0.07/0.12	% Problem  : SLH0178^1 : TPTP v8.2.0. Released v8.2.0.
0.07/0.13	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.34	% Computer : n012.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 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	% WCLimit  : 30
0.13/0.34	% DateTime : Mon Jul  3 03:40:52 EDT 2023
0.13/0.34	% CPUTime  : 
18.85/19.06	% SZS status Theorem
18.85/19.06	% Mode: cade22sinegrackle2xfaf3
18.85/19.06	% Steps: 24661
18.85/19.06	% SZS output start Proof
18.85/19.06	thf(ty_int, type, int : $tType).
18.85/19.06	thf(ty_real, type, real : $tType).
18.85/19.06	thf(ty_numeral_numeral_real, type, numeral_numeral_real : (num>real)).
18.85/19.06	thf(ty_zero_zero_int, type, zero_zero_int : int).
18.85/19.06	thf(ty_bit0, type, bit0 : (num>num)).
18.85/19.06	thf(ty_divide_divide_real, type, divide_divide_real : (real>real>real)).
18.85/19.06	thf(ty_log, type, log : (real>real>real)).
18.85/19.06	thf(ty_ord_less_eq_int, type, ord_less_eq_int : (int>int>$o)).
18.85/19.06	thf(ty_delta, type, delta : rat).
18.85/19.06	thf(ty_field_7254667332652039916t_real, type, field_7254667332652039916t_real : (rat>real)).
18.85/19.06	thf(ty_zero_zero_real, type, zero_zero_real : real).
18.85/19.06	thf(ty_archim7802044766580827645g_real, type, archim7802044766580827645g_real : (real>int)).
18.85/19.06	thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)).
18.85/19.06	thf(ty_one, type, one : num).
18.85/19.06	thf(ty_one_one_real, type, one_one_real : real).
18.85/19.06	thf(sP1,plain,sP1 <=> (![X1:int]:((ord_less_eq_int @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
18.85/19.06	thf(sP2,plain,sP2 <=> ((~(((archim7802044766580827645g_real @ zero_zero_real) = (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))))) => (~(((ord_less_eq_int @ (archim7802044766580827645g_real @ zero_zero_real)) @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
18.85/19.06	thf(sP3,plain,sP3 <=> ((ord_less_eq_int @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))) @ (archim7802044766580827645g_real @ zero_zero_real)),introduced(definition,[new_symbols(definition,[sP3])])).
18.85/19.06	thf(sP4,plain,sP4 <=> ((ord_less_eq_int @ zero_zero_int) @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))),introduced(definition,[new_symbols(definition,[sP4])])).
18.85/19.06	thf(sP5,plain,sP5 <=> ((ord_less_eq_int @ (archim7802044766580827645g_real @ zero_zero_real)) @ (archim7802044766580827645g_real @ zero_zero_real)),introduced(definition,[new_symbols(definition,[sP5])])).
18.85/19.06	thf(sP6,plain,sP6 <=> ((ord_less_eq_int @ (archim7802044766580827645g_real @ zero_zero_real)) @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))),introduced(definition,[new_symbols(definition,[sP6])])).
18.85/19.06	thf(sP7,plain,sP7 <=> (![X1:int]:((~(((~(((archim7802044766580827645g_real @ zero_zero_real) = X1))) => (~(((ord_less_eq_int @ (archim7802044766580827645g_real @ zero_zero_real)) @ X1)))))) => (~(((ord_less_eq_int @ X1) @ (archim7802044766580827645g_real @ zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP7])])).
18.85/19.06	thf(sP8,plain,sP8 <=> (![X1:int]:((~(((ord_less_eq_int @ zero_zero_int) @ X1))) => ((ord_less_eq_int @ X1) @ zero_zero_int))),introduced(definition,[new_symbols(definition,[sP8])])).
18.85/19.06	thf(sP9,plain,sP9 <=> (![X1:real]:(((ord_less_eq_real @ zero_zero_real) @ X1) => ((ord_less_eq_int @ (archim7802044766580827645g_real @ zero_zero_real)) @ (archim7802044766580827645g_real @ X1)))),introduced(definition,[new_symbols(definition,[sP9])])).
18.85/19.06	thf(sP10,plain,sP10 <=> ((archim7802044766580827645g_real @ zero_zero_real) = (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))),introduced(definition,[new_symbols(definition,[sP10])])).
18.85/19.06	thf(sP11,plain,sP11 <=> (![X1:int]:(![X2:int]:((~(((ord_less_eq_int @ X1) @ X2))) => ((ord_less_eq_int @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])).
18.85/19.06	thf(sP12,plain,sP12 <=> ((ord_less_eq_int @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))) @ zero_zero_int),introduced(definition,[new_symbols(definition,[sP12])])).
18.85/19.06	thf(sP13,plain,sP13 <=> (sP12 = ((ord_less_eq_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))) @ zero_zero_real)),introduced(definition,[new_symbols(definition,[sP13])])).
18.85/19.06	thf(sP14,plain,sP14 <=> (((ord_less_eq_real @ zero_zero_real) @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))) => sP6),introduced(definition,[new_symbols(definition,[sP14])])).
18.85/19.06	thf(sP15,plain,sP15 <=> ((archim7802044766580827645g_real @ zero_zero_real) = zero_zero_int),introduced(definition,[new_symbols(definition,[sP15])])).
18.85/19.06	thf(sP16,plain,sP16 <=> ((~(sP2)) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP16])])).
18.85/19.06	thf(sP17,plain,sP17 <=> (![X1:real]:(((ord_less_eq_int @ (archim7802044766580827645g_real @ X1)) @ zero_zero_int) = ((ord_less_eq_real @ X1) @ zero_zero_real))),introduced(definition,[new_symbols(definition,[sP17])])).
18.85/19.06	thf(sP18,plain,sP18 <=> ((~(sP4)) => sP12),introduced(definition,[new_symbols(definition,[sP18])])).
18.85/19.06	thf(sP19,plain,sP19 <=> (![X1:int]:(![X2:int]:((~(((~((X1 = X2))) => (~(((ord_less_eq_int @ X1) @ X2)))))) => (~(((ord_less_eq_int @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP19])])).
18.85/19.06	thf(sP20,plain,sP20 <=> (![X1:real]:(![X2:real]:(((ord_less_eq_real @ X1) @ X2) => ((ord_less_eq_int @ (archim7802044766580827645g_real @ X1)) @ (archim7802044766580827645g_real @ X2))))),introduced(definition,[new_symbols(definition,[sP20])])).
18.85/19.06	thf(sP21,plain,sP21 <=> ((ord_less_eq_real @ zero_zero_real) @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))),introduced(definition,[new_symbols(definition,[sP21])])).
18.85/19.06	thf(sP22,plain,sP22 <=> (![X1:real]:(((ord_less_eq_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))) @ X1) => ((ord_less_eq_int @ (archim7802044766580827645g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta))))) @ (archim7802044766580827645g_real @ X1)))),introduced(definition,[new_symbols(definition,[sP22])])).
18.85/19.06	thf(sP23,plain,sP23 <=> ((ord_less_eq_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ ((divide_divide_real @ one_one_real) @ (field_7254667332652039916t_real @ delta)))) @ zero_zero_real),introduced(definition,[new_symbols(definition,[sP23])])).
18.85/19.06	thf(sP24,plain,sP24 <=> (sP23 => sP3),introduced(definition,[new_symbols(definition,[sP24])])).
18.85/19.06	thf(conj_0,conjecture,sP4).
18.85/19.06	thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_0])).
18.85/19.06	thf(1,plain,((~(sP2) | sP10) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(2,plain,((~(sP18) | sP4) | sP12),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(3,plain,((~(sP24) | ~(sP23)) | sP3),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(4,plain,((~(sP14) | ~(sP21)) | sP6),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(5,plain,(((~(sP5) | sP4) | ~(sP10)) | ~(sP15)),inference(mating_rule,[status(thm)],[])).
18.85/19.06	thf(6,plain,((~(sP16) | sP2) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(7,plain,(~(sP8) | sP18),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(8,plain,(~(sP22) | sP24),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(9,plain,(~(sP9) | sP14),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(10,plain,(~(sP7) | sP16),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(11,plain,((~(sP13) | ~(sP12)) | sP23),inference(prop_rule,[status(thm)],[])).
18.85/19.06	thf(12,plain,(~(sP11) | sP8),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(13,plain,(~(sP20) | sP22),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(14,plain,(~(sP20) | sP9),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(15,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(16,plain,(~(sP19) | sP7),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(17,plain,(~(sP17) | sP13),inference(all_rule,[status(thm)],[])).
18.85/19.06	thf(fact_358_le__cases,axiom,sP11).
18.85/19.06	thf(fact_98_verit__comp__simplify1_I2_J,axiom,sP1).
18.85/19.06	thf(fact_179_ceiling__mono,axiom,sP20).
18.85/19.06	thf(fact_92_verit__la__disequality,axiom,sP19).
18.85/19.06	thf(fact_74_ceiling__zero,axiom,sP15).
18.85/19.06	thf(fact_5_ceiling__le__zero,axiom,sP17).
18.85/19.06	thf(fact_0__092_060open_0620_A_092_060le_062_Alog_A2_A_I1_A_P_Areal__of__rat_A_092_060delta_062_J_092_060close_062,axiom,sP21).
18.85/19.06	thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h0,fact_358_le__cases,fact_98_verit__comp__simplify1_I2_J,fact_179_ceiling__mono,fact_92_verit__la__disequality,fact_74_ceiling__zero,fact_5_ceiling__le__zero,fact_0__092_060open_0620_A_092_060le_062_Alog_A2_A_I1_A_P_Areal__of__rat_A_092_060delta_062_J_092_060close_062])).
18.85/19.06	thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])).
18.85/19.06	% SZS output end Proof
18.85/19.06	EOF