%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PHI005^2 : TPTP v9.2.0. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 02:13:38 PM UTC 2025 % Result : Theorem 13.13s 13.42s % Output : Proof 13.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PHI005^2 : TPTP v9.2.0. Released v6.1.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n023.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 : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 23:16:53 EDT 2025 % 0.13/0.34 % CPUTime : % 13.13/13.42 % SZS status Theorem % 13.13/13.42 % Mode: mode454 % 13.13/13.42 % Inferences: 3384 % 13.13/13.42 % SZS output start Proof % 13.13/13.42 thf(ty_mu, type, mu : $tType). % 13.13/13.42 thf(ty_eigen__1, type, eigen__1 : $i). % 13.13/13.42 thf(ty_eigen__0, type, eigen__0 : $i). % 13.13/13.42 thf(ty_positive, type, positive : ((mu>$i>$o)>$i>$o)). % 13.13/13.42 thf(ty_eigen__8, type, eigen__8 : $i). % 13.13/13.42 thf(ty_eigen__9, type, eigen__9 : mu). % 13.13/13.42 thf(ty_essence, type, essence : ((mu>$i>$o)>mu>$i>$o)). % 13.13/13.42 thf(ty_rel, type, rel : ($i>$i>$o)). % 13.13/13.42 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.13/13.42 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__0) @ X1) => (~((![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.13/13.42 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.13/13.42 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__1) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 13.13/13.42 thf(h1, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 13.13/13.42 thf(eigendef_eigen__9, definition, eigen__9 = (eps__1 @ (^[X1:mu]:(~((~((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__8) => ((X2 @ X1) @ eigen__8))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 13.13/13.42 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (((essence @ (^[X3:mu]:(^[X4:$i]:(![X5:mu>$i>$o]:(((positive @ X5) @ X4) => ((X5 @ X3) @ X4)))))) @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])). % 13.13/13.42 thf(sP2,plain,sP2 <=> (((rel @ eigen__0) @ eigen__1) => (~((![X1:mu]:(~((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__1) => ((X2 @ X1) @ eigen__1))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.13/13.42 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((rel @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.13/13.42 thf(sP4,plain,sP4 <=> ((((essence @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__9) @ eigen__8) => (![X1:$i]:(((rel @ eigen__8) @ X1) => (~((![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.13/13.42 thf(sP5,plain,sP5 <=> (![X1:mu]:((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__8) => ((X2 @ X1) @ eigen__8))) => (((essence @ (^[X2:mu]:(^[X3:$i]:(![X4:mu>$i>$o]:(((positive @ X4) @ X3) => ((X4 @ X2) @ X3)))))) @ X1) @ eigen__8))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.13/13.42 thf(sP6,plain,sP6 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (~((![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.13/13.42 thf(sP7,plain,sP7 <=> (((essence @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__9) @ eigen__8),introduced(definition,[new_symbols(definition,[sP7])])). % 13.13/13.42 thf(sP8,plain,sP8 <=> (![X1:mu>$i>$o]:((((essence @ X1) @ eigen__9) @ eigen__8) => (![X2:$i]:(((rel @ eigen__8) @ X2) => (~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.13/13.42 thf(sP9,plain,sP9 <=> (![X1:mu]:(~((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__1) => ((X2 @ X1) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.13/13.42 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 13.13/13.42 thf(sP11,plain,sP11 <=> (((rel @ eigen__1) @ eigen__8) => ((rel @ eigen__8) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP11])])). % 13.13/13.42 thf(sP12,plain,sP12 <=> (![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 13.13/13.42 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel @ eigen__8) @ X1) => (~((![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 13.13/13.42 thf(sP14,plain,sP14 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 13.13/13.42 thf(sP15,plain,sP15 <=> (((rel @ eigen__8) @ eigen__1) => (~(sP9))),introduced(definition,[new_symbols(definition,[sP15])])). % 13.13/13.42 thf(sP16,plain,sP16 <=> (((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((((essence @ X3) @ X1) @ X2) => (![X4:$i]:(((rel @ X2) @ X4) => (~((![X5:mu]:(~(((X3 @ X5) @ X4))))))))))))) @ eigen__8) => sP8),introduced(definition,[new_symbols(definition,[sP16])])). % 13.13/13.42 thf(sP17,plain,sP17 <=> (((rel @ eigen__1) @ eigen__8) => (![X1:mu]:(~((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__8) => ((X2 @ X1) @ eigen__8))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 13.13/13.42 thf(sP18,plain,sP18 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((rel @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.13/13.42 thf(sP19,plain,sP19 <=> ((![X1:mu>$i>$o]:(((positive @ X1) @ eigen__8) => ((X1 @ eigen__9) @ eigen__8))) => sP7),introduced(definition,[new_symbols(definition,[sP19])])). % 13.13/13.42 thf(sP20,plain,sP20 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((((essence @ X3) @ X1) @ X2) => (![X4:$i]:(((rel @ X2) @ X4) => (~((![X5:mu]:(~(((X3 @ X5) @ X4))))))))))))) @ eigen__8),introduced(definition,[new_symbols(definition,[sP20])])). % 13.13/13.42 thf(sP21,plain,sP21 <=> ((rel @ eigen__1) @ eigen__8),introduced(definition,[new_symbols(definition,[sP21])])). % 13.13/13.42 thf(sP22,plain,sP22 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__8) => ((X1 @ eigen__9) @ eigen__8))),introduced(definition,[new_symbols(definition,[sP22])])). % 13.13/13.42 thf(sP23,plain,sP23 <=> (![X1:mu]:(~((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__8) => ((X2 @ X1) @ eigen__8)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 13.13/13.42 thf(sP24,plain,sP24 <=> ((!!) @ (positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((((essence @ X3) @ X1) @ X2) => (![X4:$i]:(((rel @ X2) @ X4) => (~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 13.13/13.42 thf(sP25,plain,sP25 <=> ((rel @ eigen__8) @ eigen__1),introduced(definition,[new_symbols(definition,[sP25])])). % 13.13/13.42 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 13.13/13.42 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.13/13.42 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 13.13/13.42 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.13/13.42 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.13/13.42 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 13.13/13.42 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))). % 13.13/13.42 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))). % 13.13/13.42 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 13.13/13.42 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))). % 13.13/13.42 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 13.13/13.42 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))). % 13.13/13.42 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 13.13/13.42 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))). % 13.13/13.42 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 13.13/13.42 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 13.13/13.42 thf(def_mbox_generic,definition,(mbox_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.13/13.42 thf(def_mdia_generic,definition,(mdia_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 13.13/13.42 thf(def_mbox,definition,(mbox = (mbox_generic @ rel))). % 13.13/13.42 thf(def_mdia,definition,(mdia = (mdia_generic @ rel))). % 13.13/13.42 thf(def_mvalid,definition,(mvalid = (!!))). % 13.13/13.42 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.13/13.42 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 13.13/13.42 thf(def_god,definition,(god = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (positive @ X2)) @ (X2 @ X1))))))). % 13.13/13.42 thf(def_necessary_existence,definition,(necessary_existence = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ ((essence @ X2) @ X1)) @ (mbox @ (mexists_ind @ X2)))))))). % 13.13/13.42 thf(thmT3,conjecture,sP14). % 13.13/13.42 thf(h2,negated_conjecture,(~(sP14)),inference(assume_negation,[status(cth)],[thmT3])). % 13.13/13.42 thf(1,plain,(~(sP13) | sP15),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(2,plain,((~(sP15) | ~(sP25)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(3,plain,(~(sP8) | sP4),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(4,plain,((~(sP4) | ~(sP7)) | sP13),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(5,plain,(~(sP22) | sP16),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(6,plain,((~(sP16) | ~(sP20)) | sP8),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(7,plain,(~(sP24) | sP20),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(8,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(9,plain,(~(sP5) | sP19),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(10,plain,((~(sP19) | ~(sP22)) | sP7),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(11,plain,(sP23 | sP22),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9])). % 13.13/13.42 thf(12,plain,(~(sP18) | sP11),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(13,plain,((~(sP11) | ~(sP21)) | sP25),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(14,plain,(sP17 | ~(sP23)),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(15,plain,(sP17 | sP21),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(16,plain,(sP10 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 13.13/13.42 thf(17,plain,(~(sP12) | ~(sP10)),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(18,plain,(~(sP3) | sP18),inference(all_rule,[status(thm)],[])). % 13.13/13.42 thf(19,plain,(sP2 | sP9),inference(prop_rule,[status(thm)],[])). % 13.13/13.42 thf(20,plain,(sP6 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.13/13.42 thf(21,plain,(sP14 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.13/13.42 thf(sym,axiom,(msymmetric @ rel)). % 13.13/13.42 thf(22,plain,sP3,inference(preprocess,[status(thm)],[sym]). % 13.13/13.42 thf(axA5,axiom,(mvalid @ (positive @ necessary_existence))). % 13.13/13.42 thf(23,plain,sP24,inference(preprocess,[status(thm)],[axA5]). % 13.13/13.42 thf(corC,axiom,(mvalid @ (mdia @ (mexists_ind @ god)))). % 13.13/13.42 thf(24,plain,sP12,inference(preprocess,[status(thm)],[corC]). % 13.13/13.42 thf(thmT2,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mimplies @ (god @ X1)) @ ((essence @ god) @ X1)))))). % 13.13/13.42 thf(25,plain,sP1,inference(preprocess,[status(thm)],[thmT2]). % 13.13/13.42 thf(26,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,h2])). % 13.13/13.42 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1])). % 13.13/13.42 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0])). % 13.13/13.42 thf(0,theorem,sP14,inference(contra,[status(thm),contra(discharge,[h2])],[26,h2])). % 13.13/13.42 % SZS output end Proof %------------------------------------------------------------------------------