%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PHI006^4 : TPTP v9.2.0. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n016.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 0.15s 0.37s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : PHI006^4 : TPTP v9.2.0. Released v6.4.0. % 0.09/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.31 % Computer : n016.cluster.edu % 0.15/0.31 % Model : x86_64 x86_64 % 0.15/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.31 % Memory : 8042.1875MB % 0.15/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.31 % CPULimit : 300 % 0.15/0.31 % WCLimit : 300 % 0.15/0.31 % DateTime : Wed Oct 8 23:18:08 EDT 2025 % 0.15/0.31 % CPUTime : % 0.15/0.37 % SZS status Theorem % 0.15/0.37 % Mode: mode213 % 0.15/0.37 % Inferences: 208 % 0.15/0.37 % SZS output start Proof % 0.15/0.37 thf(ty_mu, type, mu : $tType). % 0.15/0.37 thf(ty_eigen__6, type, eigen__6 : $i). % 0.15/0.37 thf(ty_eigen__12, type, eigen__12 : mu). % 0.15/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.15/0.37 thf(ty_positive, type, positive : ((mu>$i>$o)>$i>$o)). % 0.15/0.37 thf(ty_eigen__11, type, eigen__11 : $i). % 0.15/0.37 thf(ty_eigen__8, type, eigen__8 : mu). % 0.15/0.37 thf(ty_eigen__9, type, eigen__9 : (mu>$i>$o)). % 0.15/0.37 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.15/0.37 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((![X2:mu]:($false => ((eigen__9 @ X2) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 0.15/0.37 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X2) @ X1) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 0.15/0.37 thf(h1, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 0.15/0.37 thf(eigendef_eigen__10, definition, eigen__10 = (eps__1 @ (^[X1:mu]:(~((~($false)))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 0.15/0.37 thf(eigendef_eigen__12, definition, eigen__12 = (eps__1 @ (^[X1:mu]:(~(($false => ((eigen__9 @ X1) @ eigen__11)))))), introduced(definition,[new_symbols(definition,[eigen__12])])). % 0.15/0.37 thf(eigendef_eigen__8, definition, eigen__8 = (eps__1 @ (^[X1:mu]:(~(((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__6) => ((X2 @ X1) @ eigen__6))) => (~((![X2:mu>$i>$o]:((![X3:mu>$i>$o]:(((X3 @ X1) @ eigen__6) => (![X4:$i]:(![X5:mu]:(((X2 @ X5) @ X4) => ((X3 @ X5) @ X4)))))) => (![X3:$i]:(~((![X4:mu]:(~(((X2 @ X4) @ X3)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 0.15/0.37 thf(h2, assumption, (![X1:(mu>$i>$o)>$o]:(![X2:mu>$i>$o]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])). % 0.15/0.37 thf(eigendef_eigen__9, definition, eigen__9 = (eps__2 @ (^[X1:mu>$i>$o]:(~((((X1 @ eigen__8) @ eigen__6) => (![X2:$i]:(![X3:mu]:($false => ((X1 @ X3) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 0.15/0.37 thf(sP1,plain,sP1 <=> (![X1:mu>$i>$o]:(((positive @ (^[X2:mu]:(^[X3:$i]:(~(((X1 @ X2) @ X3)))))) @ eigen__0) => (~(((positive @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.15/0.37 thf(sP2,plain,sP2 <=> (((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__0) => (~((![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X2) @ X1) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4))))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.15/0.37 thf(sP3,plain,sP3 <=> (![X1:mu>$i>$o]:(((X1 @ eigen__8) @ eigen__6) => (![X2:$i]:(![X3:mu]:($false => ((X1 @ X3) @ X2)))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.15/0.37 thf(sP4,plain,sP4 <=> (![X1:mu]:((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__6) => ((X2 @ X1) @ eigen__6))) => (~((![X2:mu>$i>$o]:((![X3:mu>$i>$o]:(((X3 @ X1) @ eigen__6) => (![X4:$i]:(![X5:mu]:(((X2 @ X5) @ X4) => ((X3 @ X5) @ X4)))))) => (![X3:$i]:(~((![X4:mu]:(~(((X2 @ X4) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.15/0.37 thf(sP5,plain,sP5 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 0.15/0.37 thf(sP6,plain,sP6 <=> (((positive @ (^[X1:mu]:(^[X2:$i]:(~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))))) @ eigen__0) => (~(((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.15/0.37 thf(sP7,plain,sP7 <=> $false,introduced(definition,[new_symbols(definition,[sP7])])). % 0.15/0.37 thf(sP8,plain,sP8 <=> (![X1:mu]:(sP7 => ((eigen__9 @ X1) @ eigen__11))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.15/0.37 thf(sP9,plain,sP9 <=> (![X1:$i]:(![X2:mu]:(sP7 => ((eigen__9 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.15/0.37 thf(sP10,plain,sP10 <=> (sP7 => ((eigen__9 @ eigen__12) @ eigen__11)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.15/0.37 thf(sP11,plain,sP11 <=> (![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X2) @ X1) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.15/0.37 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((positive @ (^[X3:mu]:(^[X4:$i]:(~(((X2 @ X3) @ X4)))))) @ X1) => (~(((positive @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.15/0.37 thf(sP13,plain,sP13 <=> (![X1:mu>$i>$o]:((![X2:mu>$i>$o]:(((X2 @ eigen__8) @ eigen__6) => (![X3:$i]:(![X4:mu]:(((X1 @ X4) @ X3) => ((X2 @ X4) @ X3)))))) => (![X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.15/0.37 thf(sP14,plain,sP14 <=> (![X1:$i]:(~((![X2:mu]:(~(sP7)))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.15/0.37 thf(sP15,plain,sP15 <=> ((~(sP2)) => ((positive @ (^[X1:mu]:(^[X2:$i]:(~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))))) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP15])])). % 0.15/0.37 thf(sP16,plain,sP16 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(~((![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP16])])). % 0.15/0.37 thf(sP17,plain,sP17 <=> (![X1:mu>$i>$o]:((~((sP5 => (~((![X2:$i]:(![X3:mu]:((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))) => ((X1 @ X3) @ X2))))))))) => ((positive @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.15/0.37 thf(sP18,plain,sP18 <=> (![X1:mu>$i>$o]:(![X2:mu>$i>$o]:((~((((positive @ X1) @ eigen__0) => (~((![X3:$i]:(![X4:mu]:(((X1 @ X4) @ X3) => ((X2 @ X4) @ X3))))))))) => ((positive @ X2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.15/0.37 thf(sP19,plain,sP19 <=> (((eigen__9 @ eigen__8) @ eigen__6) => sP9),introduced(definition,[new_symbols(definition,[sP19])])). % 0.15/0.37 thf(sP20,plain,sP20 <=> ((!!) @ (positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.15/0.37 thf(sP21,plain,sP21 <=> ((!!) @ (positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4))))))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.15/0.37 thf(sP22,plain,sP22 <=> (![X1:mu]:(~(sP7))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.15/0.37 thf(sP23,plain,sP23 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:((![X4:mu>$i>$o]:(((X4 @ X1) @ X2) => (![X5:$i]:(![X6:mu]:(((X3 @ X6) @ X5) => ((X4 @ X6) @ X5)))))) => (![X4:$i]:(~((![X5:mu]:(~(((X3 @ X5) @ X4)))))))))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP23])])). % 0.15/0.37 thf(sP24,plain,sP24 <=> (sP3 => sP14),introduced(definition,[new_symbols(definition,[sP24])])). % 0.15/0.37 thf(sP25,plain,sP25 <=> (![X1:$i]:(![X2:mu>$i>$o]:(![X3:mu>$i>$o]:((~((((positive @ X2) @ X1) => (~((![X4:$i]:(![X5:mu]:(((X2 @ X5) @ X4) => ((X3 @ X5) @ X4))))))))) => ((positive @ X3) @ X1))))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.15/0.37 thf(sP26,plain,sP26 <=> ((![X1:mu>$i>$o]:(((positive @ X1) @ eigen__6) => ((X1 @ eigen__8) @ eigen__6))) => (~(sP13))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.15/0.37 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.15/0.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~(sP7))))). % 0.15/0.37 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:sP7))). % 0.15/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.15/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.15/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.15/0.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))). % 0.15/0.37 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))). % 0.15/0.37 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.15/0.37 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))). % 0.15/0.37 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.15/0.37 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))). % 0.15/0.37 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.15/0.37 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))). % 0.15/0.37 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 0.15/0.37 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 0.15/0.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$o]:(^[X2:$i]:((!!) @ X1))))). % 0.15/0.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$o]:(^[X2:$i]:(~((![X3:$i]:(~((X1 @ X3)))))))))). % 0.15/0.37 thf(def_mvalid,definition,(mvalid = (!!))). % 0.15/0.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.15/0.37 thf(def_god,definition,(god = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (positive @ X2)) @ (X2 @ X1))))))). % 0.15/0.37 thf(def_essence,definition,(essence = (^[X1:mu>$i>$o]:(^[X2:mu]:(mforall_indset @ (^[X3:mu>$i>$o]:((mimplies @ (X3 @ X2)) @ (mbox @ (mforall_ind @ (^[X4:mu]:((mimplies @ (X1 @ X4)) @ (X3 @ X4)))))))))))). % 0.15/0.37 thf(def_necessary_existence,definition,(necessary_existence = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ ((essence @ X2) @ X1)) @ (mbox @ (mexists_ind @ X2)))))))). % 0.15/0.37 thf(conj,conjecture,sP7). % 0.15/0.37 thf(h3,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[conj])). % 0.15/0.37 thf(1,plain,(sP10 | sP7),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(2,plain,(sP8 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12])). % 0.15/0.37 thf(3,plain,~(sP7),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(4,plain,(sP9 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). % 0.15/0.37 thf(5,plain,(sP22 | sP7),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10])). % 0.15/0.37 thf(6,plain,(sP19 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(7,plain,(~(sP14) | ~(sP22)),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(8,plain,(sP3 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__9])). % 0.15/0.37 thf(9,plain,((~(sP24) | ~(sP3)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(10,plain,(~(sP13) | sP24),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(11,plain,(sP26 | sP13),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(12,plain,(sP4 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8])). % 0.15/0.37 thf(13,plain,(sP11 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 0.15/0.37 thf(14,plain,(~(sP17) | sP15),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(15,plain,((~(sP15) | sP2) | sP16),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(16,plain,((~(sP2) | ~(sP5)) | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(17,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(18,plain,((~(sP6) | ~(sP16)) | ~(sP23)),inference(prop_rule,[status(thm)],[])). % 0.15/0.37 thf(19,plain,(~(sP18) | sP17),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(20,plain,(~(sP21) | sP23),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(21,plain,(~(sP20) | sP5),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(22,plain,(~(sP25) | sP18),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(23,plain,(~(sP12) | sP1),inference(all_rule,[status(thm)],[])). % 0.15/0.37 thf(axA1a,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:((mimplies @ (positive @ (^[X2:mu]:(mnot @ (X1 @ X2))))) @ (mnot @ (positive @ X1))))))). % 0.15/0.37 thf(24,plain,sP12,inference(preprocess,[status(thm)],[axA1a]). % 0.15/0.37 thf(axA2,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ ((mand @ (positive @ X1)) @ (mbox @ (mforall_ind @ (^[X3:mu]:((mimplies @ (X1 @ X3)) @ (X2 @ X3))))))) @ (positive @ X2)))))))). % 0.15/0.37 thf(25,plain,sP25,inference(preprocess,[status(thm)],[axA2]). % 0.15/0.37 thf(axA3,axiom,(mvalid @ (positive @ god))). % 0.15/0.37 thf(26,plain,sP20,inference(preprocess,[status(thm)],[axA3]). % 0.15/0.37 thf(axA5,axiom,(mvalid @ (positive @ necessary_existence))). % 0.15/0.37 thf(27,plain,sP21,inference(preprocess,[status(thm)],[axA5]). % 0.15/0.37 thf(28,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,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])). % 0.15/0.37 thf(29,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[28,h2])). % 0.15/0.37 thf(30,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[29,h1])). % 0.15/0.37 thf(31,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[30,h0])). % 0.15/0.37 thf(0,theorem,sP7,inference(contra,[status(thm),contra(discharge,[h3])],[28,h3])). % 0.15/0.37 % SZS output end Proof %------------------------------------------------------------------------------