0.03/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.11	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.10/0.32	% Computer : n022.cluster.edu
0.10/0.32	% Model    : x86_64 x86_64
0.10/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory   : 8042.1875MB
0.10/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit : 960
0.10/0.32	% WCLimit  : 120
0.10/0.32	% DateTime : Tue Aug  9 05:16:01 EDT 2022
0.10/0.32	% CPUTime  : 
11.63/11.62	% SZS status Theorem
11.63/11.62	% Mode: cade22grackle2x6978
11.63/11.62	% Steps: 411947
11.63/11.62	% SZS output start Proof
11.63/11.62	thf(ty_set_a, type, set_a : $tType).
11.63/11.62	thf(ty_a, type, a : $tType).
11.63/11.62	thf(ty_real, type, real : $tType).
11.63/11.62	thf(ty_f, type, f : (a>a)).
11.63/11.62	thf(ty_member_a, type, member_a : (a>set_a>$o)).
11.63/11.62	thf(ty_b, type, b : a).
11.63/11.62	thf(ty_a2, type, a2 : a).
11.63/11.62	thf(ty_topolo1710226732a_real, type, topolo1710226732a_real : (set_a>(a>real)>$o)).
11.63/11.62	thf(ty_p, type, p : a).
11.63/11.62	thf(ty_eigen__0, type, eigen__0 : real).
11.63/11.62	thf(ty_eigen__1, type, eigen__1 : (a>real)).
11.63/11.62	thf(ty_elemen154694473ball_a, type, elemen154694473ball_a : (a>real>set_a)).
11.63/11.62	thf(ty_x, type, x : set_a).
11.63/11.62	thf(ty_zero_zero_real, type, zero_zero_real : real).
11.63/11.62	thf(ty_abs_abs_real, type, abs_abs_real : (real>real)).
11.63/11.62	thf(ty_one_one_real, type, one_one_real : real).
11.63/11.62	thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
11.63/11.62	thf(ty_line_open_segment_a, type, line_open_segment_a : (a>a>set_a)).
11.63/11.62	thf(ty_thesisa, type, thesisa : $o).
11.63/11.62	thf(ty_auto_ll_on_flow0_a, type, auto_ll_on_flow0_a : ((a>a)>set_a>a>real>a)).
11.63/11.62	thf(sP1,plain,sP1 <=> ((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
11.63/11.62	thf(sP2,plain,sP2 <=> ((eigen__1 @ p) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP2])])).
11.63/11.62	thf(sP3,plain,sP3 <=> ((![X1:a]:(((member_a @ X1) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((ord_less_real @ (abs_abs_real @ (eigen__1 @ X1))) @ one_one_real))) => ((![X1:a]:(((member_a @ X1) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X1) @ (eigen__1 @ X1))) @ ((line_open_segment_a @ a2) @ b)))) => thesisa)),introduced(definition,[new_symbols(definition,[sP3])])).
11.63/11.62	thf(sP4,plain,sP4 <=> ((ord_less_real @ zero_zero_real) @ eigen__0),introduced(definition,[new_symbols(definition,[sP4])])).
11.63/11.62	thf(sP5,plain,sP5 <=> ((![X1:a]:(((member_a @ X1) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X1) @ (eigen__1 @ X1))) @ ((line_open_segment_a @ a2) @ b)))) => thesisa),introduced(definition,[new_symbols(definition,[sP5])])).
11.63/11.62	thf(sP6,plain,sP6 <=> (![X1:real]:(![X2:a>real]:(((ord_less_real @ zero_zero_real) @ X1) => (((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ X1)) @ X2) => (((X2 @ p) = zero_zero_real) => ((![X3:a]:(((member_a @ X3) @ ((elemen154694473ball_a @ p) @ X1)) => ((ord_less_real @ (abs_abs_real @ (X2 @ X3))) @ one_one_real))) => ((![X3:a]:(((member_a @ X3) @ ((elemen154694473ball_a @ p) @ X1)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X3) @ (X2 @ X3))) @ ((line_open_segment_a @ a2) @ b)))) => thesisa))))))),introduced(definition,[new_symbols(definition,[sP6])])).
11.63/11.62	thf(sP7,plain,sP7 <=> (![X1:a]:(((member_a @ X1) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X1) @ (eigen__1 @ X1))) @ ((line_open_segment_a @ a2) @ b)))),introduced(definition,[new_symbols(definition,[sP7])])).
11.63/11.62	thf(sP8,plain,sP8 <=> (sP4 => (sP1 => (sP2 => sP3))),introduced(definition,[new_symbols(definition,[sP8])])).
11.63/11.62	thf(sP9,plain,sP9 <=> thesisa,introduced(definition,[new_symbols(definition,[sP9])])).
11.63/11.62	thf(sP10,plain,sP10 <=> (sP1 => (sP2 => sP3)),introduced(definition,[new_symbols(definition,[sP10])])).
11.63/11.62	thf(sP11,plain,sP11 <=> (![X1:a]:(((member_a @ X1) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((ord_less_real @ (abs_abs_real @ (eigen__1 @ X1))) @ one_one_real))),introduced(definition,[new_symbols(definition,[sP11])])).
11.63/11.62	thf(sP12,plain,sP12 <=> (![X1:a>real]:(sP4 => (((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ X1) => (((X1 @ p) = zero_zero_real) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((ord_less_real @ (abs_abs_real @ (X1 @ X2))) @ one_one_real))) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X2) @ (X1 @ X2))) @ ((line_open_segment_a @ a2) @ b)))) => sP9)))))),introduced(definition,[new_symbols(definition,[sP12])])).
11.63/11.62	thf(sP13,plain,sP13 <=> (sP2 => sP3),introduced(definition,[new_symbols(definition,[sP13])])).
11.63/11.62	thf(conj_1,conjecture,sP9).
11.63/11.62	thf(h0,negated_conjecture,(~(sP9)),inference(assume_negation,[status(cth)],[conj_1])).
11.63/11.62	thf(h1,assumption,(~((sP4 => (![X1:a>real]:(((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ X1) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X2) @ (X1 @ X2))) @ ((line_open_segment_a @ a2) @ b)))) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((ord_less_real @ (abs_abs_real @ (X1 @ X2))) @ one_one_real))) => (((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ X1) => (~(((X1 @ p) = zero_zero_real))))))))))),introduced(assumption,[])).
11.63/11.62	thf(h2,assumption,sP4,introduced(assumption,[])).
11.63/11.62	thf(h3,assumption,(~((![X1:a>real]:(((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ X1) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X2) @ (X1 @ X2))) @ ((line_open_segment_a @ a2) @ b)))) => ((![X2:a]:(((member_a @ X2) @ ((elemen154694473ball_a @ p) @ eigen__0)) => ((ord_less_real @ (abs_abs_real @ (X1 @ X2))) @ one_one_real))) => (((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ X1) => (~(((X1 @ p) = zero_zero_real)))))))))),introduced(assumption,[])).
11.63/11.62	thf(h4,assumption,(~((sP1 => (sP7 => (sP11 => (sP1 => (~(sP2)))))))),introduced(assumption,[])).
11.63/11.62	thf(h5,assumption,sP1,introduced(assumption,[])).
11.63/11.62	thf(h6,assumption,(~((sP7 => (sP11 => (sP1 => (~(sP2))))))),introduced(assumption,[])).
11.63/11.62	thf(h7,assumption,sP7,introduced(assumption,[])).
11.63/11.62	thf(h8,assumption,(~((sP11 => (sP1 => (~(sP2)))))),introduced(assumption,[])).
11.63/11.62	thf(h9,assumption,sP11,introduced(assumption,[])).
11.63/11.62	thf(h10,assumption,(~((sP1 => (~(sP2))))),introduced(assumption,[])).
11.63/11.62	thf(h11,assumption,sP2,introduced(assumption,[])).
11.63/11.62	thf(1,plain,((~(sP5) | ~(sP7)) | sP9),inference(prop_rule,[status(thm)],[])).
11.63/11.62	thf(2,plain,((~(sP3) | ~(sP11)) | sP5),inference(prop_rule,[status(thm)],[])).
11.63/11.62	thf(3,plain,((~(sP13) | ~(sP2)) | sP3),inference(prop_rule,[status(thm)],[])).
11.63/11.62	thf(4,plain,((~(sP10) | ~(sP1)) | sP13),inference(prop_rule,[status(thm)],[])).
11.63/11.62	thf(5,plain,((~(sP8) | ~(sP4)) | sP10),inference(prop_rule,[status(thm)],[])).
11.63/11.62	thf(6,plain,(~(sP12) | sP8),inference(all_rule,[status(thm)],[])).
11.63/11.62	thf(7,plain,(~(sP6) | sP12),inference(all_rule,[status(thm)],[])).
11.63/11.62	thf(conj_0,axiom,sP6).
11.63/11.62	thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h5,h11,h9,h10,h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h0,h2,h5,h7,h9,h11,conj_0])).
11.63/11.62	thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h11])],[h10,8,h5,h11])).
11.63/11.62	thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,9,h9,h10])).
11.63/11.62	thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,10,h7,h8])).
11.63/11.62	thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,11,h5,h6])).
11.63/11.62	thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,12,h4])).
11.63/11.62	thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3])).
11.63/11.62	thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (![X2:a>real]:(((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ X1)) @ X2) => ((![X3:a]:(((member_a @ X3) @ ((elemen154694473ball_a @ p) @ X1)) => ((member_a @ ((((auto_ll_on_flow0_a @ f) @ x) @ X3) @ (X2 @ X3))) @ ((line_open_segment_a @ a2) @ b)))) => ((![X3:a]:(((member_a @ X3) @ ((elemen154694473ball_a @ p) @ X1)) => ((ord_less_real @ (abs_abs_real @ (X2 @ X3))) @ one_one_real))) => (((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ X1)) @ X2) => (~(((X2 @ p) = zero_zero_real))))))))))))).
11.63/11.62	thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,14,h1])).
11.63/11.62	thf(0,theorem,sP9,inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])).
11.63/11.62	% SZS output end Proof
11.63/11.62	EOF