0.06/0.12 % Problem : SLH0266^1 : TPTP v8.2.0. Released v8.2.0. 0.06/0.12 % 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 : 30 0.12/0.33 % DateTime : Mon Jul 3 03:52:42 EDT 2023 0.12/0.33 % CPUTime : 14.47/14.90 % SZS status Theorem 14.47/14.90 % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 14.47/14.90 % Inferences: 7165 14.47/14.90 % SZS output start Proof 14.47/14.90 thf(ty_risk_Free_account, type, risk_Free_account : $tType). 14.47/14.90 thf(ty_set_nat, type, set_nat : $tType). 14.47/14.90 thf(ty_nat, type, nat : $tType). 14.47/14.90 thf(ty_real, type, real : $tType). 14.47/14.90 thf(ty_zero_zero_real, type, zero_zero_real : real). 14.47/14.90 thf(ty_finite_finite_nat, type, finite_finite_nat : (set_nat>$o)). 14.47/14.90 thf(ty_bot_bot_set_nat, type, bot_bot_set_nat : set_nat). 14.47/14.90 thf(ty_collect_nat, type, collect_nat : ((nat>$o)>set_nat)). 14.47/14.90 thf(ty_member_nat, type, member_nat : (nat>set_nat>$o)). 14.47/14.90 thf(ty_risk_F4612863212915232279period, type, risk_F4612863212915232279period : (risk_Free_account>nat)). 14.47/14.90 thf(ty_alpha, type, alpha : risk_Free_account). 14.47/14.90 thf(ty_lattic8265883725875713057ax_nat, type, lattic8265883725875713057ax_nat : (set_nat>nat)). 14.47/14.90 thf(ty_risk_F170160801229183585ccount, type, risk_F170160801229183585ccount : (risk_Free_account>nat>real)). 14.47/14.90 thf(sP1,plain,sP1 <=> (((risk_F4612863212915232279period @ alpha) = (lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))) => ((lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))) = (risk_F4612863212915232279period @ alpha))),introduced(definition,[new_symbols(definition,[sP1])])). 14.47/14.90 thf(sP2,plain,sP2 <=> ((lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))) = (risk_F4612863212915232279period @ alpha)),introduced(definition,[new_symbols(definition,[sP2])])). 14.47/14.90 thf(sP3,plain,sP3 <=> (![X1:set_nat]:((finite_finite_nat @ X1) => ((~((X1 = bot_bot_set_nat))) => ((member_nat @ (lattic8265883725875713057ax_nat @ X1)) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). 14.47/14.90 thf(sP4,plain,sP4 <=> ((collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))) = bot_bot_set_nat),introduced(definition,[new_symbols(definition,[sP4])])). 14.47/14.90 thf(sP5,plain,sP5 <=> (![X1:nat]:(((risk_F4612863212915232279period @ alpha) = X1) => (X1 = (risk_F4612863212915232279period @ alpha)))),introduced(definition,[new_symbols(definition,[sP5])])). 14.47/14.90 thf(sP6,plain,sP6 <=> ((member_nat @ (risk_F4612863212915232279period @ alpha)) @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP6])])). 14.47/14.90 thf(sP7,plain,sP7 <=> ((collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))) = (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP7])])). 14.47/14.90 thf(sP8,plain,sP8 <=> (finite_finite_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP8])])). 14.47/14.90 thf(sP9,plain,sP9 <=> ((~(sP4)) => ((member_nat @ (lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))) @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))),introduced(definition,[new_symbols(definition,[sP9])])). 14.47/14.90 thf(sP10,plain,sP10 <=> (![X1:nat]:(![X2:nat]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP10])])). 14.47/14.90 thf(sP11,plain,sP11 <=> (sP8 => sP9),introduced(definition,[new_symbols(definition,[sP11])])). 14.47/14.90 thf(sP12,plain,sP12 <=> ((risk_F4612863212915232279period @ alpha) = (lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))),introduced(definition,[new_symbols(definition,[sP12])])). 14.47/14.90 thf(sP13,plain,sP13 <=> ((member_nat @ (lattic8265883725875713057ax_nat @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))) @ (collect_nat @ (^[X1:nat]:(~((((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP13])])). 14.47/14.90 thf(conj_0,conjecture,sP6). 14.47/14.90 thf(h0,negated_conjecture,(~(sP6)),inference(assume_negation,[status(cth)],[conj_0])). 14.47/14.90 thf(1,plain,(((~(sP13) | sP6) | ~(sP2)) | ~(sP7)),inference(mating_rule,[status(thm)],[])). 14.47/14.90 thf(2,plain,sP7,inference(prop_rule,[status(thm)],[])). 14.47/14.90 thf(3,plain,((~(sP9) | sP4) | sP13),inference(prop_rule,[status(thm)],[])). 14.47/14.90 thf(4,plain,((~(sP11) | ~(sP8)) | sP9),inference(prop_rule,[status(thm)],[])). 14.47/14.90 thf(5,plain,(~(sP3) | sP11),inference(all_rule,[status(thm)],[])). 14.47/14.90 thf(6,plain,((~(sP1) | ~(sP12)) | sP2),inference(prop_rule,[status(thm)],[])). 14.47/14.90 thf(7,plain,(~(sP5) | sP1),inference(all_rule,[status(thm)],[])). 14.47/14.90 thf(8,plain,(~(sP10) | sP5),inference(all_rule,[status(thm)],[])). 14.47/14.90 thf(9,plain,sP10,inference(@eq_sym,[status(thm)],[])). 14.47/14.90 thf(fact_2__092_060open_062shortest__period_A_092_060alpha_062_A_061_AMax_A_123i_O_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_125_092_060close_062,axiom,sP12). 14.47/14.90 thf(fact_3_B,axiom,(~(sP4))). 14.47/14.90 thf(fact_4_A,axiom,sP8). 14.47/14.90 thf(fact_53_Max__in,axiom,sP3). 14.47/14.90 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,fact_2__092_060open_062shortest__period_A_092_060alpha_062_A_061_AMax_A_123i_O_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_125_092_060close_062,fact_3_B,fact_4_A,fact_53_Max__in,h0])). 14.47/14.90 thf(0,theorem,sP6,inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). 14.47/14.90 % SZS output end Proof 14.47/14.90 EOF