%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO459^6 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n020.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 03:25:42 PM UTC 2025 % Result : Theorem 0.21s 0.40s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SYO459^6 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 9 01:00:53 EDT 2025 % 0.14/0.35 % CPUTime : % 0.21/0.40 % SZS status Theorem % 0.21/0.40 % Mode: mode213 % 0.21/0.40 % Inferences: 67 % 0.21/0.40 % SZS output start Proof % 0.21/0.40 thf(ty_p, type, p : ($i>$o)). % 0.21/0.40 thf(ty_eigen__2, type, eigen__2 : $i). % 0.21/0.40 thf(ty_eigen__1, type, eigen__1 : $i). % 0.21/0.40 thf(ty_eigen__0, type, eigen__0 : $i). % 0.21/0.40 thf(ty_eigen__4, type, eigen__4 : $i). % 0.21/0.40 thf(ty_eigen__3, type, eigen__3 : $i). % 0.21/0.40 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 0.21/0.40 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.21/0.40 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 0.21/0.40 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.21/0.40 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__3) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 0.21/0.40 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.21/0.40 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.21/0.40 thf(sP3,plain,sP3 <=> ((rel_s5 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])). % 0.21/0.40 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.21/0.40 thf(sP5,plain,sP5 <=> (((rel_s5 @ eigen__3) @ eigen__4) => (p @ eigen__4)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.21/0.40 thf(sP6,plain,sP6 <=> (((rel_s5 @ eigen__1) @ eigen__3) => (~(((rel_s5 @ eigen__3) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.21/0.40 thf(sP7,plain,sP7 <=> (((rel_s5 @ eigen__1) @ eigen__2) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.21/0.40 thf(sP8,plain,sP8 <=> ((rel_s5 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP8])])). % 0.21/0.40 thf(sP9,plain,sP9 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.21/0.40 thf(sP10,plain,sP10 <=> ((~(sP7)) => ((rel_s5 @ eigen__1) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.21/0.40 thf(sP11,plain,sP11 <=> (![X1:$i]:((~((((rel_s5 @ eigen__0) @ eigen__1) => (~(((rel_s5 @ eigen__1) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.21/0.40 thf(sP12,plain,sP12 <=> (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.21/0.40 thf(sP13,plain,sP13 <=> (![X1:$i]:((~((sP8 => (~(((rel_s5 @ eigen__2) @ X1)))))) => ((rel_s5 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.21/0.40 thf(sP14,plain,sP14 <=> (p @ eigen__4),introduced(definition,[new_symbols(definition,[sP14])])). % 0.21/0.40 thf(sP15,plain,sP15 <=> (sP3 => (~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.21/0.40 thf(sP16,plain,sP16 <=> ((rel_s5 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP16])])). % 0.21/0.40 thf(sP17,plain,sP17 <=> ((~(sP6)) => ((rel_s5 @ eigen__1) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP17])])). % 0.21/0.40 thf(sP18,plain,sP18 <=> ((~((((rel_s5 @ eigen__0) @ eigen__1) => (~(sP8))))) => ((rel_s5 @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP18])])). % 0.21/0.40 thf(sP19,plain,sP19 <=> (sP8 => (~((![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.21/0.40 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.21/0.40 thf(sP21,plain,sP21 <=> (((rel_s5 @ eigen__0) @ eigen__1) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.21/0.40 thf(sP22,plain,sP22 <=> (((rel_s5 @ eigen__1) @ eigen__4) => sP14),introduced(definition,[new_symbols(definition,[sP22])])). % 0.21/0.40 thf(sP23,plain,sP23 <=> (![X1:$i]:((~((((rel_s5 @ eigen__1) @ eigen__3) => (~(((rel_s5 @ eigen__3) @ X1)))))) => ((rel_s5 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP23])])). % 0.21/0.40 thf(sP24,plain,sP24 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP24])])). % 0.21/0.40 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.21/0.40 thf(sP26,plain,sP26 <=> (sP3 => (~(sP12))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.21/0.40 thf(sP27,plain,sP27 <=> ((rel_s5 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP27])])). % 0.21/0.40 thf(sP28,plain,sP28 <=> (sP24 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.21/0.40 thf(sP29,plain,sP29 <=> (((rel_s5 @ eigen__0) @ eigen__2) => (~((![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 0.21/0.40 thf(sP30,plain,sP30 <=> ((rel_s5 @ eigen__1) @ eigen__4),introduced(definition,[new_symbols(definition,[sP30])])). % 0.21/0.40 thf(sP31,plain,sP31 <=> (![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.21/0.40 thf(sP32,plain,sP32 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__1) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP32])])). % 0.21/0.40 thf(sP33,plain,sP33 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP33])])). % 0.21/0.40 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.21/0.40 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.21/0.40 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.21/0.40 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.21/0.40 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.21/0.40 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.21/0.40 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.21/0.40 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.21/0.40 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.21/0.40 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.21/0.40 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.21/0.40 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.21/0.40 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.21/0.40 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.21/0.40 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.21/0.40 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.21/0.40 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.21/0.40 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.21/0.40 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.21/0.40 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.21/0.40 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.21/0.40 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.21/0.40 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.21/0.40 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.21/0.40 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.21/0.40 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))))))))). % 0.21/0.40 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.21/0.40 thf(def_mvalid,definition,(mvalid = (!!))). % 0.21/0.40 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.21/0.40 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.21/0.40 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.21/0.40 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 0.21/0.40 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 0.21/0.40 thf(prove,conjecture,(![X1:$i]:((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5)))))))))))))))))))). % 0.21/0.40 thf(h1,negated_conjecture,(~((![X1:$i]:((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))))))))))),inference(assume_negation,[status(cth)],[prove])). % 0.21/0.40 thf(h2,assumption,(~(((~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))))) => (~(sP25))))),introduced(assumption,[])). % 0.21/0.40 thf(h3,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))))),introduced(assumption,[])). % 0.21/0.40 thf(h4,assumption,sP25,introduced(assumption,[])). % 0.21/0.40 thf(h5,assumption,(~((sP24 => (~(sP1))))),introduced(assumption,[])). % 0.21/0.40 thf(h6,assumption,sP24,introduced(assumption,[])). % 0.21/0.40 thf(h7,assumption,sP1,introduced(assumption,[])). % 0.21/0.40 thf(1,plain,(~(sP1) | sP22),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(2,plain,((~(sP22) | ~(sP30)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(3,plain,(~(sP32) | sP23),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(4,plain,(~(sP23) | sP17),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(5,plain,((~(sP17) | sP6) | sP30),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(6,plain,((~(sP6) | ~(sP27)) | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(7,plain,(sP5 | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(8,plain,(sP5 | sP16),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(9,plain,(sP12 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 0.21/0.40 thf(10,plain,(~(sP20) | sP26),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(11,plain,((~(sP26) | ~(sP3)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(12,plain,(~(sP9) | sP32),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(13,plain,(~(sP32) | sP13),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(14,plain,(~(sP13) | sP10),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(15,plain,((~(sP10) | sP7) | sP27),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(16,plain,((~(sP7) | ~(sP8)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(17,plain,(sP15 | sP3),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(18,plain,(sP31 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 0.21/0.40 thf(19,plain,(~(sP25) | sP29),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(20,plain,((~(sP29) | ~(sP33)) | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(21,plain,(~(sP9) | sP2),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(22,plain,(~(sP2) | sP11),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(23,plain,(~(sP11) | sP18),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(24,plain,((~(sP18) | sP21) | sP33),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(25,plain,((~(sP21) | ~(sP24)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(26,plain,(sP19 | sP20),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(27,plain,(sP19 | sP8),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(28,plain,(sP4 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 0.21/0.40 thf(29,plain,(~(sP25) | sP28),inference(all_rule,[status(thm)],[])). % 0.21/0.40 thf(30,plain,((~(sP28) | ~(sP24)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.21/0.40 thf(a2,axiom,(mtransitive @ rel_s5)). % 0.21/0.40 thf(31,plain,sP9,inference(preprocess,[status(thm)],[a2]). % 0.21/0.40 thf(32,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h6,h7,h4])). % 0.21/0.40 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,32,h6,h7])). % 0.21/0.40 thf(34,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h3,33,h5])). % 0.21/0.40 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,34,h3,h4])). % 0.21/0.40 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,35,h2])). % 0.21/0.40 thf(37,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0])). % 0.21/0.40 thf(0,theorem,(![X1:$i]:((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[36,h1])). % 0.21/0.40 % SZS output end Proof %------------------------------------------------------------------------------