0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.12/0.34	% Computer : n004.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit : 1440
0.12/0.34	% WCLimit  : 180
0.12/0.34	% DateTime : Mon Jul  3 05:00:00 EDT 2023
0.12/0.34	% CPUTime  : 
15.85/15.96	% SZS status Theorem
15.85/15.96	% Mode: cade22sinegrackle2xfaf3
15.85/15.96	% Steps: 6087
15.85/15.96	% SZS output start Proof
15.85/15.96	thf(ty_set_a, type, set_a : $tType).
15.85/15.96	thf(ty_a, type, a : $tType).
15.85/15.96	thf(ty_extended_ereal, type, extended_ereal : $tType).
15.85/15.96	thf(ty_eigen__21, type, eigen__21 : set_a).
15.85/15.96	thf(ty_lower_191460856_ereal, type, lower_191460856_ereal : (a>(a>extended_ereal)>$o)).
15.85/15.96	thf(ty_eigen__23, type, eigen__23 : set_a).
15.85/15.96	thf(ty_eigen__15, type, eigen__15 : set_a).
15.85/15.96	thf(ty_x0, type, x0 : a).
15.85/15.96	thf(ty_eigen__1, type, eigen__1 : extended_ereal).
15.85/15.96	thf(ty_ord_le2001149050_ereal, type, ord_le2001149050_ereal : (extended_ereal>extended_ereal>$o)).
15.85/15.96	thf(ty_eigen__6, type, eigen__6 : extended_ereal).
15.85/15.96	thf(ty_f, type, f : (a>extended_ereal)).
15.85/15.96	thf(ty_uminus1208298309_ereal, type, uminus1208298309_ereal : (extended_ereal>extended_ereal)).
15.85/15.96	thf(ty_member_a, type, member_a : (a>set_a>$o)).
15.85/15.96	thf(ty_topolo1276428101open_a, type, topolo1276428101open_a : (set_a>$o)).
15.85/15.96	thf(ty_extend1289208545_ereal, type, extend1289208545_ereal : extended_ereal).
15.85/15.96	thf(ty_eigen__0, type, eigen__0 : extended_ereal).
15.85/15.96	thf(h0, assumption, (![X1:extended_ereal>$o]:(![X2:extended_ereal]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
15.85/15.96	thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:extended_ereal]:(~((((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~((((member_a @ x0) @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~((topolo1276428101open_a @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
15.85/15.96	thf(h1, assumption, (![X1:set_a>$o]:(![X2:set_a]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
15.85/15.96	thf(eigendef_eigen__15, definition, eigen__15 = (eps__1 @ (^[X1:set_a]:(~(((~(((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__0) @ (f @ X2)))) => (~(((member_a @ x0) @ X1)))))) => (~((topolo1276428101open_a @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__15])])).
15.85/15.96	thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:extended_ereal]:(~((((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3)))) => (~(((member_a @ x0) @ X2)))))) => (~((topolo1276428101open_a @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
15.85/15.96	thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:extended_ereal]:(~((((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((topolo1276428101open_a @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~(((member_a @ x0) @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
15.85/15.96	thf(eigendef_eigen__21, definition, eigen__21 = (eps__1 @ (^[X1:set_a]:(~(((~(((topolo1276428101open_a @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X2))))))))) => (~(((member_a @ x0) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__21])])).
15.85/15.96	thf(eigendef_eigen__23, definition, eigen__23 = (eps__1 @ (^[X1:set_a]:(~(((~((((member_a @ x0) @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X2))))))))) => (~((topolo1276428101open_a @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__23])])).
15.85/15.96	thf(sP1,plain,sP1 <=> (((f @ x0) = extend1289208545_ereal) => (((lower_191460856_ereal @ x0) @ f) = (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~((((member_a @ x0) @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~((topolo1276428101open_a @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
15.85/15.96	thf(sP2,plain,sP2 <=> ((~((((member_a @ x0) @ eigen__21) => (~((![X1:a]:(((member_a @ X1) @ eigen__21) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X1))))))))) => (~((topolo1276428101open_a @ eigen__21)))),introduced(definition,[new_symbols(definition,[sP2])])).
15.85/15.96	thf(sP3,plain,sP3 <=> (((lower_191460856_ereal @ x0) @ f) = (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3)))) => (~(((member_a @ x0) @ X2)))))) => (~((topolo1276428101open_a @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
15.85/15.96	thf(sP4,plain,sP4 <=> (((ord_le2001149050_ereal @ eigen__1) @ (f @ x0)) => (~((![X1:set_a]:((~((((member_a @ x0) @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X2))))))))) => (~((topolo1276428101open_a @ X1)))))))),introduced(definition,[new_symbols(definition,[sP4])])).
15.85/15.96	thf(sP5,plain,sP5 <=> (![X1:set_a]:((~(((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X2)))) => (~(((member_a @ x0) @ X1)))))) => (~((topolo1276428101open_a @ X1))))),introduced(definition,[new_symbols(definition,[sP5])])).
15.85/15.96	thf(sP6,plain,sP6 <=> (![X1:a]:(((member_a @ X1) @ eigen__21) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])).
15.85/15.96	thf(sP7,plain,sP7 <=> ((f @ x0) = extend1289208545_ereal),introduced(definition,[new_symbols(definition,[sP7])])).
15.85/15.96	thf(sP8,plain,sP8 <=> (![X1:set_a]:((~(((topolo1276428101open_a @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__0) @ (f @ X2))))))))) => (~(((member_a @ x0) @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])).
15.85/15.96	thf(sP9,plain,sP9 <=> ((~(((![X1:a]:(((member_a @ X1) @ eigen__15) => ((ord_le2001149050_ereal @ eigen__0) @ (f @ X1)))) => (~(((member_a @ x0) @ eigen__15)))))) => (~((topolo1276428101open_a @ eigen__15)))),introduced(definition,[new_symbols(definition,[sP9])])).
15.85/15.96	thf(sP10,plain,sP10 <=> (![X1:set_a]:((~(((topolo1276428101open_a @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X2))))))))) => (~(((member_a @ x0) @ X1))))),introduced(definition,[new_symbols(definition,[sP10])])).
15.85/15.96	thf(sP11,plain,sP11 <=> (((ord_le2001149050_ereal @ eigen__6) @ (f @ x0)) => (~((![X1:set_a]:((~((((member_a @ x0) @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X2))))))))) => (~((topolo1276428101open_a @ X1)))))))),introduced(definition,[new_symbols(definition,[sP11])])).
15.85/15.96	thf(sP12,plain,sP12 <=> (topolo1276428101open_a @ eigen__15),introduced(definition,[new_symbols(definition,[sP12])])).
15.85/15.96	thf(sP13,plain,sP13 <=> ((~(sP7)) => sP3),introduced(definition,[new_symbols(definition,[sP13])])).
15.85/15.96	thf(sP14,plain,sP14 <=> ((member_a @ x0) @ eigen__15),introduced(definition,[new_symbols(definition,[sP14])])).
15.85/15.96	thf(sP15,plain,sP15 <=> (((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((lower_191460856_ereal @ x0) @ f)),introduced(definition,[new_symbols(definition,[sP15])])).
15.85/15.96	thf(sP16,plain,sP16 <=> (((lower_191460856_ereal @ x0) @ f) = (~((![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((topolo1276428101open_a @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~(((member_a @ x0) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
15.85/15.96	thf(sP17,plain,sP17 <=> (![X1:set_a]:((~(((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__0) @ (f @ X2)))) => (~(((member_a @ x0) @ X1)))))) => (~((topolo1276428101open_a @ X1))))),introduced(definition,[new_symbols(definition,[sP17])])).
15.85/15.96	thf(sP18,plain,sP18 <=> (![X1:set_a]:((~((((member_a @ x0) @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__1) @ (f @ X2))))))))) => (~((topolo1276428101open_a @ X1))))),introduced(definition,[new_symbols(definition,[sP18])])).
15.85/15.96	thf(sP19,plain,sP19 <=> ((ord_le2001149050_ereal @ eigen__0) @ (f @ x0)),introduced(definition,[new_symbols(definition,[sP19])])).
15.85/15.96	thf(sP20,plain,sP20 <=> (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((topolo1276428101open_a @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~(((member_a @ x0) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP20])])).
15.85/15.96	thf(sP21,plain,sP21 <=> (![X1:a]:(((member_a @ X1) @ eigen__15) => ((ord_le2001149050_ereal @ eigen__0) @ (f @ X1)))),introduced(definition,[new_symbols(definition,[sP21])])).
15.85/15.96	thf(sP22,plain,sP22 <=> (((member_a @ x0) @ eigen__21) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP22])])).
15.85/15.96	thf(sP23,plain,sP23 <=> (![X1:a]:(((f @ X1) = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((lower_191460856_ereal @ X1) @ f))),introduced(definition,[new_symbols(definition,[sP23])])).
15.85/15.96	thf(sP24,plain,sP24 <=> (((ord_le2001149050_ereal @ eigen__6) @ (f @ x0)) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP24])])).
15.85/15.96	thf(sP25,plain,sP25 <=> ((~((((member_a @ x0) @ eigen__23) => (~((![X1:a]:(((member_a @ X1) @ eigen__23) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X1))))))))) => (~((topolo1276428101open_a @ eigen__23)))),introduced(definition,[new_symbols(definition,[sP25])])).
15.85/15.96	thf(sP26,plain,sP26 <=> ((~(((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)))) => sP13),introduced(definition,[new_symbols(definition,[sP26])])).
15.85/15.96	thf(sP27,plain,sP27 <=> (topolo1276428101open_a @ eigen__23),introduced(definition,[new_symbols(definition,[sP27])])).
15.85/15.96	thf(sP28,plain,sP28 <=> (((lower_191460856_ereal @ x0) @ f) = (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~((((member_a @ x0) @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~((topolo1276428101open_a @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP28])])).
15.85/15.96	thf(sP29,plain,sP29 <=> (sP19 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP29])])).
15.85/15.96	thf(sP30,plain,sP30 <=> (topolo1276428101open_a @ eigen__21),introduced(definition,[new_symbols(definition,[sP30])])).
15.85/15.96	thf(sP31,plain,sP31 <=> (![X1:a>extended_ereal]:(![X2:a]:(((X1 @ X2) = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((lower_191460856_ereal @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP31])])).
15.85/15.96	thf(sP32,plain,sP32 <=> (((member_a @ x0) @ eigen__23) => (~((![X1:a]:(((member_a @ X1) @ eigen__23) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X1))))))),introduced(definition,[new_symbols(definition,[sP32])])).
15.85/15.96	thf(sP33,plain,sP33 <=> ((member_a @ x0) @ eigen__21),introduced(definition,[new_symbols(definition,[sP33])])).
15.85/15.96	thf(sP34,plain,sP34 <=> ((ord_le2001149050_ereal @ eigen__1) @ (f @ x0)),introduced(definition,[new_symbols(definition,[sP34])])).
15.85/15.96	thf(sP35,plain,sP35 <=> ((![X1:a]:(((member_a @ X1) @ eigen__23) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X1)))) => (~(((member_a @ x0) @ eigen__23)))),introduced(definition,[new_symbols(definition,[sP35])])).
15.85/15.96	thf(sP36,plain,sP36 <=> (![X1:a]:(((member_a @ X1) @ eigen__23) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X1)))),introduced(definition,[new_symbols(definition,[sP36])])).
15.85/15.96	thf(sP37,plain,sP37 <=> (sP34 => (~(sP10))),introduced(definition,[new_symbols(definition,[sP37])])).
15.85/15.96	thf(sP38,plain,sP38 <=> ((~(sP35)) => (~(sP27))),introduced(definition,[new_symbols(definition,[sP38])])).
15.85/15.96	thf(sP39,plain,sP39 <=> (sP19 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP39])])).
15.85/15.96	thf(sP40,plain,sP40 <=> ((member_a @ x0) @ eigen__23),introduced(definition,[new_symbols(definition,[sP40])])).
15.85/15.96	thf(sP41,plain,sP41 <=> (sP21 => (~(sP14))),introduced(definition,[new_symbols(definition,[sP41])])).
15.85/15.96	thf(sP42,plain,sP42 <=> (sP12 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP42])])).
15.85/15.96	thf(sP43,plain,sP43 <=> (((lower_191460856_ereal @ x0) @ f) = sP20),introduced(definition,[new_symbols(definition,[sP43])])).
15.85/15.96	thf(sP44,plain,sP44 <=> ((ord_le2001149050_ereal @ eigen__6) @ (f @ x0)),introduced(definition,[new_symbols(definition,[sP44])])).
15.85/15.96	thf(sP45,plain,sP45 <=> ((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)),introduced(definition,[new_symbols(definition,[sP45])])).
15.85/15.96	thf(sP46,plain,sP46 <=> ((~((sP30 => (~(sP6))))) => (~(sP33))),introduced(definition,[new_symbols(definition,[sP46])])).
15.85/15.96	thf(sP47,plain,sP47 <=> (sP30 => (~(sP6))),introduced(definition,[new_symbols(definition,[sP47])])).
15.85/15.96	thf(sP48,plain,sP48 <=> (![X1:set_a]:((~((((member_a @ x0) @ X1) => (~((![X2:a]:(((member_a @ X2) @ X1) => ((ord_le2001149050_ereal @ eigen__6) @ (f @ X2))))))))) => (~((topolo1276428101open_a @ X1))))),introduced(definition,[new_symbols(definition,[sP48])])).
15.85/15.96	thf(sP49,plain,sP49 <=> ((~(sP42)) => (~(sP14))),introduced(definition,[new_symbols(definition,[sP49])])).
15.85/15.96	thf(sP50,plain,sP50 <=> (sP45 => sP43),introduced(definition,[new_symbols(definition,[sP50])])).
15.85/15.96	thf(sP51,plain,sP51 <=> (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~((((member_a @ x0) @ X2) => (~((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3))))))))) => (~((topolo1276428101open_a @ X2))))))))),introduced(definition,[new_symbols(definition,[sP51])])).
15.85/15.96	thf(sP52,plain,sP52 <=> (![X1:extended_ereal]:(((ord_le2001149050_ereal @ X1) @ (f @ x0)) => (~((![X2:set_a]:((~(((![X3:a]:(((member_a @ X3) @ X2) => ((ord_le2001149050_ereal @ X1) @ (f @ X3)))) => (~(((member_a @ x0) @ X2)))))) => (~((topolo1276428101open_a @ X2))))))))),introduced(definition,[new_symbols(definition,[sP52])])).
15.85/15.96	thf(sP53,plain,sP53 <=> ((lower_191460856_ereal @ x0) @ f),introduced(definition,[new_symbols(definition,[sP53])])).
15.85/15.96	thf(conj_0,conjecture,(~(sP16))).
15.85/15.96	thf(h2,negated_conjecture,sP16,inference(assume_negation,[status(cth)],[conj_0])).
15.85/15.96	thf(1,plain,((~(sP35) | ~(sP36)) | ~(sP40)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(2,plain,((~(sP38) | sP35) | ~(sP27)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(3,plain,((~(sP22) | ~(sP33)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(4,plain,(~(sP5) | sP38),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(5,plain,((~(sP42) | ~(sP12)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(6,plain,((~(sP2) | sP22) | ~(sP30)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(7,plain,((~(sP49) | sP42) | ~(sP14)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(8,plain,(~(sP18) | sP2),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(9,plain,(~(sP8) | sP49),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(10,plain,(sP32 | sP36),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(11,plain,(sP32 | sP40),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(12,plain,(sP25 | sP27),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(13,plain,(sP25 | ~(sP32)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(14,plain,(sP47 | sP6),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(15,plain,(sP47 | sP30),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(16,plain,(sP48 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__23])).
15.85/15.96	thf(17,plain,(sP41 | sP14),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(18,plain,(sP41 | sP21),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(19,plain,(sP46 | sP33),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(20,plain,(sP46 | ~(sP47)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(21,plain,((~(sP11) | ~(sP44)) | ~(sP48)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(22,plain,(sP9 | sP12),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(23,plain,(sP9 | ~(sP41)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(24,plain,(sP10 | ~(sP46)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__21])).
15.85/15.96	thf(25,plain,(~(sP51) | sP11),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(26,plain,(sP17 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15])).
15.85/15.96	thf(27,plain,((~(sP37) | ~(sP34)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(28,plain,((~(sP29) | ~(sP19)) | ~(sP17)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(29,plain,(~(sP20) | sP37),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(30,plain,(~(sP52) | sP29),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(31,plain,(sP24 | sP5),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(32,plain,(sP24 | sP44),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(33,plain,(sP52 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
15.85/15.96	thf(34,plain,(sP4 | sP18),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(35,plain,(sP4 | sP34),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(36,plain,((~(sP3) | ~(sP53)) | sP52),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(37,plain,((~(sP3) | sP53) | ~(sP52)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(38,plain,(sP39 | sP8),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(39,plain,(sP39 | sP19),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(40,plain,((~(sP15) | ~(sP45)) | sP53),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(41,plain,(sP51 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
15.85/15.96	thf(42,plain,((~(sP13) | sP7) | sP3),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(43,plain,(sP20 | ~(sP39)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
15.85/15.96	thf(44,plain,((~(sP43) | ~(sP53)) | sP20),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(45,plain,(~(sP23) | sP15),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(46,plain,((~(sP28) | ~(sP53)) | sP51),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(47,plain,((~(sP28) | sP53) | ~(sP51)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(48,plain,((~(sP26) | sP45) | sP13),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(49,plain,((~(sP16) | ~(sP53)) | ~(sP20)),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(50,plain,((~(sP16) | sP53) | sP20),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(51,plain,((~(sP50) | ~(sP45)) | sP43),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(52,plain,(~(sP31) | sP23),inference(all_rule,[status(thm)],[])).
15.85/15.96	thf(53,plain,((~(sP1) | ~(sP7)) | sP28),inference(prop_rule,[status(thm)],[])).
15.85/15.96	thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,sP26).
15.85/15.96	thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,sP50).
15.85/15.96	thf(fact_3_lsc__at__MInfty,axiom,sP31).
15.85/15.96	thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,sP1).
15.85/15.96	thf(54,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,h2,fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,fact_3_lsc__at__MInfty,fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062])).
15.85/15.96	thf(55,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[54,h1])).
15.85/15.96	thf(56,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[55,h0])).
15.85/15.96	thf(0,theorem,(~(sP16)),inference(contra,[status(thm),contra(discharge,[h2])],[54,h2])).
15.85/15.96	% SZS output end Proof
15.85/15.96	EOF