.74/119.29 % SZS output end Proof 119.74/119.29 EOF