%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO470^6 : 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 : n018.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 03:25:48 PM UTC 2025 % Result : Theorem 1.04s 1.56s % Output : Proof 1.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO470^6 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n018.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 : Thu Oct 9 01:25:08 EDT 2025 % 0.13/0.34 % CPUTime : % 1.04/1.56 % SZS status Theorem % 1.04/1.56 % Mode: mode506 % 1.04/1.56 % Inferences: 62549 % 1.04/1.56 % SZS output start Proof % 1.04/1.56 thf(ty_eigen__6, type, eigen__6 : $i). % 1.04/1.56 thf(ty_p, type, p : ($i>$o)). % 1.04/1.56 thf(ty_eigen__0, type, eigen__0 : $i). % 1.04/1.56 thf(ty_eigen__4, type, eigen__4 : $i). % 1.04/1.56 thf(ty_eigen__3, type, eigen__3 : $i). % 1.04/1.56 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 1.04/1.56 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.04/1.56 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__0) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 1.04/1.56 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__4) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 1.04/1.56 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))) => (~(((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.04/1.56 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 1.04/1.56 thf(sP1,plain,sP1 <=> (![X1:$i]:((rel_s5 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 1.04/1.56 thf(sP2,plain,sP2 <=> (((rel_s5 @ eigen__0) @ eigen__0) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.04/1.56 thf(sP3,plain,sP3 <=> (((rel_s5 @ eigen__0) @ eigen__3) => (p @ eigen__3)),introduced(definition,[new_symbols(definition,[sP3])])). % 1.04/1.56 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.04/1.56 thf(sP5,plain,sP5 <=> ((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.04/1.56 thf(sP6,plain,sP6 <=> ((~((((rel_s5 @ eigen__3) @ eigen__4) => (~(((rel_s5 @ eigen__4) @ eigen__6)))))) => ((rel_s5 @ eigen__3) @ eigen__6)),introduced(definition,[new_symbols(definition,[sP6])])). % 1.04/1.56 thf(sP7,plain,sP7 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__3) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.04/1.56 thf(sP8,plain,sP8 <=> ((rel_s5 @ eigen__4) @ eigen__6),introduced(definition,[new_symbols(definition,[sP8])])). % 1.04/1.56 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 1.04/1.56 thf(sP10,plain,sP10 <=> (((~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1)))) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.04/1.56 thf(sP11,plain,sP11 <=> (((rel_s5 @ eigen__3) @ eigen__4) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.04/1.56 thf(sP12,plain,sP12 <=> (((rel_s5 @ eigen__0) @ eigen__0) => (~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.04/1.56 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => ((rel_s5 @ X1) @ eigen__3))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.04/1.56 thf(sP14,plain,sP14 <=> ((rel_s5 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP14])])). % 1.04/1.56 thf(sP15,plain,sP15 <=> ((rel_s5 @ eigen__3) @ eigen__6),introduced(definition,[new_symbols(definition,[sP15])])). % 1.04/1.56 thf(sP16,plain,sP16 <=> (![X1:$i]:((~((((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.04/1.56 thf(sP17,plain,sP17 <=> ((~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))))) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1)))),introduced(definition,[new_symbols(definition,[sP17])])). % 1.04/1.56 thf(sP18,plain,sP18 <=> (((rel_s5 @ eigen__6) @ eigen__3) => (p @ eigen__3)),introduced(definition,[new_symbols(definition,[sP18])])). % 1.04/1.56 thf(sP19,plain,sP19 <=> (![X1:$i]:((~((sP14 => (~(((rel_s5 @ eigen__4) @ X1)))))) => ((rel_s5 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 1.04/1.56 thf(sP20,plain,sP20 <=> (sP15 => ((rel_s5 @ eigen__6) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP20])])). % 1.04/1.56 thf(sP21,plain,sP21 <=> (p @ eigen__3),introduced(definition,[new_symbols(definition,[sP21])])). % 1.04/1.56 thf(sP22,plain,sP22 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.04/1.56 thf(sP23,plain,sP23 <=> (sP8 => (~((![X1:$i]:(((rel_s5 @ eigen__6) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 1.04/1.56 thf(sP24,plain,sP24 <=> (![X1:$i]:(((rel_s5 @ eigen__6) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP24])])). % 1.04/1.56 thf(sP25,plain,sP25 <=> (((rel_s5 @ eigen__0) @ eigen__4) => sP9),introduced(definition,[new_symbols(definition,[sP25])])). % 1.04/1.56 thf(sP26,plain,sP26 <=> ((~((((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__4)))))) => sP14),introduced(definition,[new_symbols(definition,[sP26])])). % 1.04/1.56 thf(sP27,plain,sP27 <=> ((rel_s5 @ eigen__6) @ eigen__3),introduced(definition,[new_symbols(definition,[sP27])])). % 1.04/1.56 thf(sP28,plain,sP28 <=> (((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP28])])). % 1.04/1.56 thf(sP29,plain,sP29 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP29])])). % 1.04/1.56 thf(sP30,plain,sP30 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP30])])). % 1.04/1.56 thf(sP31,plain,sP31 <=> ((rel_s5 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP31])])). % 1.04/1.56 thf(sP32,plain,sP32 <=> (![X1:$i]:(~((((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))) => (~(((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP32])])). % 1.04/1.56 thf(sP33,plain,sP33 <=> (((rel_s5 @ eigen__0) @ eigen__3) => ((rel_s5 @ eigen__3) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP33])])). % 1.04/1.56 thf(sP34,plain,sP34 <=> ((rel_s5 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP34])])). % 1.04/1.56 thf(sP35,plain,sP35 <=> ((rel_s5 @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP35])])). % 1.04/1.56 thf(sP36,plain,sP36 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 1.04/1.56 thf(sP37,plain,sP37 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP37])])). % 1.04/1.56 thf(sP38,plain,sP38 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP38])])). % 1.04/1.56 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 1.04/1.56 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 1.04/1.56 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.04/1.56 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.04/1.56 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 1.04/1.56 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.04/1.56 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 1.04/1.56 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 1.04/1.56 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 1.04/1.56 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 1.04/1.56 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 1.04/1.56 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 1.04/1.56 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 1.04/1.56 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.04/1.56 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 1.04/1.56 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.04/1.56 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 1.04/1.56 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 1.04/1.56 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 1.04/1.56 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 1.04/1.56 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 1.04/1.56 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 1.04/1.56 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)))))))). % 1.04/1.56 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 1.04/1.56 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 1.04/1.56 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 1.04/1.56 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 1.04/1.56 thf(def_mvalid,definition,(mvalid = (!!))). % 1.04/1.56 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.04/1.56 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.04/1.56 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.04/1.56 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 1.04/1.56 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 1.04/1.56 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))) => (~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))))))))))))). % 1.04/1.56 thf(h1,negated_conjecture,(~(sP32)),inference(assume_negation,[status(cth)],[prove])). % 1.04/1.56 thf(1,plain,(~(sP19) | sP6),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(2,plain,((~(sP6) | sP11) | sP15),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(3,plain,((~(sP11) | ~(sP14)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(4,plain,(~(sP16) | sP26),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(5,plain,((~(sP26) | sP28) | sP14),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(6,plain,((~(sP28) | ~(sP35)) | ~(sP34)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(7,plain,(~(sP7) | sP19),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(8,plain,(~(sP7) | sP16),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(9,plain,((~(sP33) | ~(sP38)) | sP35),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(10,plain,(~(sP13) | sP20),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(11,plain,((~(sP20) | ~(sP15)) | sP27),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(12,plain,(~(sP30) | sP7),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(13,plain,(~(sP37) | sP13),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(14,plain,(~(sP29) | sP33),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(15,plain,(~(sP24) | sP18),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(16,plain,((~(sP18) | ~(sP27)) | sP21),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(17,plain,(sP23 | sP24),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(18,plain,(sP23 | sP8),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(19,plain,(sP9 | ~(sP23)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 1.04/1.56 thf(20,plain,(sP25 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(21,plain,(sP25 | sP34),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(22,plain,(sP36 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 1.04/1.56 thf(23,plain,(sP3 | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(24,plain,(sP3 | sP38),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(25,plain,(~(sP4) | sP12),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(26,plain,((~(sP12) | ~(sP31)) | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(27,plain,(sP22 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 1.04/1.56 thf(28,plain,((~(sP2) | ~(sP31)) | sP4),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(29,plain,(sP17 | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(30,plain,(sP17 | ~(sP36)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(31,plain,(~(sP37) | sP29),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(32,plain,(~(sP1) | sP31),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(33,plain,(~(sP36) | sP2),inference(all_rule,[status(thm)],[])). % 1.04/1.56 thf(34,plain,(sP5 | sP36),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(35,plain,(sP5 | sP22),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(36,plain,((~(sP10) | ~(sP17)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 1.04/1.56 thf(37,plain,(sP32 | sP10),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.04/1.56 thf(a3,axiom,(msymmetric @ rel_s5)). % 1.04/1.56 thf(38,plain,sP37,inference(preprocess,[status(thm)],[a3]). % 1.04/1.56 thf(a2,axiom,(mtransitive @ rel_s5)). % 1.04/1.56 thf(39,plain,sP30,inference(preprocess,[status(thm)],[a2]). % 1.04/1.56 thf(a1,axiom,(mreflexive @ rel_s5)). % 1.04/1.56 thf(40,plain,sP1,inference(preprocess,[status(thm)],[a1]). % 1.04/1.56 thf(41,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,h1])). % 1.04/1.56 thf(42,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[41,h0])). % 1.04/1.56 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))) => (~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4)))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[41,h1])). % 1.04/1.56 % SZS output end Proof %------------------------------------------------------------------------------