0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.09/0.29 Computer : n017.cluster.edu 0.09/0.29 Model : x86_64 x86_64 0.09/0.29 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.29 RAMPerCPU : 8042.1875MB 0.09/0.29 OS : Linux 3.10.0-693.el7.x86_64 0.09/0.29 % CPULimit : 960 0.09/0.29 % DateTime : Tue Aug 9 02:34:59 EDT 2022 0.09/0.30 % CPUTime : 102.09/102.57 % SZS status Theorem 102.09/102.57 % Mode: mode453 102.09/102.57 % Inferences: 477 102.09/102.57 % SZS output start Proof 102.09/102.57 thf(ty_cP, type, cP : ($i>$o)). 102.09/102.57 thf(ty_eigen__11, type, eigen__11 : $i). 102.09/102.57 thf(ty_eigen__10, type, eigen__10 : $i). 102.09/102.57 thf(ty_eigen__8, type, eigen__8 : ($i>$o)). 102.09/102.57 thf(ty_eigen__9, type, eigen__9 : $i). 102.09/102.57 thf(ty_cQ, type, cQ : ($i>$o)). 102.09/102.57 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). 102.09/102.57 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~(((eigen__8 @ X1) => (~(((cQ @ X1) => (~((cP @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). 102.09/102.57 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~(((~(((cQ @ X1) => (~((cP @ X1)))))) => (cP @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__10])])). 102.09/102.57 thf(h1, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). 102.09/102.57 thf(eigendef_eigen__8, definition, eigen__8 = (eps__1 @ (^[X1:$i>$o]:(~(((~(((![X2:$i]:((X1 @ X2) => (cP @ X2))) => (~((![X2:$i]:((X1 @ X2) => (cQ @ X2)))))))) => (![X2:$i]:((X1 @ X2) => (~(((cQ @ X2) => (~((cP @ X2))))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). 102.09/102.57 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~(((~(((cQ @ X1) => (~((cP @ X1)))))) => (cQ @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__9])])). 102.09/102.57 thf(sP1,plain,sP1 <=> ((~(((![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cP @ X1))) => (~((![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cQ @ X1)))))))) => (~((![X1:$i>$o]:((~(((![X2:$i]:((X1 @ X2) => (cP @ X2))) => (~((![X2:$i]:((X1 @ X2) => (cQ @ X2)))))))) => (![X2:$i]:((X1 @ X2) => (~(((cQ @ X2) => (~((cP @ X2))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). 102.09/102.57 thf(sP2,plain,sP2 <=> (![X1:$i]:((eigen__8 @ X1) => (~(((cQ @ X1) => (~((cP @ X1)))))))),introduced(definition,[new_symbols(definition,[sP2])])). 102.09/102.57 thf(sP3,plain,sP3 <=> ((cQ @ eigen__9) => (~((cP @ eigen__9)))),introduced(definition,[new_symbols(definition,[sP3])])). 102.09/102.57 thf(sP4,plain,sP4 <=> (![X1:$i]:((eigen__8 @ X1) => (cP @ X1))),introduced(definition,[new_symbols(definition,[sP4])])). 102.09/102.57 thf(sP5,plain,sP5 <=> ((cQ @ eigen__11) => (~((cP @ eigen__11)))),introduced(definition,[new_symbols(definition,[sP5])])). 102.09/102.57 thf(sP6,plain,sP6 <=> (![X1:$i>$o]:((~(((![X2:$i]:((X1 @ X2) => (cP @ X2))) => (~((![X2:$i]:((X1 @ X2) => (cQ @ X2)))))))) => (![X2:$i]:((X1 @ X2) => (~(((cQ @ X2) => (~((cP @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). 102.09/102.57 thf(sP7,plain,sP7 <=> (cP @ eigen__10),introduced(definition,[new_symbols(definition,[sP7])])). 102.09/102.57 thf(sP8,plain,sP8 <=> (cQ @ eigen__11),introduced(definition,[new_symbols(definition,[sP8])])). 102.09/102.57 thf(sP9,plain,sP9 <=> ((![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cP @ X1))) => (~((![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cQ @ X1)))))),introduced(definition,[new_symbols(definition,[sP9])])). 102.09/102.57 thf(sP10,plain,sP10 <=> (sP4 => (~((![X1:$i]:((eigen__8 @ X1) => (cQ @ X1)))))),introduced(definition,[new_symbols(definition,[sP10])])). 102.09/102.57 thf(sP11,plain,sP11 <=> ((eigen__8 @ eigen__11) => (cP @ eigen__11)),introduced(definition,[new_symbols(definition,[sP11])])). 102.09/102.57 thf(sP12,plain,sP12 <=> (![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cQ @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). 102.09/102.57 thf(sP13,plain,sP13 <=> ((eigen__8 @ eigen__11) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP13])])). 102.09/102.57 thf(sP14,plain,sP14 <=> (![X1:$i]:((~(((cQ @ X1) => (~((cP @ X1)))))) => (cP @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). 102.09/102.57 thf(sP15,plain,sP15 <=> (cQ @ eigen__9),introduced(definition,[new_symbols(definition,[sP15])])). 102.09/102.57 thf(sP16,plain,sP16 <=> ((cQ @ eigen__10) => (~(sP7))),introduced(definition,[new_symbols(definition,[sP16])])). 102.09/102.57 thf(sP17,plain,sP17 <=> (![X1:$i>$o]:((~(((![X2:$i]:((X1 @ X2) => (cP @ X2))) => (~((![X2:$i]:((X1 @ X2) => (cQ @ X2)))))))) => (~((![X2:$i>$o]:((~(((![X3:$i]:((X2 @ X3) => (cP @ X3))) => (~((![X3:$i]:((X2 @ X3) => (cQ @ X3)))))))) => (![X3:$i]:((X2 @ X3) => (X1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP17])])). 102.09/102.57 thf(sP18,plain,sP18 <=> (eigen__8 @ eigen__11),introduced(definition,[new_symbols(definition,[sP18])])). 102.09/102.57 thf(sP19,plain,sP19 <=> (![X1:$i]:((eigen__8 @ X1) => (cQ @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). 102.09/102.57 thf(sP20,plain,sP20 <=> ((~(sP16)) => sP7),introduced(definition,[new_symbols(definition,[sP20])])). 102.09/102.57 thf(sP21,plain,sP21 <=> ((~(sP10)) => sP2),introduced(definition,[new_symbols(definition,[sP21])])). 102.09/102.57 thf(sP22,plain,sP22 <=> ((~(sP3)) => sP15),introduced(definition,[new_symbols(definition,[sP22])])). 102.09/102.57 thf(sP23,plain,sP23 <=> (sP18 => sP8),introduced(definition,[new_symbols(definition,[sP23])])). 102.09/102.57 thf(sP24,plain,sP24 <=> (cP @ eigen__11),introduced(definition,[new_symbols(definition,[sP24])])). 102.09/102.57 thf(cTHM590_pme,conjecture,(~(sP17))). 102.09/102.57 thf(h2,negated_conjecture,sP17,inference(assume_negation,[status(cth)],[cTHM590_pme])). 102.09/102.57 thf(1,plain,((~(sP11) | ~(sP18)) | sP24),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(2,plain,((~(sP23) | ~(sP18)) | sP8),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(3,plain,(~(sP19) | sP23),inference(all_rule,[status(thm)],[])). 102.09/102.57 thf(4,plain,(~(sP4) | sP11),inference(all_rule,[status(thm)],[])). 102.09/102.57 thf(5,plain,((~(sP5) | ~(sP8)) | ~(sP24)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(6,plain,(sP13 | sP5),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(7,plain,(sP13 | sP18),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(8,plain,(sP10 | sP19),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(9,plain,(sP10 | sP4),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(10,plain,(sP2 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). 102.09/102.57 thf(11,plain,(sP21 | ~(sP2)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(12,plain,(sP21 | ~(sP10)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(13,plain,(sP3 | sP15),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(14,plain,(sP22 | ~(sP15)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(15,plain,(sP22 | ~(sP3)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(16,plain,(sP16 | sP7),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(17,plain,(sP20 | ~(sP7)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(18,plain,(sP20 | ~(sP16)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(19,plain,(sP14 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])). 102.09/102.57 thf(20,plain,(sP12 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])). 102.09/102.57 thf(21,plain,((~(sP9) | ~(sP14)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(22,plain,(sP6 | ~(sP21)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8])). 102.09/102.57 thf(23,plain,((~(sP1) | sP9) | ~(sP6)),inference(prop_rule,[status(thm)],[])). 102.09/102.57 thf(24,plain,(~(sP17) | sP1),inference(all_rule,[status(thm)],[])). 102.09/102.57 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h2])). 102.09/102.57 thf(26,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[25,h1])). 102.09/102.57 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[26,h0])). 102.09/102.57 thf(0,theorem,(~(sP17)),inference(contra,[status(thm),contra(discharge,[h2])],[25,h2])). 102.09/102.57 % SZS output end Proof 102.09/102.57 EOF