%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET583^7 : TPTP v9.2.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n015.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 02:25:57 PM UTC 2025 % Result : Theorem 0.12s 0.36s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET583^7 : TPTP v9.2.0. Released v5.5.0. % 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Oct 8 14:39:53 EDT 2025 % 0.12/0.33 % CPUTime : % 0.12/0.36 % SZS status Theorem % 0.12/0.36 % Mode: mode213 % 0.12/0.36 % Inferences: 42 % 0.12/0.36 % SZS output start Proof % 0.12/0.36 thf(ty_mu, type, mu : $tType). % 0.12/0.36 thf(ty_subset, type, subset : (mu>mu>$i>$o)). % 0.12/0.36 thf(ty_eigen__2, type, eigen__2 : mu). % 0.12/0.36 thf(ty_eigen__1, type, eigen__1 : mu). % 0.12/0.36 thf(ty_eigen__0, type, eigen__0 : $i). % 0.12/0.36 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 0.12/0.36 thf(ty_qmltpeq, type, qmltpeq : (mu>mu>$i>$o)). % 0.12/0.36 thf(sP1,plain,sP1 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((((((qmltpeq @ eigen__1) @ X1) @ eigen__0) => (~(((((subset @ eigen__1) @ X1) @ eigen__0) => (~((((subset @ X1) @ eigen__1) @ eigen__0))))))) => (~(((~(((((subset @ eigen__1) @ X1) @ eigen__0) => (~((((subset @ X1) @ eigen__1) @ eigen__0)))))) => (((qmltpeq @ eigen__1) @ X1) @ eigen__0))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.12/0.36 thf(sP2,plain,sP2 <=> (((subset @ eigen__2) @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])). % 0.12/0.36 thf(sP3,plain,sP3 <=> (((((qmltpeq @ eigen__1) @ eigen__2) @ eigen__0) => (~(((((subset @ eigen__1) @ eigen__2) @ eigen__0) => (~(sP2)))))) => (~(((~(((((subset @ eigen__1) @ eigen__2) @ eigen__0) => (~(sP2))))) => (((qmltpeq @ eigen__1) @ eigen__2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.12/0.36 thf(sP4,plain,sP4 <=> ((exists_in_world @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP4])])). % 0.12/0.36 thf(sP5,plain,sP5 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (~((((((qmltpeq @ X1) @ X2) @ eigen__0) => (~(((((subset @ X1) @ X2) @ eigen__0) => (~((((subset @ X2) @ X1) @ eigen__0))))))) => (~(((~(((((subset @ X1) @ X2) @ eigen__0) => (~((((subset @ X2) @ X1) @ eigen__0)))))) => (((qmltpeq @ X1) @ X2) @ eigen__0))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.12/0.36 thf(sP6,plain,sP6 <=> ((~(((((subset @ eigen__1) @ eigen__2) @ eigen__0) => (~(sP2))))) => (((qmltpeq @ eigen__1) @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.12/0.36 thf(sP7,plain,sP7 <=> (sP4 => sP1),introduced(definition,[new_symbols(definition,[sP7])])). % 0.12/0.36 thf(sP8,plain,sP8 <=> (((subset @ eigen__1) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])). % 0.12/0.36 thf(sP9,plain,sP9 <=> (((qmltpeq @ eigen__1) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])). % 0.12/0.36 thf(sP10,plain,sP10 <=> (sP8 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.12/0.36 thf(sP11,plain,sP11 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (~((((((qmltpeq @ X2) @ X3) @ X1) => (~(((((subset @ X2) @ X3) @ X1) => (~((((subset @ X3) @ X2) @ X1))))))) => (~(((~(((((subset @ X2) @ X3) @ X1) => (~((((subset @ X3) @ X2) @ X1)))))) => (((qmltpeq @ X2) @ X3) @ X1)))))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.12/0.36 thf(sP12,plain,sP12 <=> (((exists_in_world @ eigen__2) @ eigen__0) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.12/0.36 thf(sP13,plain,sP13 <=> ((exists_in_world @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP13])])). % 0.12/0.36 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.12/0.36 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.12/0.36 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.12/0.36 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.12/0.36 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.12/0.36 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.12/0.36 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.12/0.36 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.12/0.36 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.12/0.36 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.12/0.36 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.12/0.36 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.12/0.36 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.12/0.36 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 0.12/0.36 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.12/0.36 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.12/0.36 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.12/0.36 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.12/0.36 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.12/0.36 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.12/0.36 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.12/0.36 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.12/0.36 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.12/0.36 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.12/0.36 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 0.12/0.36 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.12/0.36 thf(def_mvalid,definition,(mvalid = (!!))). % 0.12/0.36 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.12/0.36 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.12/0.36 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.12/0.36 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 0.12/0.36 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 0.12/0.36 thf(prove_extensionality,conjecture,(![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((~((~((~(((~((~((((subset @ X2) @ X3) @ X1))))) => (~((((subset @ X3) @ X2) @ X1)))))))))) => (((qmltpeq @ X2) @ X3) @ X1)))))))). % 0.12/0.36 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((~(((((subset @ X2) @ X3) @ X1) => (~((((subset @ X3) @ X2) @ X1)))))) => (((qmltpeq @ X2) @ X3) @ X1))))))))),inference(assume_negation,[status(cth)],[prove_extensionality])). % 0.12/0.36 thf(h1,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((~(((((subset @ X1) @ X2) @ eigen__0) => (~((((subset @ X2) @ X1) @ eigen__0)))))) => (((qmltpeq @ X1) @ X2) @ eigen__0)))))))),introduced(assumption,[])). % 0.12/0.36 thf(h2,assumption,(~((sP4 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((~(((((subset @ eigen__1) @ X1) @ eigen__0) => (~((((subset @ X1) @ eigen__1) @ eigen__0)))))) => (((qmltpeq @ eigen__1) @ X1) @ eigen__0))))))),introduced(assumption,[])). % 0.12/0.36 thf(h3,assumption,sP4,introduced(assumption,[])). % 0.12/0.36 thf(h4,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((~(((((subset @ eigen__1) @ X1) @ eigen__0) => (~((((subset @ X1) @ eigen__1) @ eigen__0)))))) => (((qmltpeq @ eigen__1) @ X1) @ eigen__0)))))),introduced(assumption,[])). % 0.12/0.36 thf(h5,assumption,(~((sP13 => sP6))),introduced(assumption,[])). % 0.12/0.36 thf(h6,assumption,sP13,introduced(assumption,[])). % 0.12/0.36 thf(h7,assumption,(~(sP6)),introduced(assumption,[])). % 0.12/0.36 thf(h8,assumption,(~(sP10)),introduced(assumption,[])). % 0.12/0.36 thf(h9,assumption,(~(sP9)),introduced(assumption,[])). % 0.12/0.36 thf(h10,assumption,sP8,introduced(assumption,[])). % 0.12/0.36 thf(h11,assumption,sP2,introduced(assumption,[])). % 0.12/0.36 thf(1,plain,((~(sP10) | ~(sP8)) | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(2,plain,((~(sP6) | sP10) | sP9),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(3,plain,(sP3 | sP6),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(4,plain,(~(sP1) | sP12),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(5,plain,((~(sP12) | ~(sP13)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(6,plain,(~(sP11) | sP5),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(7,plain,(~(sP5) | sP7),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(8,plain,((~(sP7) | ~(sP4)) | sP1),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(equal_defn,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mequiv @ ((qmltpeq @ X1) @ X2)) @ ((mand @ ((subset @ X1) @ X2)) @ ((subset @ X2) @ X1))))))))). % 0.12/0.36 thf(9,plain,sP11,inference(preprocess,[status(thm)],[equal_defn]). % 0.12/0.36 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h3,h6,h10,h11,h9])). % 0.12/0.36 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,10,h10,h11])). % 0.12/0.36 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,11,h8,h9])). % 0.12/0.36 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,12,h6,h7])). % 0.12/0.36 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,13,h5])). % 0.12/0.36 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,14,h3,h4])). % 0.12/0.36 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,15,h2])). % 0.12/0.36 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,16,h1])). % 0.12/0.36 thf(0,theorem,(![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((~((~((~(((~((~((((subset @ X2) @ X3) @ X1))))) => (~((((subset @ X3) @ X2) @ X1)))))))))) => (((qmltpeq @ X2) @ X3) @ X1))))))),inference(contra,[status(thm),contra(discharge,[h0])],[17,h0])). % 0.12/0.36 % SZS output end Proof %------------------------------------------------------------------------------