0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.09 % Command : lash -P picomus -M modes -p tstp -t %d %s 0.08/0.27 % Computer : n023.cluster.edu 0.08/0.27 % Model : x86_64 x86_64 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.27 % Memory : 8042.1875MB 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.27 % CPULimit : 960 0.08/0.27 % WCLimit : 120 0.08/0.27 % DateTime : Tue Aug 9 05:48:13 EDT 2022 0.08/0.27 % CPUTime : 1.14/1.36 % SZS status Theorem 1.14/1.36 % Mode: cade22grackle2x6978 1.14/1.36 % Steps: 0 1.14/1.36 % SZS output start Proof 1.14/1.36 thf(ty_list_VEBT_VEBT, type, list_VEBT_VEBT : $tType). 1.14/1.36 thf(ty_real, type, real : $tType). 1.14/1.36 thf(ty_option_nat, type, option_nat : $tType). 1.14/1.36 thf(ty_nat, type, nat : $tType). 1.14/1.36 thf(ty_vEBT_VEBT, type, vEBT_VEBT : $tType). 1.14/1.36 thf(ty_option4927543243414619207at_nat, type, option4927543243414619207at_nat : $tType). 1.14/1.36 thf(ty_num, type, num : $tType). 1.14/1.36 thf(ty_product_prod_nat_nat, type, product_prod_nat_nat : $tType). 1.14/1.36 thf(ty_set_VEBT_VEBT, type, set_VEBT_VEBT : $tType). 1.14/1.36 thf(ty_vEBT_vebt_member, type, vEBT_vebt_member : (vEBT_VEBT>nat>$o)). 1.14/1.36 thf(ty_ord_less_nat, type, ord_less_nat : (nat>nat>$o)). 1.14/1.36 thf(ty_mi, type, mi : nat). 1.14/1.36 thf(ty_vEBT_VEBT_high, type, vEBT_VEBT_high : (nat>nat>nat)). 1.14/1.36 thf(ty_vEBT_VEBT_mul, type, vEBT_VEBT_mul : (option_nat>option_nat>option_nat)). 1.14/1.36 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)). 1.14/1.36 thf(ty_m, type, m : nat). 1.14/1.36 thf(ty_power_power_nat, type, power_power_nat : (nat>nat>nat)). 1.14/1.36 thf(ty_some_P7363390416028606310at_nat, type, some_P7363390416028606310at_nat : (product_prod_nat_nat>option4927543243414619207at_nat)). 1.14/1.36 thf(ty_summary, type, summary : vEBT_VEBT). 1.14/1.36 thf(ty_vEBT_Node, type, vEBT_Node : (option4927543243414619207at_nat>nat>list_VEBT_VEBT>vEBT_VEBT>vEBT_VEBT)). 1.14/1.36 thf(ty_eigen__6, type, eigen__6 : nat). 1.14/1.36 thf(ty_eigen__1, type, eigen__1 : nat). 1.14/1.36 thf(ty_ma, type, ma : nat). 1.14/1.36 thf(ty_vEBT_vebt_mint, type, vEBT_vebt_mint : (vEBT_VEBT>option_nat)). 1.14/1.36 thf(ty_some_nat, type, some_nat : (nat>option_nat)). 1.14/1.36 thf(ty_if_option_nat, type, if_option_nat : ($o>option_nat>option_nat>option_nat)). 1.14/1.36 thf(ty_eigen__3, type, eigen__3 : nat). 1.14/1.36 thf(ty_vEBT_VEBT_low, type, vEBT_VEBT_low : (nat>nat>nat)). 1.14/1.36 thf(ty_vEBT_VEBT_greater, type, vEBT_VEBT_greater : (option_nat>option_nat>$o)). 1.14/1.36 thf(ty_product_Pair_nat_nat, type, product_Pair_nat_nat : (nat>nat>product_prod_nat_nat)). 1.14/1.36 thf(ty_treeList, type, treeList : list_VEBT_VEBT). 1.14/1.36 thf(ty_na, type, na : nat). 1.14/1.36 thf(ty_vEBT_VEBT_add, type, vEBT_VEBT_add : (option_nat>option_nat>option_nat)). 1.14/1.36 thf(ty_zero_zero_real, type, zero_zero_real : real). 1.14/1.36 thf(ty_one, type, one : num). 1.14/1.36 thf(ty_vEBT_vebt_maxt, type, vEBT_vebt_maxt : (vEBT_VEBT>option_nat)). 1.14/1.36 thf(ty_eigen__2, type, eigen__2 : nat). 1.14/1.36 thf(ty_eigen__0, type, eigen__0 : real). 1.14/1.36 thf(ty_numeral_numeral_real, type, numeral_numeral_real : (num>real)). 1.14/1.36 thf(ty_divide_divide_nat, type, divide_divide_nat : (nat>nat>nat)). 1.14/1.36 thf(ty_eigen__4, type, eigen__4 : nat). 1.14/1.36 thf(ty_eigen__5, type, eigen__5 : nat). 1.14/1.36 thf(ty_ord_less_eq_nat, type, ord_less_eq_nat : (nat>nat>$o)). 1.14/1.36 thf(ty_bit0, type, bit0 : (num>num)). 1.14/1.36 thf(ty_za, type, za : nat). 1.14/1.36 thf(ty_set_VEBT_VEBT2, type, set_VEBT_VEBT2 : (list_VEBT_VEBT>set_VEBT_VEBT)). 1.14/1.36 thf(ty_xa, type, xa : nat). 1.14/1.36 thf(ty_deg, type, deg : nat). 1.14/1.36 thf(ty_numeral_numeral_nat, type, numeral_numeral_nat : (num>nat)). 1.14/1.36 thf(ty_pr, type, pr : nat). 1.14/1.36 thf(ty_the_nat, type, the_nat : (option_nat>nat)). 1.14/1.36 thf(ty_member_VEBT_VEBT, type, member_VEBT_VEBT : (vEBT_VEBT>set_VEBT_VEBT>$o)). 1.14/1.36 thf(ty_none_nat, type, none_nat : option_nat). 1.14/1.36 thf(ty_size_s6755466524823107622T_VEBT, type, size_s6755466524823107622T_VEBT : (list_VEBT_VEBT>nat)). 1.14/1.36 thf(ty_nth_VEBT_VEBT, type, nth_VEBT_VEBT : (list_VEBT_VEBT>nat>vEBT_VEBT)). 1.14/1.36 thf(ty_cos_real, type, cos_real : (real>real)). 1.14/1.36 thf(ty_vEBT_V8194947554948674370ptions, type, vEBT_V8194947554948674370ptions : (vEBT_VEBT>nat>$o)). 1.14/1.36 thf(ty_vEBT_vebt_pred, type, vEBT_vebt_pred : (vEBT_VEBT>nat>option_nat)). 1.14/1.36 thf(sP1,plain,sP1 <=> ((vEBT_vebt_member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))),introduced(definition,[new_symbols(definition,[sP1])])). 1.14/1.36 thf(sP2,plain,sP2 <=> (za = mi),introduced(definition,[new_symbols(definition,[sP2])])). 1.14/1.36 thf(conj_0,conjecture,sP1). 1.14/1.36 thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[conj_0])). 1.14/1.36 thf(h1,assumption,(mi = ma),introduced(assumption,[])). 1.14/1.36 thf(h2,assumption,(![X1:nat]:(((ord_less_nat @ X1) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)) => (~((((((vEBT_VEBT_high @ ma) @ na) = X1) => ((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ ma) @ na))) => (~((![X2:nat]:((~(((((vEBT_VEBT_high @ X2) @ na) = X1) => (~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ X2) @ na))))))) => (~((((ord_less_eq_nat @ X2) @ ma) => (~(((ord_less_nat @ mi) @ X2))))))))))))))),introduced(assumption,[])). 1.14/1.36 thf(fact_2_abe,axiom,sP1). 1.14/1.36 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h3,assumption,(~((((vEBT_VEBT_high @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))) = ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))),introduced(assumption,[])). 1.14/1.36 thf(h4,assumption,((vEBT_vebt_member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))),introduced(assumption,[])). 1.14/1.36 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h3,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h5,assumption,((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) => (~(((((ord_less_nat @ mi) @ xa) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (some_nat @ mi))) => (~(((~(((ord_less_nat @ mi) @ xa))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = none_nat)))))))),introduced(assumption,[])). 1.14/1.36 thf(h6,assumption,((~((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))))))),introduced(assumption,[])). 1.14/1.36 thf(h7,assumption,(~((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat))),introduced(assumption,[])). 1.14/1.36 thf(h8,assumption,(~(((((ord_less_nat @ mi) @ xa) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (some_nat @ mi))) => (~(((~(((ord_less_nat @ mi) @ xa))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = none_nat))))))),introduced(assumption,[])). 1.14/1.36 thf(3,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h5,h6,h4,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h9,assumption,(((ord_less_nat @ mi) @ xa) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (some_nat @ mi))),introduced(assumption,[])). 1.14/1.36 thf(h10,assumption,((~(((ord_less_nat @ mi) @ xa))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = none_nat)),introduced(assumption,[])). 1.14/1.36 thf(h11,assumption,(~(((ord_less_nat @ mi) @ xa))),introduced(assumption,[])). 1.14/1.36 thf(h12,assumption,(((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (some_nat @ mi)),introduced(assumption,[])). 1.14/1.36 thf(4,plain,$false,inference(tab_conflict,[status(thm),assumptions([h11,h9,h10,h8,h5,h6,h4,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h13,assumption,((ord_less_nat @ mi) @ xa),introduced(assumption,[])). 1.14/1.36 thf(h14,assumption,(((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = none_nat),introduced(assumption,[])). 1.14/1.36 thf(5,plain,$false,inference(tab_conflict,[status(thm),assumptions([h13,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h15,assumption,(((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat),introduced(assumption,[])). 1.14/1.36 thf(h16,assumption,(((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),introduced(assumption,[])). 1.14/1.36 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h15,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h17,assumption,(~(((~(((~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~((![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)))))) => (~(((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one)))))))),introduced(assumption,[])). 1.14/1.36 thf(h18,assumption,(~(((~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~((![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,[])). 1.14/1.36 thf(h19,assumption,((ord_less_eq_real @ eigen__0) @ (numeral_numeral_real @ (bit0 @ one))),introduced(assumption,[])). 1.14/1.36 thf(h20,assumption,(~((((ord_less_eq_real @ zero_zero_real) @ eigen__0) => (~((![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,[])). 1.14/1.36 thf(h21,assumption,((cos_real @ eigen__0) = zero_zero_real),introduced(assumption,[])). 1.14/1.36 thf(h22,assumption,((ord_less_eq_real @ zero_zero_real) @ eigen__0),introduced(assumption,[])). 1.14/1.36 thf(h23,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,[])). 1.14/1.36 thf(h24,assumption,((((ord_less_nat @ ((vEBT_VEBT_high @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (size_s6755466524823107622T_VEBT @ treeList)) => (~(sP1))) => (za = ma)),introduced(assumption,[])). 1.14/1.36 thf(h25,assumption,sP2,introduced(assumption,[])). 1.14/1.36 thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h24,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[fact_2_abe,h0])). 1.14/1.36 thf(h26,assumption,(((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = (some_nat @ eigen__1)),introduced(assumption,[])). 1.14/1.36 thf(h27,assumption,((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ pr)) @ eigen__2),introduced(assumption,[])). 1.14/1.36 thf(h28,assumption,((ord_less_nat @ ((vEBT_VEBT_low @ xa) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)),introduced(assumption,[])). 1.14/1.36 thf(h29,assumption,((ord_less_nat @ ((vEBT_VEBT_high @ xa) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)),introduced(assumption,[])). 1.14/1.36 thf(h30,assumption,(((~(((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))) => (~(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (((if_option_nat @ (((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) @ (((if_option_nat @ ((ord_less_nat @ mi) @ xa)) @ (some_nat @ mi)) @ none_nat)) @ ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),introduced(assumption,[])). 1.14/1.36 thf(h31,assumption,((~((((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) => ((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (some_nat @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ ((vEBT_vebt_pred @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))),introduced(assumption,[])). 1.14/1.36 thf(h32,assumption,(~(((~(((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))) => (~(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),introduced(assumption,[])). 1.14/1.36 thf(h33,assumption,(((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (((if_option_nat @ (((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) @ (((if_option_nat @ ((ord_less_nat @ mi) @ xa)) @ (some_nat @ mi)) @ none_nat)) @ ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))))))),introduced(assumption,[])). 1.14/1.36 thf(fact_3_False,axiom,(~(sP2))). 1.14/1.36 thf(8,plain,$false,inference(tab_conflict,[status(thm),assumptions([h32,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(h34,assumption,(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) => ((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)),introduced(assumption,[])). 1.14/1.36 thf(h35,assumption,(((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (some_nat @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ ((vEBT_vebt_pred @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))),introduced(assumption,[])). 1.14/1.36 thf(h36,assumption,(~(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))))),introduced(assumption,[])). 1.14/1.36 thf(h37,assumption,((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat),introduced(assumption,[])). 1.14/1.36 thf(9,plain,$false,inference(tab_conflict,[status(thm),assumptions([h36,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(h38,assumption,((ord_less_nat @ za) @ xa),introduced(assumption,[])). 1.14/1.36 thf(h39,assumption,((vEBT_vebt_member @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ za),introduced(assumption,[])). 1.14/1.36 thf(h40,assumption,(~((mi = ma))),introduced(assumption,[])). 1.14/1.36 thf(h41,assumption,(![X1:vEBT_VEBT]:(((member_VEBT_VEBT @ X1) @ (set_VEBT_VEBT2 @ treeList)) => (![X2:nat]:(~(((vEBT_V8194947554948674370ptions @ X1) @ X2)))))),introduced(assumption,[])). 1.14/1.36 thf(h42,assumption,((some_nat @ eigen__6) = (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ pr))),introduced(assumption,[])). 1.14/1.36 thf(10,plain,$false,inference(tab_conflict,[status(thm),assumptions([h36,h42,h40,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(11,plain,$false,inference(tab_conflict,[status(thm),assumptions([h37,h42,h40,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(12,plain,$false,inference(tab_imp,[status(thm),assumptions([h42,h40,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[h34,10,11,h36,h37])). 1.14/1.36 thf(fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:nat]:(~(((some_nat @ X1) = (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ pr))))))))). 1.14/1.36 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h40,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__6)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,12,h42])). 1.14/1.36 thf(h43,assumption,((some_nat @ eigen__5) = (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ pr))),introduced(assumption,[])). 1.14/1.36 thf(14,plain,$false,inference(tab_conflict,[status(thm),assumptions([h36,h43,h41,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(15,plain,$false,inference(tab_conflict,[status(thm),assumptions([h37,h43,h41,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(16,plain,$false,inference(tab_imp,[status(thm),assumptions([h43,h41,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[h34,14,15,h36,h37])). 1.14/1.36 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h41,h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h43]),tab_negall(eigenvar,eigen__5)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,16,h43])). 1.14/1.36 thf(fact_178__C4_Ohyps_C_I8_J,axiom,((mi = ma) => (![X1:vEBT_VEBT]:(((member_VEBT_VEBT @ X1) @ (set_VEBT_VEBT2 @ treeList)) => (![X2:nat]:(~(((vEBT_V8194947554948674370ptions @ X1) @ X2)))))))). 1.14/1.36 thf(18,plain,$false,inference(tab_imp,[status(thm),assumptions([h38,h39,h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h40]),tab_imp(discharge,[h41])],[fact_178__C4_Ohyps_C_I8_J,13,17,h40,h41])). 1.14/1.36 thf(fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,axiom,(~((((ord_less_nat @ za) @ xa) => (~(((vEBT_vebt_member @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ za))))))). 1.14/1.36 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h37,h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h38,h39])],[fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,18,h38,h39])). 1.14/1.36 thf(20,plain,$false,inference(tab_imp,[status(thm),assumptions([h34,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[h34,9,19,h36,h37])). 1.14/1.36 thf(h44,assumption,((some_nat @ eigen__4) = (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ pr))),introduced(assumption,[])). 1.14/1.36 thf(21,plain,$false,inference(tab_conflict,[status(thm),assumptions([h36,h44,h40,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(22,plain,$false,inference(tab_conflict,[status(thm),assumptions([h37,h44,h40,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(fact_960_i1,axiom,(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) => ((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))). 1.14/1.36 thf(23,plain,$false,inference(tab_imp,[status(thm),assumptions([h44,h40,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[fact_960_i1,21,22,h36,h37])). 1.14/1.36 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h40,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__4)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,23,h44])). 1.14/1.36 thf(h45,assumption,((some_nat @ eigen__3) = (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ pr))),introduced(assumption,[])). 1.14/1.36 thf(25,plain,$false,inference(tab_conflict,[status(thm),assumptions([h36,h45,h41,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(26,plain,$false,inference(tab_conflict,[status(thm),assumptions([h37,h45,h41,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0])],[h25,fact_3_False])). 1.14/1.36 thf(27,plain,$false,inference(tab_imp,[status(thm),assumptions([h45,h41,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[fact_960_i1,25,26,h36,h37])). 1.14/1.36 thf(28,plain,$false,inference(tab_negall,[status(thm),assumptions([h41,h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__3)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,27,h45])). 1.14/1.36 thf(29,plain,$false,inference(tab_imp,[status(thm),assumptions([h38,h39,h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h40]),tab_imp(discharge,[h41])],[fact_178__C4_Ohyps_C_I8_J,24,28,h40,h41])). 1.14/1.36 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h35,h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h38,h39])],[fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,29,h38,h39])). 1.14/1.36 thf(31,plain,$false,inference(tab_imp,[status(thm),assumptions([h33,h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h34]),tab_imp(discharge,[h35])],[h31,20,30,h34,h35])). 1.14/1.36 thf(32,plain,$false,inference(tab_imp,[status(thm),assumptions([h30,h31,h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h32]),tab_imp(discharge,[h33])],[h30,8,31,h32,h33])). 1.14/1.36 thf(fact_1245__C1_C,axiom,(~(((((~(((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))) => (~(((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (((if_option_nat @ (((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) @ (((if_option_nat @ ((ord_less_nat @ mi) @ xa)) @ (some_nat @ mi)) @ none_nat)) @ ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) => (~(((~((((vEBT_VEBT_greater @ (some_nat @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) => ((vEBT_vebt_mint @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (some_nat @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ ((vEBT_vebt_pred @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))). 1.14/1.36 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h30,h31])],[fact_1245__C1_C,32,h30,h31])). 1.14/1.36 thf(fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,axiom,(~((((ord_less_nat @ ((vEBT_VEBT_low @ xa) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)) => (~(((ord_less_nat @ ((vEBT_VEBT_high @ xa) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)))))))). 1.14/1.36 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h27,h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h28,h29])],[fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,33,h28,h29])). 1.14/1.36 thf(fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,axiom,(~((![X1:nat]:(~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ pr)) @ X1))))))). 1.14/1.36 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h26,h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__2)],[fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,34,h27])). 1.14/1.36 thf(fact_636__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:nat]:(~((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = (some_nat @ X1)))))))). 1.14/1.36 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h25,h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__1)],[fact_636__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,35,h26])). 1.14/1.36 thf(fact_102__C20_C,axiom,((~(((((ord_less_nat @ ((vEBT_VEBT_high @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (size_s6755466524823107622T_VEBT @ treeList)) => (~(sP1))) => (za = ma)))) => sP2)). 1.14/1.36 thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h25])],[fact_102__C20_C,7,36,h24,h25])). 1.14/1.36 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h22,h23])],[h20,37,h22,h23])). 1.14/1.36 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h20,h21])],[h18,38,h20,h21])). 1.14/1.36 thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,39,h18,h19])). 1.14/1.36 thf(fact_7884_cos__is__zero,axiom,(~((![X1:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X1) => (~((![X2:real]:((~(((~((((ord_less_eq_real @ zero_zero_real) @ X2) => (~(((cos_real @ X2) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X2) @ (numeral_numeral_real @ (bit0 @ one)))))))) => (X2 = X1)))))))) => (~(((cos_real @ X1) = zero_zero_real)))))) => (~(((ord_less_eq_real @ X1) @ (numeral_numeral_real @ (bit0 @ one)))))))))). 1.14/1.36 thf(41,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__0)],[fact_7884_cos__is__zero,40,h17])). 1.14/1.36 thf(42,plain,$false,inference(tab_imp,[status(thm),assumptions([h14,h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h6,6,41,h15,h16])). 1.14/1.36 thf(43,plain,$false,inference(tab_imp,[status(thm),assumptions([h12,h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h10,5,42,h13,h14])). 1.14/1.36 thf(44,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h5,h6,h4,h2,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,4,43,h11,h12])). 1.14/1.36 thf(45,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,44,h9,h10])). 1.14/1.36 thf(46,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,3,45,h7,h8])). 1.14/1.36 thf(fact_969__C2_C,axiom,(~((((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) => (~(((((ord_less_nat @ mi) @ xa) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = (some_nat @ mi))) => (~(((~(((ord_less_nat @ mi) @ xa))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = none_nat)))))))) => (~(((~((((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat))) => (((vEBT_vebt_pred @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)) @ xa) = ((vEBT_VEBT_add @ ((vEBT_VEBT_mul @ (some_nat @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (vEBT_vebt_maxt @ ((nth_VEBT_VEBT @ treeList) @ (the_nat @ ((vEBT_vebt_pred @ summary) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))))). 1.14/1.36 thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h0]),tab_negimp(discharge,[h5,h6])],[fact_969__C2_C,46,h5,h6])). 1.14/1.36 thf(fact_4_aaa,axiom,((((vEBT_VEBT_high @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))) = ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))) => ((vEBT_vebt_member @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((vEBT_VEBT_low @ za) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one))))))). 1.14/1.36 thf(48,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_4_aaa,2,47,h3,h4])). 1.14/1.36 thf(fact_99__C4_Ohyps_C_I11_J,axiom,((~((mi = ma))) => (![X1:nat]:(((ord_less_nat @ X1) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)) => (~((((((vEBT_VEBT_high @ ma) @ na) = X1) => ((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ ma) @ na))) => (~((![X2:nat]:((~(((((vEBT_VEBT_high @ X2) @ na) = X1) => (~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ X2) @ na))))))) => (~((((ord_less_eq_nat @ X2) @ ma) => (~(((ord_less_nat @ mi) @ X2))))))))))))))))). 1.14/1.36 thf(49,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_99__C4_Ohyps_C_I11_J,1,48,h1,h2])). 1.14/1.36 thf(0,theorem,sP1,inference(contra,[status(thm),contra(discharge,[h0])],[49,h0])). 1.14/1.36 % SZS output end Proof 1.14/1.36 EOF