0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.13/0.34	% Computer   : n015.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   : 180
0.13/0.34	% DateTime   : Thu Aug 29 13:56:52 EDT 2019
0.13/0.34	% CPUTime    : 
107.89/108.04	% SZS status Theorem
107.89/108.04	% Mode: mode447
107.89/108.04	% Inferences: 120
107.89/108.04	% SZS output start Proof
107.89/108.04	thf(ty_a, type, a : $tType).
107.89/108.04	thf(ty_eigen__6, type, eigen__6 : (a>$o)).
107.89/108.04	thf(ty_eigen__7, type, eigen__7 : a).
107.89/108.04	thf(ty_eigen__1, type, eigen__1 : (a>$o)).
107.89/108.04	thf(ty_eigen__0, type, eigen__0 : (a>$o)).
107.89/108.04	thf(ty_eigen__5, type, eigen__5 : ((a>$o)>$o)).
107.89/108.04	thf(ty_t, type, t : a).
107.89/108.04	thf(ty_cA, type, cA : ((a>$o)>$o)).
107.89/108.04	thf(h0, assumption, (![X1:(a>$o)>$o]:(![X2:a>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
107.89/108.04	thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:a>$o]:(~(((~(((cA @ X1) => (~((![X2:a]:((t = X2) => (X1 @ X2)))))))) => (~(((cA @ X1) => (~((X1 @ t))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
107.89/108.04	thf(h1, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
107.89/108.04	thf(eigendef_eigen__7, definition, eigen__7 = (eps__1 @ (^[X1:a]:(~(((t = X1) => (eigen__1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
107.89/108.04	thf(h2, assumption, (![X1:((a>$o)>$o)>$o]:(![X2:(a>$o)>$o]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])).
107.89/108.04	thf(eigendef_eigen__5, definition, eigen__5 = (eps__2 @ (^[X1:(a>$o)>$o]:(~(((~(((![X2:a>$o]:((X1 @ X2) => (![X3:a]:((t = X3) => (X1 @ (^[X4:a]:((~((X3 = X4))) => (X2 @ X4)))))))) => (~((X1 @ (^[X2:a]:$false))))))) => (X1 @ ((=) @ t))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
107.89/108.04	thf(sP1,plain,sP1 <=> (![X1:a>$o]:((~(((![X2:a>$o]:((~(((cA @ X2) => (~((![X3:a]:((X1 @ X3) => (X2 @ X3)))))))) => (~(((cA @ X2) => (~((X2 @ t)))))))) => (~((![X2:a]:((X1 @ X2) => (eigen__1 @ X2)))))))) => (~((![X2:(a>$o)>$o]:((~(((![X3:a>$o]:((X2 @ X3) => (![X4:a]:((X1 @ X4) => (X2 @ (^[X5:a]:((~((X4 = X5))) => (X3 @ X5)))))))) => (~((X2 @ (^[X3:a]:$false))))))) => (X2 @ X1))))))),introduced(definition,[new_symbols(definition,[sP1])])).
107.89/108.04	thf(sP2,plain,sP2 <=> ((![X1:a>$o]:((eigen__5 @ X1) => (![X2:a]:((t = X2) => (eigen__5 @ (^[X3:a]:((~((X2 = X3))) => (X1 @ X3)))))))) => (~((eigen__5 @ (^[X1:a]:$false))))),introduced(definition,[new_symbols(definition,[sP2])])).
107.89/108.04	thf(sP3,plain,sP3 <=> (![X1:a]:((t = X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
107.89/108.04	thf(sP4,plain,sP4 <=> ((cA @ eigen__6) => (~((eigen__6 @ t)))),introduced(definition,[new_symbols(definition,[sP4])])).
107.89/108.04	thf(sP5,plain,sP5 <=> ((t = eigen__7) => (eigen__1 @ eigen__7)),introduced(definition,[new_symbols(definition,[sP5])])).
107.89/108.04	thf(sP6,plain,sP6 <=> ((~(((cA @ eigen__6) => (~((![X1:a]:((t = X1) => (eigen__6 @ X1)))))))) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP6])])).
107.89/108.04	thf(sP7,plain,sP7 <=> (![X1:(a>$o)>$o]:((~(((![X2:a>$o]:((X1 @ X2) => (![X3:a]:((t = X3) => (X1 @ (^[X4:a]:((~((X3 = X4))) => (X2 @ X4)))))))) => (~((X1 @ (^[X2:a]:$false))))))) => (X1 @ ((=) @ t)))),introduced(definition,[new_symbols(definition,[sP7])])).
107.89/108.04	thf(sP8,plain,sP8 <=> (eigen__5 @ ((=) @ t)),introduced(definition,[new_symbols(definition,[sP8])])).
107.89/108.04	thf(sP9,plain,sP9 <=> (t = eigen__7),introduced(definition,[new_symbols(definition,[sP9])])).
107.89/108.04	thf(sP10,plain,sP10 <=> (eigen__6 @ t),introduced(definition,[new_symbols(definition,[sP10])])).
107.89/108.04	thf(sP11,plain,sP11 <=> (t = t),introduced(definition,[new_symbols(definition,[sP11])])).
107.89/108.04	thf(sP12,plain,sP12 <=> (eigen__1 @ eigen__7),introduced(definition,[new_symbols(definition,[sP12])])).
107.89/108.04	thf(sP13,plain,sP13 <=> (![X1:a>$o]:((~(((cA @ X1) => (~((![X2:a]:((t = X2) => (X1 @ X2)))))))) => (~(((cA @ X1) => (~((X1 @ t)))))))),introduced(definition,[new_symbols(definition,[sP13])])).
107.89/108.04	thf(sP14,plain,sP14 <=> (![X1:a]:((t = X1) => (eigen__5 @ ((=) @ X1)))),introduced(definition,[new_symbols(definition,[sP14])])).
107.89/108.04	thf(sP15,plain,sP15 <=> ((~(sP2)) => sP8),introduced(definition,[new_symbols(definition,[sP15])])).
107.89/108.04	thf(sP16,plain,sP16 <=> ((~((sP13 => (~(sP3))))) => (~(sP7))),introduced(definition,[new_symbols(definition,[sP16])])).
107.89/108.04	thf(sP17,plain,sP17 <=> (cA @ eigen__6),introduced(definition,[new_symbols(definition,[sP17])])).
107.89/108.04	thf(sP18,plain,sP18 <=> ((eigen__5 @ (^[X1:a]:$false)) => sP14),introduced(definition,[new_symbols(definition,[sP18])])).
107.89/108.04	thf(sP19,plain,sP19 <=> (sP13 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP19])])).
107.89/108.04	thf(sP20,plain,sP20 <=> (sP11 => sP10),introduced(definition,[new_symbols(definition,[sP20])])).
107.89/108.04	thf(sP21,plain,sP21 <=> (cA @ eigen__0),introduced(definition,[new_symbols(definition,[sP21])])).
107.89/108.04	thf(sP22,plain,sP22 <=> (sP11 => sP8),introduced(definition,[new_symbols(definition,[sP22])])).
107.89/108.04	thf(sP23,plain,sP23 <=> (sP17 => (~((![X1:a]:((t = X1) => (eigen__6 @ X1)))))),introduced(definition,[new_symbols(definition,[sP23])])).
107.89/108.04	thf(sP24,plain,sP24 <=> (eigen__1 @ t),introduced(definition,[new_symbols(definition,[sP24])])).
107.89/108.04	thf(sP25,plain,sP25 <=> (![X1:a>$o]:((eigen__5 @ X1) => (![X2:a]:((t = X2) => (eigen__5 @ (^[X3:a]:((~((X2 = X3))) => (X1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP25])])).
107.89/108.04	thf(sP26,plain,sP26 <=> (![X1:a]:((t = X1) => (eigen__6 @ X1))),introduced(definition,[new_symbols(definition,[sP26])])).
107.89/108.04	thf(sP27,plain,sP27 <=> (eigen__5 @ (^[X1:a]:$false)),introduced(definition,[new_symbols(definition,[sP27])])).
107.89/108.04	thf(cDOMLEMMA5_pme,conjecture,(~(((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (cA @ X1))) => (~((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (~((![X2:a>$o]:((~(((![X3:a>$o]:((~(((cA @ X3) => (~((![X4:a]:((X2 @ X4) => (X3 @ X4)))))))) => (~(((cA @ X3) => (~((X3 @ t)))))))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (~((![X3:(a>$o)>$o]:((~(((![X4:a>$o]:((X3 @ X4) => (![X5:a]:((X2 @ X5) => (X3 @ (^[X6:a]:((~((X5 = X6))) => (X4 @ X6)))))))) => (~((X3 @ (^[X4:a]:$false))))))) => (X3 @ X2))))))))))))))))).
107.89/108.04	thf(h3,negated_conjecture,((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (cA @ X1))) => (~((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (~((![X2:a>$o]:((~(((![X3:a>$o]:((~(((cA @ X3) => (~((![X4:a]:((X2 @ X4) => (X3 @ X4)))))))) => (~(((cA @ X3) => (~((X3 @ t)))))))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (~((![X3:(a>$o)>$o]:((~(((![X4:a>$o]:((X3 @ X4) => (![X5:a]:((X2 @ X5) => (X3 @ (^[X6:a]:((~((X5 = X6))) => (X4 @ X6)))))))) => (~((X3 @ (^[X4:a]:$false))))))) => (X3 @ X2)))))))))))))),inference(assume_negation,[status(cth)],[cDOMLEMMA5_pme])).
107.89/108.04	thf(h4,assumption,(~((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (cA @ X1))))),introduced(assumption,[])).
107.89/108.04	thf(h5,assumption,(~((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (~((![X2:a>$o]:((~(((![X3:a>$o]:((~(((cA @ X3) => (~((![X4:a]:((X2 @ X4) => (X3 @ X4)))))))) => (~(((cA @ X3) => (~((X3 @ t)))))))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (~((![X3:(a>$o)>$o]:((~(((![X4:a>$o]:((X3 @ X4) => (![X5:a]:((X2 @ X5) => (X3 @ (^[X6:a]:((~((X5 = X6))) => (X4 @ X6)))))))) => (~((X3 @ (^[X4:a]:$false))))))) => (X3 @ X2))))))))))))),introduced(assumption,[])).
107.89/108.04	thf(h6,assumption,(~(((~(((eigen__0 @ t) => (~(sP21))))) => sP21))),introduced(assumption,[])).
107.89/108.04	thf(h7,assumption,(~(((eigen__0 @ t) => (~(sP21))))),introduced(assumption,[])).
107.89/108.04	thf(h8,assumption,(~(sP21)),introduced(assumption,[])).
107.89/108.04	thf(h9,assumption,(eigen__0 @ t),introduced(assumption,[])).
107.89/108.04	thf(h10,assumption,sP21,introduced(assumption,[])).
107.89/108.04	thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h3,h2,h1,h0])],[h10,h8])).
107.89/108.04	thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,1,h9,h10])).
107.89/108.04	thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,2,h7,h8])).
107.89/108.04	thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h4,3,h6])).
107.89/108.04	thf(h11,assumption,(~(((~((sP24 => (~((cA @ eigen__1)))))) => (~(sP1))))),introduced(assumption,[])).
107.89/108.04	thf(h12,assumption,(~((sP24 => (~((cA @ eigen__1)))))),introduced(assumption,[])).
107.89/108.04	thf(h13,assumption,sP1,introduced(assumption,[])).
107.89/108.04	thf(h14,assumption,sP24,introduced(assumption,[])).
107.89/108.04	thf(h15,assumption,(cA @ eigen__1),introduced(assumption,[])).
107.89/108.04	thf(5,plain,sP11,inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(6,plain,(~(sP14) | sP22),inference(all_rule,[status(thm)],[])).
107.89/108.04	thf(7,plain,((~(sP22) | ~(sP11)) | sP8),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(8,plain,((~(sP24) | sP12) | ~(sP9)),inference(mating_rule,[status(thm)],[])).
107.89/108.04	thf(9,plain,((~(sP20) | ~(sP11)) | sP10),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(10,plain,(~(sP26) | sP20),inference(all_rule,[status(thm)],[])).
107.89/108.04	thf(11,plain,((~(sP18) | ~(sP27)) | sP14),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(12,plain,(~(sP25) | sP18),inference(all_rule,[status(thm)],[])).
107.89/108.04	thf(13,plain,((~(sP4) | ~(sP17)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(14,plain,(sP23 | sP26),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(15,plain,(sP23 | sP17),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(16,plain,(sP2 | sP27),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(17,plain,(sP2 | sP25),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(18,plain,(sP5 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(19,plain,(sP5 | sP9),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(20,plain,(sP6 | sP4),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(21,plain,(sP6 | ~(sP23)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(22,plain,(sP15 | ~(sP8)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(23,plain,(sP15 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(24,plain,(sP3 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7])).
107.89/108.04	thf(25,plain,(sP13 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
107.89/108.04	thf(26,plain,(sP7 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5])).
107.89/108.04	thf(27,plain,((~(sP19) | ~(sP13)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(28,plain,((~(sP16) | sP19) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
107.89/108.04	thf(29,plain,(~(sP1) | sP16),inference(all_rule,[status(thm)],[])).
107.89/108.04	thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h5,h3,h2,h1,h0])],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,h14,h13])).
107.89/108.04	thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,30,h14,h15])).
107.89/108.04	thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,31,h12,h13])).
107.89/108.04	thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h5,32,h11])).
107.89/108.04	thf(34,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h2,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,4,33,h4,h5])).
107.89/108.04	thf(35,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[34,h2])).
107.89/108.04	thf(36,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[35,h1])).
107.89/108.04	thf(37,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[36,h0])).
107.89/108.04	thf(0,theorem,(~(((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (cA @ X1))) => (~((![X1:a>$o]:((~(((X1 @ t) => (~((cA @ X1)))))) => (~((![X2:a>$o]:((~(((![X3:a>$o]:((~(((cA @ X3) => (~((![X4:a]:((X2 @ X4) => (X3 @ X4)))))))) => (~(((cA @ X3) => (~((X3 @ t)))))))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (~((![X3:(a>$o)>$o]:((~(((![X4:a>$o]:((X3 @ X4) => (![X5:a]:((X2 @ X5) => (X3 @ (^[X6:a]:((~((X5 = X6))) => (X4 @ X6)))))))) => (~((X3 @ (^[X4:a]:$false))))))) => (X3 @ X2)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h3])],[34,h3])).
107.89/108.04	% SZS output end Proof
107.89/108.04	EOF