0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.35 Computer : n023.cluster.edu 0.12/0.35 Model : x86_64 x86_64 0.12/0.35 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.35 RAMPerCPU : 8042.1875MB 0.12/0.35 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.36 % CPULimit : 960 0.12/0.36 % DateTime : Tue Aug 9 03:20:43 EDT 2022 0.12/0.36 % CPUTime : 56.49/56.96 % SZS status Theorem 56.49/56.96 % Mode: mode466 56.49/56.96 % Inferences: 74728 56.49/56.96 % SZS output start Proof 56.49/56.96 thf(ty_eigen__35, type, eigen__35 : ($i>$o)). 56.49/56.96 thf(ty_eigen__52, type, eigen__52 : ($i>$o)). 56.49/56.96 thf(ty_eigen__0, type, eigen__0 : $i). 56.49/56.96 thf(ty_eigen__59, type, eigen__59 : ($i>$o)). 56.49/56.96 thf(ty_eigen__67, type, eigen__67 : $i). 56.49/56.96 thf(ty_eigen__51, type, eigen__51 : $i). 56.49/56.96 thf(ty_eigen__65, type, eigen__65 : ($i>$o)). 56.49/56.96 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). 56.49/56.96 thf(eigendef_eigen__51, definition, eigen__51 = (eps__0 @ (^[X1:$i]:(~(((~((eigen__35 @ X1))) => (~((eigen__35 @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__51])])). 56.49/56.96 thf(eigendef_eigen__67, definition, eigen__67 = (eps__0 @ (^[X1:$i]:(~(((~((eigen__65 @ X1))) => (~((eigen__52 @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__67])])). 56.49/56.96 thf(h1, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). 56.49/56.96 thf(eigendef_eigen__65, definition, eigen__65 = (eps__1 @ (^[X1:$i>$o]:(~(((~(((![X2:$i]:((~((eigen__59 @ X2))) => (~((eigen__52 @ X2))))) => (~((![X2:$i]:((eigen__59 @ X2) => (X1 @ X2)))))))) => (![X2:$i]:((~((X1 @ X2))) => (~((eigen__52 @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__65])])). 56.49/56.96 thf(eigendef_eigen__35, definition, eigen__35 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i]:((~((X1 @ X2))) => (~((X1 @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__35])])). 56.49/56.96 thf(eigendef_eigen__59, definition, eigen__59 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i>$o]:((~(((![X3:$i]:((~((X1 @ X3))) => (~((eigen__52 @ X3))))) => (~((![X3:$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:$i]:((~((X2 @ X3))) => (~((eigen__52 @ X3))))))))))), introduced(definition,[new_symbols(definition,[eigen__59])])). 56.49/56.96 thf(eigendef_eigen__52, definition, eigen__52 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((~((X2 @ X4))) => (~((X1 @ X4))))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:((~((X3 @ X4))) => (~((X1 @ X4)))))))))))), introduced(definition,[new_symbols(definition,[eigen__52])])). 56.49/56.96 thf(sP1,plain,sP1 <=> (![X1:$i]:((~((eigen__65 @ X1))) => (~((eigen__52 @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])). 56.49/56.96 thf(sP2,plain,sP2 <=> (![X1:($i>$o)>($i>$o)>$i>$o]:((~(((~((![X2:$i]:((~($false)) => (((X1 @ (^[X3:$i]:(~($false)))) @ (^[X3:$i]:$false)) @ X2))))) => (~((![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i>$o]:((~(((![X5:$i]:((~((X3 @ X5))) => (((X1 @ X2) @ X3) @ X5))) => (~((![X5:$i]:((~((((X1 @ X3) @ X4) @ X5))) => (X4 @ X5)))))))) => (![X5:$i]:((~((X4 @ X5))) => (((X1 @ X2) @ X4) @ X5)))))))))))) => (~((![X2:$i>$o]:(![X3:$i]:((~((X2 @ X3))) => (((X1 @ X2) @ X2) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP2])])). 56.49/56.96 thf(sP3,plain,sP3 <=> (![X1:$i]:((~((eigen__59 @ X1))) => (~((eigen__52 @ X1))))),introduced(definition,[new_symbols(definition,[sP3])])). 56.49/56.96 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((~((X2 @ X4))) => (~((X1 @ X4))))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:((~((X3 @ X4))) => (~((X1 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP4])])). 56.49/56.96 thf(sP5,plain,sP5 <=> ((~((![X1:$i]:$false))) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP5])])). 56.49/56.96 thf(sP6,plain,sP6 <=> (![X1:$i]:((~((eigen__35 @ X1))) => (~((eigen__35 @ X1))))),introduced(definition,[new_symbols(definition,[sP6])])). 56.49/56.96 thf(sP7,plain,sP7 <=> ((~((eigen__35 @ eigen__51))) => (~((eigen__35 @ eigen__51)))),introduced(definition,[new_symbols(definition,[sP7])])). 56.49/56.96 thf(sP8,plain,sP8 <=> ((~((eigen__59 @ eigen__67))) => (~((eigen__52 @ eigen__67)))),introduced(definition,[new_symbols(definition,[sP8])])). 56.49/56.96 thf(sP9,plain,sP9 <=> (![X1:$i>$o]:(![X2:$i>$o]:((~(((![X3:$i]:((~((X1 @ X3))) => (~((eigen__52 @ X3))))) => (~((![X3:$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:$i]:((~((X2 @ X3))) => (~((eigen__52 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP9])])). 56.49/56.96 thf(sP10,plain,sP10 <=> (eigen__52 @ eigen__67),introduced(definition,[new_symbols(definition,[sP10])])). 56.49/56.96 thf(sP11,plain,sP11 <=> (![X1:$i]:$false),introduced(definition,[new_symbols(definition,[sP11])])). 56.49/56.96 thf(sP12,plain,sP12 <=> (sP3 => (~((![X1:$i]:((eigen__59 @ X1) => (eigen__65 @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])). 56.49/56.96 thf(sP13,plain,sP13 <=> ((~(sP5)) => (~((![X1:$i>$o]:(![X2:$i]:((~((X1 @ X2))) => (~((X1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP13])])). 56.49/56.96 thf(sP14,plain,sP14 <=> ((~((eigen__65 @ eigen__67))) => (~(sP10))),introduced(definition,[new_symbols(definition,[sP14])])). 56.49/56.96 thf(sP15,plain,sP15 <=> $false,introduced(definition,[new_symbols(definition,[sP15])])). 56.49/56.96 thf(sP16,plain,sP16 <=> ((eigen__59 @ eigen__67) => (eigen__65 @ eigen__67)),introduced(definition,[new_symbols(definition,[sP16])])). 56.49/56.96 thf(sP17,plain,sP17 <=> (![X1:$i>$o]:(![X2:$i]:((~((X1 @ X2))) => (~((X1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP17])])). 56.49/56.96 thf(sP18,plain,sP18 <=> ((~(sP12)) => sP1),introduced(definition,[new_symbols(definition,[sP18])])). 56.49/56.96 thf(sP19,plain,sP19 <=> (![X1:($i>$o)>($i>$o)>$i>$o]:(![X2:($i>$o)>($i>$o)>$i>$o]:((~(((~((![X3:$i]:((~((((X1 @ (^[X4:$i]:(~(sP15)))) @ (^[X4:$i]:sP15)) @ X3))) => (((X2 @ (^[X4:$i]:(~(sP15)))) @ (^[X4:$i]:sP15)) @ X3))))) => (~((![X3:$i>$o]:(![X4:$i>$o]:(![X5:$i>$o]:((~(((![X6:$i]:((~((((X1 @ X3) @ X4) @ X6))) => (((X2 @ X3) @ X4) @ X6))) => (~((![X6:$i]:((~((((X2 @ X4) @ X5) @ X6))) => (((X1 @ X4) @ X5) @ X6)))))))) => (![X6:$i]:((~((((X1 @ X3) @ X5) @ X6))) => (((X2 @ X3) @ X5) @ X6)))))))))))) => (~((![X3:$i>$o]:(![X4:$i]:((~((((X1 @ X3) @ X3) @ X4))) => (((X2 @ X3) @ X3) @ X4))))))))),introduced(definition,[new_symbols(definition,[sP19])])). 56.49/56.96 thf(sP20,plain,sP20 <=> (![X1:$i>$o]:((~((sP3 => (~((![X2:$i]:((eigen__59 @ X2) => (X1 @ X2)))))))) => (![X2:$i]:((~((X1 @ X2))) => (~((eigen__52 @ X2))))))),introduced(definition,[new_symbols(definition,[sP20])])). 56.49/56.96 thf(sP21,plain,sP21 <=> (eigen__59 @ eigen__67),introduced(definition,[new_symbols(definition,[sP21])])). 56.49/56.96 thf(sP22,plain,sP22 <=> (eigen__35 @ eigen__51),introduced(definition,[new_symbols(definition,[sP22])])). 56.49/56.96 thf(sP23,plain,sP23 <=> (![X1:$i]:((eigen__59 @ X1) => (eigen__65 @ X1))),introduced(definition,[new_symbols(definition,[sP23])])). 56.49/56.96 thf(sP24,plain,sP24 <=> (eigen__65 @ eigen__67),introduced(definition,[new_symbols(definition,[sP24])])). 56.49/56.96 thf(cTHM120D_pme,conjecture,(~(sP19))). 56.49/56.96 thf(h2,negated_conjecture,sP19,inference(assume_negation,[status(cth)],[cTHM120D_pme])). 56.49/56.96 thf(1,plain,((~(sP8) | sP21) | ~(sP10)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(2,plain,((~(sP16) | ~(sP21)) | sP24),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(3,plain,(~(sP23) | sP16),inference(all_rule,[status(thm)],[])). 56.49/56.96 thf(4,plain,(~(sP3) | sP8),inference(all_rule,[status(thm)],[])). 56.49/56.96 thf(5,plain,(sP14 | sP10),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(6,plain,(sP14 | ~(sP24)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(7,plain,(sP12 | sP23),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(8,plain,(sP12 | sP3),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(9,plain,(sP1 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__67])). 56.49/56.96 thf(10,plain,(sP18 | ~(sP1)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(11,plain,(sP18 | ~(sP12)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(12,plain,(sP20 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__65])). 56.49/56.96 thf(13,plain,(sP9 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__59])). 56.49/56.96 thf(14,plain,(sP7 | sP22),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(15,plain,(sP7 | ~(sP22)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(16,plain,(sP4 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__52])). 56.49/56.96 thf(17,plain,(sP6 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__51])). 56.49/56.96 thf(18,plain,~(sP15),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(19,plain,((~(sP5) | sP11) | ~(sP4)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(20,plain,((~(sP13) | sP5) | ~(sP17)),inference(prop_rule,[status(thm)],[])). 56.49/56.96 thf(21,plain,(sP17 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__35])). 56.49/56.96 thf(22,plain,(~(sP2) | sP13),inference(all_rule,[status(thm)],[])). 56.49/56.96 thf(23,plain,(~(sP19) | sP2),inference(all_rule,[status(thm)],[])). 56.49/56.96 thf(24,plain,(~(sP11) | sP15),inference(all_rule,[status(thm)],[])). 56.49/56.96 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h2])). 56.49/56.96 thf(26,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[25,h1])). 56.49/56.96 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[26,h0])). 56.49/56.96 thf(0,theorem,(~(sP19)),inference(contra,[status(thm),contra(discharge,[h2])],[25,h2])). 56.49/56.96 % SZS output end Proof 56.49/56.96 EOF