%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO442^1 : 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 : n019.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 03:25:36 PM UTC 2025 % Result : Theorem 4.54s 4.95s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.12 % Problem : SYO442^1 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n019.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 01:11:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.54/4.95 % SZS status Theorem % 4.54/4.95 % Mode: mode506 % 4.54/4.95 % Inferences: 64547 % 4.54/4.95 % SZS output start Proof % 4.54/4.95 thf(ty_p, type, p : ($i>$o)). % 4.54/4.95 thf(ty_eigen__2, type, eigen__2 : $i). % 4.54/4.95 thf(ty_eigen__0, type, eigen__0 : $i). % 4.54/4.95 thf(ty_eigen__4, type, eigen__4 : $i). % 4.54/4.95 thf(ty_eigen__5, type, eigen__5 : $i). % 4.54/4.95 thf(ty_eigen__11, type, eigen__11 : $i). % 4.54/4.95 thf(ty_eigen__10, type, eigen__10 : $i). % 4.54/4.95 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 4.54/4.95 thf(ty_eigen__8, type, eigen__8 : $i). % 4.54/4.95 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 4.54/4.95 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__10) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 4.54/4.95 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) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))) => (~(((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 4.54/4.95 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__4) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 4.54/4.95 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__5) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 4.54/4.95 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 4.54/4.95 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 4.54/4.95 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__4) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 4.54/4.95 thf(sP1,plain,sP1 <=> (![X1:$i]:((rel_s5 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 4.54/4.95 thf(sP2,plain,sP2 <=> (((rel_s5 @ eigen__8) @ eigen__5) => (~(((rel_s5 @ eigen__5) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP2])])). % 4.54/4.95 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 4.54/4.95 thf(sP4,plain,sP4 <=> (p @ eigen__5),introduced(definition,[new_symbols(definition,[sP4])])). % 4.54/4.95 thf(sP5,plain,sP5 <=> ((~((((rel_s5 @ eigen__8) @ eigen__10) => (~(((rel_s5 @ eigen__10) @ eigen__11)))))) => ((rel_s5 @ eigen__8) @ eigen__11)),introduced(definition,[new_symbols(definition,[sP5])])). % 4.54/4.95 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (![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,[sP6])])). % 4.54/4.95 thf(sP7,plain,sP7 <=> (((rel_s5 @ eigen__2) @ eigen__0) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 4.54/4.95 thf(sP8,plain,sP8 <=> (((rel_s5 @ eigen__11) @ eigen__8) => (p @ eigen__8)),introduced(definition,[new_symbols(definition,[sP8])])). % 4.54/4.95 thf(sP9,plain,sP9 <=> (((rel_s5 @ eigen__5) @ eigen__8) => (p @ eigen__8)),introduced(definition,[new_symbols(definition,[sP9])])). % 4.54/4.95 thf(sP10,plain,sP10 <=> (((rel_s5 @ eigen__8) @ eigen__11) => ((rel_s5 @ eigen__11) @ eigen__8)),introduced(definition,[new_symbols(definition,[sP10])])). % 4.54/4.95 thf(sP11,plain,sP11 <=> ((rel_s5 @ eigen__8) @ eigen__5),introduced(definition,[new_symbols(definition,[sP11])])). % 4.54/4.95 thf(sP12,plain,sP12 <=> ((rel_s5 @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP12])])). % 4.54/4.95 thf(sP13,plain,sP13 <=> ((rel_s5 @ eigen__8) @ eigen__10),introduced(definition,[new_symbols(definition,[sP13])])). % 4.54/4.95 thf(sP14,plain,sP14 <=> (((rel_s5 @ eigen__5) @ eigen__5) => sP4),introduced(definition,[new_symbols(definition,[sP14])])). % 4.54/4.95 thf(sP15,plain,sP15 <=> ((~(sP2)) => ((rel_s5 @ eigen__8) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP15])])). % 4.54/4.95 thf(sP16,plain,sP16 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 4.54/4.95 thf(sP17,plain,sP17 <=> (![X1:$i]:((~((sP13 => (~(((rel_s5 @ eigen__10) @ X1)))))) => ((rel_s5 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP17])])). % 4.54/4.95 thf(sP18,plain,sP18 <=> (((rel_s5 @ eigen__4) @ eigen__5) => sP4),introduced(definition,[new_symbols(definition,[sP18])])). % 4.54/4.95 thf(sP19,plain,sP19 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP19])])). % 4.54/4.95 thf(sP20,plain,sP20 <=> (((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (p @ X4))))))))))))) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP20])])). % 4.54/4.95 thf(sP21,plain,sP21 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 4.54/4.95 thf(sP22,plain,sP22 <=> (((rel_s5 @ eigen__0) @ eigen__2) => ((rel_s5 @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP22])])). % 4.54/4.95 thf(sP23,plain,sP23 <=> ((rel_s5 @ eigen__5) @ eigen__5),introduced(definition,[new_symbols(definition,[sP23])])). % 4.54/4.95 thf(sP24,plain,sP24 <=> (((rel_s5 @ eigen__8) @ eigen__4) => (~(((rel_s5 @ eigen__4) @ eigen__10)))),introduced(definition,[new_symbols(definition,[sP24])])). % 4.54/4.95 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel_s5 @ eigen__8) @ X1) => ((rel_s5 @ X1) @ eigen__8))),introduced(definition,[new_symbols(definition,[sP25])])). % 4.54/4.95 thf(sP26,plain,sP26 <=> ((rel_s5 @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP26])])). % 4.54/4.95 thf(sP27,plain,sP27 <=> ((rel_s5 @ eigen__10) @ eigen__11),introduced(definition,[new_symbols(definition,[sP27])])). % 4.54/4.95 thf(sP28,plain,sP28 <=> ((rel_s5 @ eigen__8) @ eigen__4),introduced(definition,[new_symbols(definition,[sP28])])). % 4.54/4.95 thf(sP29,plain,sP29 <=> (![X1:$i]:(((rel_s5 @ eigen__10) @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 4.54/4.95 thf(sP30,plain,sP30 <=> (sP26 => sP12),introduced(definition,[new_symbols(definition,[sP30])])). % 4.54/4.95 thf(sP31,plain,sP31 <=> ((![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))))))))))))) => (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2)))))),introduced(definition,[new_symbols(definition,[sP31])])). % 4.54/4.95 thf(sP32,plain,sP32 <=> ((rel_s5 @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP32])])). % 4.54/4.95 thf(sP33,plain,sP33 <=> (![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => ((rel_s5 @ X1) @ eigen__4))),introduced(definition,[new_symbols(definition,[sP33])])). % 4.54/4.95 thf(sP34,plain,sP34 <=> (![X1:$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,[sP34])])). % 4.54/4.95 thf(sP35,plain,sP35 <=> (![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP35])])). % 4.54/4.95 thf(sP36,plain,sP36 <=> (![X1:$i]:((~((sP11 => (~(((rel_s5 @ eigen__5) @ X1)))))) => ((rel_s5 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP36])])). % 4.54/4.95 thf(sP37,plain,sP37 <=> (![X1:$i]:(((rel_s5 @ eigen__11) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP37])])). % 4.54/4.95 thf(sP38,plain,sP38 <=> ((rel_s5 @ eigen__4) @ eigen__10),introduced(definition,[new_symbols(definition,[sP38])])). % 4.54/4.95 thf(sP39,plain,sP39 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))),introduced(definition,[new_symbols(definition,[sP39])])). % 4.54/4.95 thf(sP40,plain,sP40 <=> (((rel_s5 @ eigen__5) @ eigen__8) => sP11),introduced(definition,[new_symbols(definition,[sP40])])). % 4.54/4.95 thf(sP41,plain,sP41 <=> (((rel_s5 @ eigen__0) @ eigen__0) => (~(sP16))),introduced(definition,[new_symbols(definition,[sP41])])). % 4.54/4.95 thf(sP42,plain,sP42 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP42])])). % 4.54/4.95 thf(sP43,plain,sP43 <=> (sP27 => (~(sP37))),introduced(definition,[new_symbols(definition,[sP43])])). % 4.54/4.95 thf(sP44,plain,sP44 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP44])])). % 4.54/4.95 thf(sP45,plain,sP45 <=> (((rel_s5 @ eigen__0) @ eigen__4) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP45])])). % 4.54/4.95 thf(sP46,plain,sP46 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__8) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__8) @ X2)))),introduced(definition,[new_symbols(definition,[sP46])])). % 4.54/4.95 thf(sP47,plain,sP47 <=> (![X1:$i]:(~((((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))) => (~(((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP47])])). % 4.54/4.95 thf(sP48,plain,sP48 <=> (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => ((rel_s5 @ X1) @ eigen__5))),introduced(definition,[new_symbols(definition,[sP48])])). % 4.54/4.95 thf(sP49,plain,sP49 <=> ((rel_s5 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP49])])). % 4.54/4.95 thf(sP50,plain,sP50 <=> (sP38 => sP29),introduced(definition,[new_symbols(definition,[sP50])])). % 4.54/4.95 thf(sP51,plain,sP51 <=> ((rel_s5 @ eigen__5) @ eigen__8),introduced(definition,[new_symbols(definition,[sP51])])). % 4.54/4.95 thf(sP52,plain,sP52 <=> (sP49 => sP16),introduced(definition,[new_symbols(definition,[sP52])])). % 4.54/4.95 thf(sP53,plain,sP53 <=> ((rel_s5 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP53])])). % 4.54/4.95 thf(sP54,plain,sP54 <=> (sP42 => (~(sP34))),introduced(definition,[new_symbols(definition,[sP54])])). % 4.54/4.95 thf(sP55,plain,sP55 <=> (sP13 => (~(sP27))),introduced(definition,[new_symbols(definition,[sP55])])). % 4.54/4.95 thf(sP56,plain,sP56 <=> ((~(sP24)) => sP13),introduced(definition,[new_symbols(definition,[sP56])])). % 4.54/4.95 thf(sP57,plain,sP57 <=> (![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,[sP57])])). % 4.54/4.95 thf(sP58,plain,sP58 <=> (![X1:$i]:((~((sP28 => (~(((rel_s5 @ eigen__4) @ X1)))))) => ((rel_s5 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP58])])). % 4.54/4.95 thf(sP59,plain,sP59 <=> (p @ eigen__8),introduced(definition,[new_symbols(definition,[sP59])])). % 4.54/4.95 thf(sP60,plain,sP60 <=> (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP60])])). % 4.54/4.95 thf(sP61,plain,sP61 <=> ((rel_s5 @ eigen__8) @ eigen__11),introduced(definition,[new_symbols(definition,[sP61])])). % 4.54/4.95 thf(sP62,plain,sP62 <=> (sP53 => sP35),introduced(definition,[new_symbols(definition,[sP62])])). % 4.54/4.95 thf(sP63,plain,sP63 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP63])])). % 4.54/4.95 thf(sP64,plain,sP64 <=> ((rel_s5 @ eigen__11) @ eigen__8),introduced(definition,[new_symbols(definition,[sP64])])). % 4.54/4.95 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 4.54/4.95 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 4.54/4.95 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 4.54/4.95 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 4.54/4.95 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 4.54/4.95 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 4.54/4.95 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 4.54/4.95 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 4.54/4.95 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 4.54/4.95 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 4.54/4.95 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 4.54/4.95 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 4.54/4.95 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 4.54/4.95 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 4.54/4.95 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 4.54/4.95 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 4.54/4.95 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 4.54/4.95 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 4.54/4.95 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 4.54/4.95 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 4.54/4.95 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 4.54/4.95 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 4.54/4.95 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)))))))). % 4.54/4.95 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 4.54/4.95 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 4.54/4.95 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 4.54/4.95 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 4.54/4.95 thf(def_mvalid,definition,(mvalid = (!!))). % 4.54/4.95 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 4.54/4.95 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 4.54/4.95 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 4.54/4.95 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 4.54/4.95 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 4.54/4.95 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((![X5:$i]:(((rel_s5 @ X4) @ X5) => (p @ X5))))))))))))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3)))))))))) => (~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (p @ X3))))))))) => (![X2:$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))))))))))))))))))))))))). % 4.54/4.95 thf(h1,negated_conjecture,(~(sP47)),inference(assume_negation,[status(cth)],[prove])). % 4.54/4.95 thf(1,plain,(~(sP17) | sP5),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(2,plain,((~(sP5) | sP55) | sP61),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(3,plain,((~(sP55) | ~(sP13)) | ~(sP27)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(4,plain,(~(sP58) | sP56),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(5,plain,((~(sP56) | sP24) | sP13),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(6,plain,((~(sP24) | ~(sP28)) | ~(sP38)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(7,plain,((~(sP40) | ~(sP51)) | sP11),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(8,plain,(~(sP46) | sP17),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(9,plain,(~(sP36) | sP15),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(10,plain,((~(sP15) | sP2) | sP28),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(11,plain,((~(sP2) | ~(sP11)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(12,plain,(~(sP46) | sP58),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(13,plain,(~(sP46) | sP36),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(14,plain,(~(sP48) | sP40),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(15,plain,(~(sP60) | sP14),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(16,plain,((~(sP14) | ~(sP23)) | sP4),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(17,plain,((~(sP41) | ~(sP49)) | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(18,plain,(~(sP25) | sP10),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(19,plain,((~(sP10) | ~(sP61)) | sP64),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(20,plain,(~(sP37) | sP8),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(21,plain,((~(sP8) | ~(sP64)) | sP59),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(22,plain,(sP43 | sP37),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(23,plain,(sP43 | sP27),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(24,plain,(sP29 | ~(sP43)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). % 4.54/4.95 thf(25,plain,(sP50 | ~(sP29)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(26,plain,(sP50 | sP38),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(27,plain,(sP3 | ~(sP50)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])). % 4.54/4.95 thf(28,plain,(~(sP57) | sP45),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(29,plain,((~(sP45) | ~(sP53)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(30,plain,(~(sP44) | sP46),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(31,plain,(~(sP63) | sP25),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(32,plain,(~(sP39) | sP52),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(33,plain,((~(sP52) | ~(sP49)) | sP16),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(34,plain,(sP9 | ~(sP59)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(35,plain,(sP9 | sP51),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(36,plain,(sP60 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 4.54/4.95 thf(37,plain,(~(sP63) | sP48),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(38,plain,(~(sP1) | sP23),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(39,plain,(~(sP63) | sP33),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(40,plain,(~(sP33) | sP30),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(41,plain,((~(sP30) | ~(sP26)) | sP12),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(42,plain,(~(sP21) | sP41),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(43,plain,(~(sP1) | sP49),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(44,plain,(~(sP63) | sP19),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(45,plain,(~(sP19) | sP22),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(46,plain,((~(sP22) | ~(sP42)) | sP32),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(47,plain,(~(sP34) | sP7),inference(all_rule,[status(thm)],[])). % 4.54/4.95 thf(48,plain,((~(sP7) | ~(sP32)) | sP21),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(49,plain,(sP18 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(50,plain,(sP18 | sP26),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(51,plain,(sP35 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 4.54/4.95 thf(52,plain,(sP62 | ~(sP35)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(53,plain,(sP62 | sP53),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(54,plain,(sP39 | ~(sP62)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 4.54/4.95 thf(55,plain,(sP31 | ~(sP39)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(56,plain,(sP31 | sP57),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(57,plain,(sP54 | sP34),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(58,plain,(sP54 | sP42),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(59,plain,(sP57 | ~(sP54)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 4.54/4.95 thf(60,plain,(sP6 | ~(sP57)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(61,plain,(sP6 | sP39),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(62,plain,((~(sP20) | ~(sP31)) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 4.54/4.95 thf(63,plain,(sP47 | sP20),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 4.54/4.95 thf(a3,axiom,(msymmetric @ rel_s5)). % 4.54/4.95 thf(64,plain,sP63,inference(preprocess,[status(thm)],[a3]). % 4.54/4.95 thf(a2,axiom,(mtransitive @ rel_s5)). % 4.54/4.95 thf(65,plain,sP44,inference(preprocess,[status(thm)],[a2]). % 4.54/4.95 thf(a1,axiom,(mreflexive @ rel_s5)). % 4.54/4.95 thf(66,plain,sP1,inference(preprocess,[status(thm)],[a1]). % 4.54/4.95 thf(67,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,h1])). % 4.54/4.95 thf(68,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0])). % 4.54/4.95 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((![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))))))))))))))))))))) => (![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) => (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])],[67,h1])). % 4.54/4.95 % SZS output end Proof %------------------------------------------------------------------------------