0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.33 Computer : n015.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 : 1440 0.12/0.33 % DateTime : Mon Jul 3 06:22:39 EDT 2023 0.12/0.33 % CPUTime : 2.96/3.23 % SZS status Theorem 2.96/3.23 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 2.96/3.23 % Inferences: 1 2.96/3.23 % SZS output start Proof 2.96/3.23 thf(conj_0,conjecture,((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d))))))). 2.96/3.23 thf(h0,negated_conjecture,(~(((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d)))))))),inference(assume_negation,[status(cth)],[conj_0])). 2.96/3.23 tff(pax136, axiom, (p136=>(fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))), file('', pax136)). 2.96/3.23 tff(pax127, axiom, (p127=>(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), file('', pax127)). 2.96/3.23 tff(pax93, axiom, (p93=>![X36:real, X37:int]:(ford_less_eq_real @ X36 @ (fring_1_of_int_real @ X37)=>ford_less_eq_int @ (farchim1371465213g_real @ X36) @ X37)), file('', pax93)). 2.96/3.23 tff(pax99, axiom, (p99=>ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), file('', pax99)). 2.96/3.23 fof(ax40, axiom, p136, file('', ax40)). 2.96/3.23 fof(ax49, axiom, p127, file('', ax49)). 2.96/3.23 tff(pax46, axiom, (p46=>![X54:int]:(farchim1371465213g_real @ (fring_1_of_int_real @ X54))=(X54)), file('', pax46)). 2.96/3.23 tff(nax166, axiom, (p166<=ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), file('', nax166)). 2.96/3.23 fof(ax10, axiom, ~(p166), file('', ax10)). 2.96/3.23 fof(ax83, axiom, p93, file('', ax83)). 2.96/3.23 fof(ax77, axiom, p99, file('', ax77)). 2.96/3.23 fof(ax130, axiom, p46, file('', ax130)). 2.96/3.23 tff(c_0_12, plain, (~p136|(fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))), inference(fof_nnf,[status(thm)],[pax136])). 2.96/3.23 tff(c_0_13, plain, (~p127|(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), inference(fof_nnf,[status(thm)],[pax127])). 2.96/3.23 tff(c_0_14, plain, ![X155:real, X156:int]:(~p93|(~ford_less_eq_real @ X155 @ (fring_1_of_int_real @ X156)|ford_less_eq_int @ (farchim1371465213g_real @ X155) @ X156)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax93])])])). 2.96/3.23 tff(c_0_15, plain, (~p99|ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), inference(fof_nnf,[status(thm)],[pax99])). 2.96/3.23 thf(c_0_16, plain, ((fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))|~p136), inference(split_conjunct,[status(thm)],[c_0_12])). 2.96/3.23 thf(c_0_17, plain, (p136), inference(split_conjunct,[status(thm)],[ax40])). 2.96/3.23 thf(c_0_18, plain, ((fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))|~p127), inference(split_conjunct,[status(thm)],[c_0_13])). 2.96/3.23 thf(c_0_19, plain, (p127), inference(split_conjunct,[status(thm)],[ax49])). 2.96/3.23 tff(c_0_20, plain, ![X199:int]:(~p46|(farchim1371465213g_real @ (fring_1_of_int_real @ X199))=(X199)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax46])])])). 2.96/3.23 tff(c_0_21, plain, (~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))|p166), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax166])])). 2.96/3.23 fof(c_0_22, plain, ~p166, inference(fof_simplification,[status(thm)],[ax10])). 2.96/3.23 thf(c_0_23, plain, ![X3:int, X1:real]:(ford_less_eq_int @ (farchim1371465213g_real @ X1) @ X3|~p93|~ford_less_eq_real @ X1 @ (fring_1_of_int_real @ X3)), inference(split_conjunct,[status(thm)],[c_0_14])). 2.96/3.23 thf(c_0_24, plain, (p93), inference(split_conjunct,[status(thm)],[ax83])). 2.96/3.23 thf(c_0_25, plain, (ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))|~p99), inference(split_conjunct,[status(thm)],[c_0_15])). 2.96/3.23 thf(c_0_26, plain, (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))=(fring_1_of_int_real @ fd), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])). 2.96/3.23 thf(c_0_27, plain, (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])). 2.96/3.23 thf(c_0_28, plain, (p99), inference(split_conjunct,[status(thm)],[ax77])). 2.96/3.23 thf(c_0_29, plain, ![X3:int]:((farchim1371465213g_real @ (fring_1_of_int_real @ X3))=(X3)|~p46), inference(split_conjunct,[status(thm)],[c_0_20])). 2.96/3.23 thf(c_0_30, plain, (p46), inference(split_conjunct,[status(thm)],[ax130])). 2.96/3.23 thf(c_0_31, plain, (p166|~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(split_conjunct,[status(thm)],[c_0_21])). 2.96/3.23 thf(c_0_32, plain, (~p166), inference(split_conjunct,[status(thm)],[c_0_22])). 2.96/3.23 thf(c_0_33, plain, ![X3:int, X1:real]:(ford_less_eq_int @ (farchim1371465213g_real @ X1) @ X3|~ford_less_eq_real @ X1 @ (fring_1_of_int_real @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])). 2.96/3.23 thf(c_0_34, plain, ford_less_eq_real @ (fring_1_of_int_real @ fd) @ (fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27]), c_0_28])])). 2.96/3.23 thf(c_0_35, plain, ![X3:int]:(farchim1371465213g_real @ (fring_1_of_int_real @ X3))=(X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])). 2.96/3.23 thf(c_0_36, plain, ~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))), inference(sr,[status(thm)],[c_0_31, c_0_32])). 2.96/3.23 thf(c_0_37, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), ['proof']). 2.96/3.23 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])). 2.96/3.23 thf(0,theorem,((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d)))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])). 2.96/3.23 % SZS output end Proof 2.96/3.23 EOF