0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s 0.13/0.34 % Computer : n017.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 : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 06:42:15 EDT 2022 0.20/0.34 % CPUTime : 82.93/82.94 % SZS status Theorem 82.93/82.94 % Mode: cade22grackle2x1e4e 82.93/82.94 % Steps: 119797 82.93/82.94 % SZS output start Proof 82.93/82.94 thf(ty_num, type, num : $tType). 82.93/82.94 thf(ty_real, type, real : $tType). 82.93/82.94 thf(ty_vEBT_VEBT, type, vEBT_VEBT : $tType). 82.93/82.94 thf(ty_nat, type, nat : $tType). 82.93/82.94 thf(ty_info, type, info : option4927543243414619207at_nat). 82.93/82.94 thf(ty_vEBT_V8194947554948674370ptions, type, vEBT_V8194947554948674370ptions : (vEBT_VEBT>nat>$o)). 82.93/82.94 thf(ty_vEBT_VEBT_high, type, vEBT_VEBT_high : (nat>nat>nat)). 82.93/82.94 thf(ty_vEBT_Node, type, vEBT_Node : (option4927543243414619207at_nat>nat>list_VEBT_VEBT>vEBT_VEBT>vEBT_VEBT)). 82.93/82.94 thf(ty_vEBT_V5719532721284313246member, type, vEBT_V5719532721284313246member : (vEBT_VEBT>nat>$o)). 82.93/82.94 thf(ty_deg, type, deg : nat). 82.93/82.94 thf(ty_divide_divide_nat, type, divide_divide_nat : (nat>nat>nat)). 82.93/82.94 thf(ty_numeral_numeral_nat, type, numeral_numeral_nat : (num>nat)). 82.93/82.94 thf(ty_one, type, one : num). 82.93/82.94 thf(ty_vEBT_VEBT_low, type, vEBT_VEBT_low : (nat>nat>nat)). 82.93/82.94 thf(ty_cos_real, type, cos_real : (real>real)). 82.93/82.94 thf(ty_x, type, x : nat). 82.93/82.94 thf(ty_treeList, type, treeList : list_VEBT_VEBT). 82.93/82.94 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)). 82.93/82.94 thf(ty_zero_zero_real, type, zero_zero_real : real). 82.93/82.94 thf(ty_numeral_numeral_real, type, numeral_numeral_real : (num>real)). 82.93/82.94 thf(ty_bit0, type, bit0 : (num>num)). 82.93/82.94 thf(ty_nth_VEBT_VEBT, type, nth_VEBT_VEBT : (list_VEBT_VEBT>nat>vEBT_VEBT)). 82.93/82.94 thf(ty_vEBT_VEBT_membermima, type, vEBT_VEBT_membermima : (vEBT_VEBT>nat>$o)). 82.93/82.94 thf(ty_eigen__0, type, eigen__0 : real). 82.93/82.94 thf(ty_summary, type, summary : vEBT_VEBT). 82.93/82.94 thf(sP1,plain,sP1 <=> ((vEBT_VEBT_membermima @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x),introduced(definition,[new_symbols(definition,[sP1])])). 82.93/82.94 thf(sP2,plain,sP2 <=> (![X1:vEBT_VEBT]:((vEBT_V8194947554948674370ptions @ X1) = (^[X2:nat]:((~(((vEBT_VEBT_membermima @ X1) @ X2))) => ((vEBT_V5719532721284313246member @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). 82.93/82.94 thf(sP3,plain,sP3 <=> ((~(sP1)) => ((vEBT_V5719532721284313246member @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x)),introduced(definition,[new_symbols(definition,[sP3])])). 82.93/82.94 thf(sP4,plain,sP4 <=> ((vEBT_V8194947554948674370ptions @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) = (^[X1:nat]:((~(((vEBT_VEBT_membermima @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ X1))) => ((vEBT_V5719532721284313246member @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). 82.93/82.94 thf(sP5,plain,sP5 <=> ((~(((vEBT_V5719532721284313246member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) => ((vEBT_VEBT_membermima @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))),introduced(definition,[new_symbols(definition,[sP5])])). 82.93/82.94 thf(sP6,plain,sP6 <=> ((vEBT_VEBT_membermima @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))),introduced(definition,[new_symbols(definition,[sP6])])). 82.93/82.94 thf(sP7,plain,sP7 <=> (vEBT_V8194947554948674370ptions = (^[X1:vEBT_VEBT]:(^[X2:nat]:((~(((vEBT_VEBT_membermima @ X1) @ X2))) => ((vEBT_V5719532721284313246member @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP7])])). 82.93/82.94 thf(sP8,plain,sP8 <=> (((vEBT_V5719532721284313246member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) => ((vEBT_V5719532721284313246member @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x)),introduced(definition,[new_symbols(definition,[sP8])])). 82.93/82.94 thf(sP9,plain,sP9 <=> ((vEBT_V5719532721284313246member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ x) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))),introduced(definition,[new_symbols(definition,[sP9])])). 82.93/82.94 thf(sP10,plain,sP10 <=> (sP6 => sP1),introduced(definition,[new_symbols(definition,[sP10])])). 82.93/82.94 thf(sP11,plain,sP11 <=> (((vEBT_V8194947554948674370ptions @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x) = sP3),introduced(definition,[new_symbols(definition,[sP11])])). 82.93/82.94 thf(sP12,plain,sP12 <=> ((vEBT_V8194947554948674370ptions @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x),introduced(definition,[new_symbols(definition,[sP12])])). 82.93/82.94 thf(sP13,plain,sP13 <=> ((vEBT_V5719532721284313246member @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ x),introduced(definition,[new_symbols(definition,[sP13])])). 82.93/82.94 thf(sP14,plain,sP14 <=> (![X1:nat]:(((vEBT_V8194947554948674370ptions @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ X1) = ((~(((vEBT_VEBT_membermima @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ X1))) => ((vEBT_V5719532721284313246member @ ((((vEBT_Node @ info) @ deg) @ treeList) @ summary)) @ X1)))),introduced(definition,[new_symbols(definition,[sP14])])). 82.93/82.94 thf(conj_0,conjecture,sP12). 82.93/82.94 thf(h0,negated_conjecture,(~(sP12)),inference(assume_negation,[status(cth)],[conj_0])). 82.93/82.94 thf(h1,assumption,(~(((~(((~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (~((![X1:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X1) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (X1 = eigen__0)))))))) => (~(((cos_real @ eigen__0) = zero_zero_real)))))),introduced(assumption,[])). 82.93/82.94 thf(h2,assumption,(~(((~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (~((![X1:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X1) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (X1 = eigen__0)))))))),introduced(assumption,[])). 82.93/82.94 thf(h3,assumption,((cos_real @ eigen__0) = zero_zero_real),introduced(assumption,[])). 82.93/82.94 thf(h4,assumption,(~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))),introduced(assumption,[])). 82.93/82.94 thf(h5,assumption,(![X1:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X1) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (X1 = eigen__0))),introduced(assumption,[])). 82.93/82.94 thf(h6,assumption,((ord_less_eq_real @ zero_zero_real) @ eigen__0),introduced(assumption,[])). 82.93/82.94 thf(h7,assumption,((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one))),introduced(assumption,[])). 82.93/82.94 thf(1,plain,(sP3 | ~(sP13)),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(2,plain,(sP3 | ~(sP1)),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(3,plain,((~(sP11) | sP12) | ~(sP3)),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(4,plain,(~(sP14) | sP11),inference(all_rule,[status(thm)],[])). 82.93/82.94 thf(5,plain,(~(sP4) | sP14),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(6,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])). 82.93/82.94 thf(7,plain,((~(sP5) | sP9) | sP6),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(8,plain,((~(sP10) | ~(sP6)) | sP1),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(9,plain,((~(sP8) | ~(sP9)) | sP13),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(10,plain,(~(sP7) | sP2),inference(prop_rule,[status(thm)],[])). 82.93/82.94 thf(fact_0_both__member__options__def,axiom,sP7). 82.93/82.94 thf(fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,sP5). 82.93/82.94 thf(fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,sP10). 82.93/82.94 thf(fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,sP8). 82.93/82.94 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,fact_0_both__member__options__def,fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,h0])). 82.93/82.94 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,11,h6,h7])). 82.93/82.94 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,12,h4,h5])). 82.93/82.94 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3])). 82.93/82.94 thf(fact_7306_cos__is__zero,axiom,(~((![X1:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X1) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (~((![X2:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X2) => (~(((cos_real @ X2) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X2) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (X2 = X1)))))))) => (~(((cos_real @ X1) = zero_zero_real)))))))). 82.93/82.94 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_7306_cos__is__zero,14,h1])). 82.93/82.94 thf(0,theorem,sP12,inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])). 82.93/82.94 % SZS output end Proof 82.93/82.95 EOF