0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.33	% Computer : n012.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit : 1440
0.13/0.33	% WCLimit  : 180
0.13/0.33	% DateTime : Mon Jul  3 08:22:07 EDT 2023
0.13/0.33	% CPUTime  : 
0.52/0.70	% SZS status Theorem
0.52/0.70	% Mode: cade22sinegrackle2x6978
0.52/0.70	% Steps: 8275
0.52/0.70	% SZS output start Proof
0.52/0.70	thf(ty_set_a, type, set_a : $tType).
0.52/0.70	thf(ty_a, type, a : $tType).
0.52/0.70	thf(ty_real, type, real : $tType).
0.52/0.70	thf(ty_f, type, f : (a>a)).
0.52/0.70	thf(ty_member_a, type, member_a : (a>set_a>$o)).
0.52/0.70	thf(ty_b, type, b : a).
0.52/0.70	thf(ty_a2, type, a2 : a).
0.52/0.70	thf(ty_topolo1710226732a_real, type, topolo1710226732a_real : (set_a>(a>real)>$o)).
0.52/0.70	thf(ty_p, type, p : a).
0.52/0.70	thf(ty_eigen__0, type, eigen__0 : real).
0.52/0.70	thf(ty_eigen__1, type, eigen__1 : (a>real)).
0.52/0.70	thf(ty_elemen154694473ball_a, type, elemen154694473ball_a : (a>real>set_a)).
0.52/0.70	thf(ty_x, type, x : set_a).
0.52/0.70	thf(ty_zero_zero_real, type, zero_zero_real : real).
0.52/0.70	thf(ty_abs_abs_real, type, abs_abs_real : (real>real)).
0.52/0.70	thf(ty_one_one_real, type, one_one_real : real).
0.52/0.70	thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
0.52/0.70	thf(ty_line_open_segment_a, type, line_open_segment_a : (a>a>set_a)).
0.52/0.70	thf(ty_thesisa, type, thesisa : $o).
0.52/0.70	thf(ty_auto_ll_on_flow0_a, type, auto_ll_on_flow0_a : ((a>a)>set_a>a>real>a)).
0.52/0.70	thf(sP1,plain,sP1 <=> ((eigen__1 @ p) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP1])])).
0.52/0.70	thf(sP2,plain,sP2 <=> (![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,[sP2])])).
0.52/0.70	thf(sP3,plain,sP3 <=> (![X1:a>real]:(((ord_less_real @ zero_zero_real) @ eigen__0) => (((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)))) => thesisa)))))),introduced(definition,[new_symbols(definition,[sP3])])).
0.52/0.70	thf(sP4,plain,sP4 <=> thesisa,introduced(definition,[new_symbols(definition,[sP4])])).
0.52/0.70	thf(sP5,plain,sP5 <=> (sP2 => ((![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)))) => sP4)),introduced(definition,[new_symbols(definition,[sP5])])).
0.52/0.70	thf(sP6,plain,sP6 <=> ((![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)))) => sP4),introduced(definition,[new_symbols(definition,[sP6])])).
0.52/0.70	thf(sP7,plain,sP7 <=> (sP1 => sP5),introduced(definition,[new_symbols(definition,[sP7])])).
0.52/0.70	thf(sP8,plain,sP8 <=> ((topolo1710226732a_real @ ((elemen154694473ball_a @ p) @ eigen__0)) @ eigen__1),introduced(definition,[new_symbols(definition,[sP8])])).
0.52/0.70	thf(sP9,plain,sP9 <=> ((ord_less_real @ zero_zero_real) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])).
0.52/0.70	thf(sP10,plain,sP10 <=> (sP8 => sP7),introduced(definition,[new_symbols(definition,[sP10])])).
0.52/0.70	thf(sP11,plain,sP11 <=> (![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,[sP11])])).
0.52/0.70	thf(sP12,plain,sP12 <=> (![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)))) => sP4))))))),introduced(definition,[new_symbols(definition,[sP12])])).
0.52/0.70	thf(sP13,plain,sP13 <=> (sP9 => sP10),introduced(definition,[new_symbols(definition,[sP13])])).
0.52/0.70	thf(conj_1,conjecture,sP4).
0.52/0.70	thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_1])).
0.52/0.70	thf(h1,assumption,(~((sP9 => (![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,[])).
0.52/0.70	thf(h2,assumption,sP9,introduced(assumption,[])).
0.52/0.70	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,[])).
0.52/0.70	thf(h4,assumption,(~((sP8 => (sP11 => (sP2 => (sP8 => (~(sP1)))))))),introduced(assumption,[])).
0.52/0.70	thf(h5,assumption,sP8,introduced(assumption,[])).
0.52/0.70	thf(h6,assumption,(~((sP11 => (sP2 => (sP8 => (~(sP1))))))),introduced(assumption,[])).
0.52/0.70	thf(h7,assumption,sP11,introduced(assumption,[])).
0.52/0.70	thf(h8,assumption,(~((sP2 => (sP8 => (~(sP1)))))),introduced(assumption,[])).
0.52/0.70	thf(h9,assumption,sP2,introduced(assumption,[])).
0.52/0.70	thf(h10,assumption,(~((sP8 => (~(sP1))))),introduced(assumption,[])).
0.52/0.70	thf(h11,assumption,sP1,introduced(assumption,[])).
0.52/0.70	thf(1,plain,((~(sP6) | ~(sP11)) | sP4),inference(prop_rule,[status(thm)],[])).
0.52/0.70	thf(2,plain,((~(sP5) | ~(sP2)) | sP6),inference(prop_rule,[status(thm)],[])).
0.52/0.70	thf(3,plain,((~(sP7) | ~(sP1)) | sP5),inference(prop_rule,[status(thm)],[])).
0.52/0.70	thf(4,plain,((~(sP10) | ~(sP8)) | sP7),inference(prop_rule,[status(thm)],[])).
0.52/0.70	thf(5,plain,((~(sP13) | ~(sP9)) | sP10),inference(prop_rule,[status(thm)],[])).
0.52/0.70	thf(6,plain,(~(sP3) | sP13),inference(all_rule,[status(thm)],[])).
0.52/0.70	thf(7,plain,(~(sP12) | sP3),inference(all_rule,[status(thm)],[])).
0.52/0.70	thf(fact_4_that,axiom,sP12).
0.52/0.70	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,h2,h5,h7,h9,h11,h0,fact_4_that])).
0.52/0.70	thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h11])],[h10,8,h5,h11])).
0.52/0.70	thf(10,plain,$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])).
0.52/0.70	thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,10,h7,h8])).
0.52/0.70	thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,11,h5,h6])).
0.52/0.70	thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,12,h4])).
0.52/0.70	thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3])).
0.52/0.70	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))))))))))))).
0.52/0.70	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])).
0.52/0.70	thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])).
0.52/0.70	% SZS output end Proof
0.52/0.70	EOF