%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYN052^7 : 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 : n024.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 03:17:41 PM UTC 2025 % Result : Theorem 82.07s 82.27s % Output : Proof 82.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN052^7 : 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 % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Oct 8 15:21:53 EDT 2025 % 0.12/0.34 % CPUTime : % 82.07/82.27 % SZS status Theorem % 82.07/82.27 % Mode: mode460 % 82.07/82.27 % Inferences: 38922 % 82.07/82.27 % SZS output start Proof % 82.07/82.27 thf(ty_mu, type, mu : $tType). % 82.07/82.27 thf(ty_p, type, p : ($i>$o)). % 82.07/82.27 thf(ty_eigen__12, type, eigen__12 : $i). % 82.07/82.27 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 82.07/82.27 thf(ty_eigen__2, type, eigen__2 : $i). % 82.07/82.27 thf(ty_eigen__1, type, eigen__1 : $i). % 82.07/82.27 thf(ty_eigen__0, type, eigen__0 : $i). % 82.07/82.27 thf(ty_eigen__4, type, eigen__4 : mu). % 82.07/82.27 thf(ty_eigen__5, type, eigen__5 : $i). % 82.07/82.27 thf(ty_big_f, type, big_f : (mu>$i>$o)). % 82.07/82.27 thf(ty_eigen__3, type, eigen__3 : $i). % 82.07/82.27 thf(ty_eigen__63, type, eigen__63 : $i). % 82.07/82.27 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 82.07/82.27 thf(ty_eigen__62, type, eigen__62 : $i). % 82.07/82.27 thf(ty_eigen__64, type, eigen__64 : mu). % 82.07/82.27 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 82.07/82.27 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__3) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__12])])). % 82.07/82.27 thf(h1, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 82.07/82.27 thf(eigendef_eigen__64, definition, eigen__64 = (eps__1 @ (^[X1:mu]:(~((~(((exists_in_world @ X1) @ eigen__0))))))), introduced(definition,[new_symbols(definition,[eigen__64])])). % 82.07/82.27 thf(sP1,plain,sP1 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 82.07/82.27 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel_s4 @ eigen__62) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_f @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 82.07/82.27 thf(sP3,plain,sP3 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 82.07/82.27 thf(sP4,plain,sP4 <=> (![X1:$i]:((~((((rel_s4 @ eigen__2) @ eigen__3) => (~(((rel_s4 @ eigen__3) @ X1)))))) => ((rel_s4 @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP4])])). % 82.07/82.27 thf(sP5,plain,sP5 <=> ((exists_in_world @ eigen__4) @ eigen__3),introduced(definition,[new_symbols(definition,[sP5])])). % 82.07/82.27 thf(sP6,plain,sP6 <=> (![X1:$i]:((~((((exists_in_world @ eigen__64) @ eigen__0) => (~(((rel_s4 @ eigen__0) @ X1)))))) => ((exists_in_world @ eigen__64) @ X1))),introduced(definition,[new_symbols(definition,[sP6])])). % 82.07/82.27 thf(sP7,plain,sP7 <=> (![X1:$i]:((~((((exists_in_world @ eigen__64) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ X1)))))) => ((exists_in_world @ eigen__64) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 82.07/82.27 thf(sP8,plain,sP8 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP8])])). % 82.07/82.27 thf(sP9,plain,sP9 <=> ((~((((exists_in_world @ eigen__64) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ eigen__63)))))) => ((exists_in_world @ eigen__64) @ eigen__63)),introduced(definition,[new_symbols(definition,[sP9])])). % 82.07/82.27 thf(sP10,plain,sP10 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__3) => (~(((![X2:$i]:(((rel_s4 @ eigen__3) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3)))))) => (~((![X2:$i]:(((rel_s4 @ eigen__3) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 82.07/82.27 thf(sP11,plain,sP11 <=> ((~((((rel_s4 @ eigen__1) @ eigen__62) => (~(((rel_s4 @ eigen__62) @ eigen__63)))))) => ((rel_s4 @ eigen__1) @ eigen__63)),introduced(definition,[new_symbols(definition,[sP11])])). % 82.07/82.27 thf(sP12,plain,sP12 <=> ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__4) @ X2)))))) => (~((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__4) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 82.07/82.27 thf(sP13,plain,sP13 <=> ((big_f @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP13])])). % 82.07/82.27 thf(sP14,plain,sP14 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__63) => (![X2:$i]:(((rel_s4 @ eigen__63) @ X2) => ((big_f @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP14])])). % 82.07/82.27 thf(sP15,plain,sP15 <=> (sP8 => (~(((rel_s4 @ eigen__2) @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP15])])). % 82.07/82.27 thf(sP16,plain,sP16 <=> (((exists_in_world @ eigen__64) @ eigen__1) => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__64) @ X2)))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__64) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 82.07/82.27 thf(sP17,plain,sP17 <=> ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__64) @ X2)))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__64) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 82.07/82.27 thf(sP18,plain,sP18 <=> ((exists_in_world @ eigen__64) @ eigen__1),introduced(definition,[new_symbols(definition,[sP18])])). % 82.07/82.27 thf(sP19,plain,sP19 <=> (sP18 => (~(((rel_s4 @ eigen__1) @ eigen__63)))),introduced(definition,[new_symbols(definition,[sP19])])). % 82.07/82.27 thf(sP20,plain,sP20 <=> (((rel_s4 @ eigen__1) @ eigen__62) => (~(((rel_s4 @ eigen__62) @ eigen__63)))),introduced(definition,[new_symbols(definition,[sP20])])). % 82.07/82.27 thf(sP21,plain,sP21 <=> ((rel_s4 @ eigen__3) @ eigen__12),introduced(definition,[new_symbols(definition,[sP21])])). % 82.07/82.27 thf(sP22,plain,sP22 <=> (![X1:mu]:(~(((exists_in_world @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP22])])). % 82.07/82.27 thf(sP23,plain,sP23 <=> (![X1:$i]:(((rel_s4 @ eigen__63) @ X1) => ((big_f @ eigen__64) @ X1))),introduced(definition,[new_symbols(definition,[sP23])])). % 82.07/82.27 thf(sP24,plain,sP24 <=> ((rel_s4 @ eigen__3) @ eigen__5),introduced(definition,[new_symbols(definition,[sP24])])). % 82.07/82.27 thf(sP25,plain,sP25 <=> ((rel_s4 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP25])])). % 82.07/82.27 thf(sP26,plain,sP26 <=> (((exists_in_world @ eigen__64) @ eigen__0) => (~(((rel_s4 @ eigen__0) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP26])])). % 82.07/82.27 thf(sP27,plain,sP27 <=> (sP23 => (![X1:$i]:(((rel_s4 @ eigen__63) @ X1) => (p @ X1)))),introduced(definition,[new_symbols(definition,[sP27])])). % 82.07/82.27 thf(sP28,plain,sP28 <=> (sP24 => sP13),introduced(definition,[new_symbols(definition,[sP28])])). % 82.07/82.27 thf(sP29,plain,sP29 <=> (![X1:$i]:(![X2:$i]:((~((((exists_in_world @ eigen__64) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((exists_in_world @ eigen__64) @ X2)))),introduced(definition,[new_symbols(definition,[sP29])])). % 82.07/82.27 thf(sP30,plain,sP30 <=> (sP5 => (~(sP12))),introduced(definition,[new_symbols(definition,[sP30])])). % 82.07/82.27 thf(sP31,plain,sP31 <=> ((rel_s4 @ eigen__63) @ eigen__63),introduced(definition,[new_symbols(definition,[sP31])])). % 82.07/82.27 thf(sP32,plain,sP32 <=> ((rel_s4 @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP32])])). % 82.07/82.27 thf(sP33,plain,sP33 <=> ((rel_s4 @ eigen__1) @ eigen__62),introduced(definition,[new_symbols(definition,[sP33])])). % 82.07/82.27 thf(sP34,plain,sP34 <=> (sP32 => ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (p @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((big_f @ eigen__4) @ X1))))),introduced(definition,[new_symbols(definition,[sP34])])). % 82.07/82.27 thf(sP35,plain,sP35 <=> (((rel_s4 @ eigen__1) @ eigen__63) => sP27),introduced(definition,[new_symbols(definition,[sP35])])). % 82.07/82.27 thf(sP36,plain,sP36 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__64) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2)))))),introduced(definition,[new_symbols(definition,[sP36])])). % 82.07/82.27 thf(sP37,plain,sP37 <=> (sP3 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~(((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3)))))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 82.07/82.27 thf(sP38,plain,sP38 <=> ((exists_in_world @ eigen__64) @ eigen__63),introduced(definition,[new_symbols(definition,[sP38])])). % 82.07/82.27 thf(sP39,plain,sP39 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP39])])). % 82.07/82.27 thf(sP40,plain,sP40 <=> ((rel_s4 @ eigen__1) @ eigen__63),introduced(definition,[new_symbols(definition,[sP40])])). % 82.07/82.27 thf(sP41,plain,sP41 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_f @ X2) @ X4)))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_f @ X2) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP41])])). % 82.07/82.27 thf(sP42,plain,sP42 <=> ((rel_s4 @ eigen__2) @ eigen__12),introduced(definition,[new_symbols(definition,[sP42])])). % 82.07/82.27 thf(sP43,plain,sP43 <=> ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (p @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((big_f @ eigen__4) @ X1)))),introduced(definition,[new_symbols(definition,[sP43])])). % 82.07/82.27 thf(sP44,plain,sP44 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_f @ eigen__4) @ X2)))))),introduced(definition,[new_symbols(definition,[sP44])])). % 82.07/82.27 thf(sP45,plain,sP45 <=> (sP42 => (p @ eigen__12)),introduced(definition,[new_symbols(definition,[sP45])])). % 82.07/82.27 thf(sP46,plain,sP46 <=> (![X1:$i]:(((rel_s4 @ eigen__63) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP46])])). % 82.07/82.27 thf(sP47,plain,sP47 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__1) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP47])])). % 82.07/82.27 thf(sP48,plain,sP48 <=> (sP25 => sP10),introduced(definition,[new_symbols(definition,[sP48])])). % 82.07/82.27 thf(sP49,plain,sP49 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP49])])). % 82.07/82.27 thf(sP50,plain,sP50 <=> ((~(sP26)) => sP18),introduced(definition,[new_symbols(definition,[sP50])])). % 82.07/82.27 thf(sP51,plain,sP51 <=> (![X1:$i]:(~((![X2:mu]:(~(((exists_in_world @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP51])])). % 82.07/82.27 thf(sP52,plain,sP52 <=> (p @ eigen__63),introduced(definition,[new_symbols(definition,[sP52])])). % 82.07/82.27 thf(sP53,plain,sP53 <=> (sP31 => sP52),introduced(definition,[new_symbols(definition,[sP53])])). % 82.07/82.27 thf(sP54,plain,sP54 <=> ((~((((rel_s4 @ eigen__2) @ eigen__3) => (~(sP21))))) => sP42),introduced(definition,[new_symbols(definition,[sP54])])). % 82.07/82.27 thf(sP55,plain,sP55 <=> ((rel_s4 @ eigen__62) @ eigen__63),introduced(definition,[new_symbols(definition,[sP55])])). % 82.07/82.27 thf(sP56,plain,sP56 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((big_f @ eigen__4) @ X1))),introduced(definition,[new_symbols(definition,[sP56])])). % 82.07/82.27 thf(sP57,plain,sP57 <=> ((exists_in_world @ eigen__64) @ eigen__0),introduced(definition,[new_symbols(definition,[sP57])])). % 82.07/82.27 thf(sP58,plain,sP58 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~(((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3)))))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_f @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP58])])). % 82.07/82.27 thf(sP59,plain,sP59 <=> ((rel_s4 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP59])])). % 82.07/82.27 thf(sP60,plain,sP60 <=> (sP59 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP60])])). % 82.07/82.27 thf(sP61,plain,sP61 <=> (sP38 => sP23),introduced(definition,[new_symbols(definition,[sP61])])). % 82.07/82.27 thf(sP62,plain,sP62 <=> (sP21 => (p @ eigen__12)),introduced(definition,[new_symbols(definition,[sP62])])). % 82.07/82.27 thf(sP63,plain,sP63 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP63])])). % 82.07/82.27 thf(sP64,plain,sP64 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP64])])). % 82.07/82.27 thf(sP65,plain,sP65 <=> (sP55 => sP14),introduced(definition,[new_symbols(definition,[sP65])])). % 82.07/82.27 thf(sP66,plain,sP66 <=> (![X1:$i]:((~((sP33 => (~(((rel_s4 @ eigen__62) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP66])])). % 82.07/82.27 thf(sP67,plain,sP67 <=> (![X1:mu]:(![X2:$i]:(![X3:$i]:((~((((exists_in_world @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((exists_in_world @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP67])])). % 82.07/82.27 thf(sP68,plain,sP68 <=> ((~(sP15)) => sP25),introduced(definition,[new_symbols(definition,[sP68])])). % 82.07/82.27 thf(sP69,plain,sP69 <=> (p @ eigen__12),introduced(definition,[new_symbols(definition,[sP69])])). % 82.07/82.27 thf(sP70,plain,sP70 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__2) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__2) @ X2)))),introduced(definition,[new_symbols(definition,[sP70])])). % 82.07/82.27 thf(sP71,plain,sP71 <=> (![X1:$i]:((~((sP8 => (~(((rel_s4 @ eigen__2) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP71])])). % 82.07/82.27 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 82.07/82.27 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 82.07/82.27 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 82.07/82.27 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 82.07/82.27 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 82.07/82.27 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 82.07/82.27 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 82.07/82.27 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 82.07/82.27 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 82.07/82.27 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 82.07/82.27 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 82.07/82.27 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 82.07/82.27 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 82.07/82.27 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 82.07/82.27 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 82.07/82.27 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 82.07/82.27 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 82.07/82.27 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 82.07/82.27 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 82.07/82.27 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 82.07/82.27 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 82.07/82.27 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 82.07/82.27 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 82.07/82.27 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 82.07/82.27 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))))))))). % 82.07/82.27 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 82.07/82.27 thf(def_mvalid,definition,(mvalid = (!!))). % 82.07/82.27 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 82.07/82.27 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 82.07/82.27 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 82.07/82.27 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 82.07/82.27 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 82.07/82.27 thf(pel22,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4)))))))))))))))). % 82.07/82.27 thf(h2,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6)))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))))))))))))),inference(assume_negation,[status(cth)],[pel22])). % 82.07/82.27 thf(h3,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (p @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_f @ X3) @ X5)))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_f @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (p @ X5))))))))))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_f @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_f @ X4) @ X5))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3)))))))))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h4,assumption,(~((sP63 => (sP41 => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h5,assumption,sP63,introduced(assumption,[])). % 82.07/82.27 thf(h6,assumption,(~((sP41 => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2)))))))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h7,assumption,sP41,introduced(assumption,[])). % 82.07/82.27 thf(h8,assumption,((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h9,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4)))))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h10,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_f @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2)))))))),introduced(assumption,[])). % 82.07/82.27 thf(h11,assumption,(~((sP8 => (sP39 => (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_f @ X2) @ X3))))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h12,assumption,sP8,introduced(assumption,[])). % 82.07/82.27 thf(h13,assumption,(~((sP39 => (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_f @ X2) @ X3)))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h14,assumption,sP39,introduced(assumption,[])). % 82.07/82.27 thf(h15,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_f @ X2) @ X3))))))))),introduced(assumption,[])). % 82.07/82.27 thf(h16,assumption,(~((sP59 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__3) => (![X2:$i]:(((rel_s4 @ eigen__3) @ X2) => ((big_f @ X1) @ X2)))))))),introduced(assumption,[])). % 82.07/82.28 thf(h17,assumption,sP59,introduced(assumption,[])). % 82.07/82.28 thf(h18,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__3) => (![X2:$i]:(((rel_s4 @ eigen__3) @ X2) => ((big_f @ X1) @ X2))))))),introduced(assumption,[])). % 82.07/82.28 thf(h19,assumption,(~((sP5 => sP56))),introduced(assumption,[])). % 82.07/82.28 thf(h20,assumption,sP5,introduced(assumption,[])). % 82.07/82.28 thf(h21,assumption,(~(sP56)),introduced(assumption,[])). % 82.07/82.28 thf(h22,assumption,(~(sP28)),introduced(assumption,[])). % 82.07/82.28 thf(h23,assumption,sP24,introduced(assumption,[])). % 82.07/82.28 thf(h24,assumption,(~(sP13)),introduced(assumption,[])). % 82.07/82.28 thf(1,plain,((~(sP60) | ~(sP59)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(2,plain,((~(sP15) | ~(sP8)) | ~(sP59)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(3,plain,((~(sP68) | sP15) | sP25),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(4,plain,((~(sP54) | sP60) | sP42),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(5,plain,((~(sP34) | ~(sP32)) | sP43),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(6,plain,((~(sP28) | ~(sP24)) | sP13),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(7,plain,(~(sP56) | sP28),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(8,plain,((~(sP43) | ~(sP64)) | sP56),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(9,plain,(~(sP44) | sP34),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(10,plain,(sP12 | sP44),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(11,plain,(~(sP4) | sP54),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(12,plain,(~(sP71) | sP68),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(13,plain,((~(sP30) | ~(sP5)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(14,plain,((~(sP45) | ~(sP42)) | sP69),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(15,plain,(~(sP39) | sP45),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(16,plain,(sP62 | ~(sP69)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(17,plain,(sP62 | sP21),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(18,plain,(sP64 | ~(sP62)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])). % 82.07/82.28 thf(19,plain,(~(sP10) | sP30),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(20,plain,((~(sP48) | ~(sP25)) | sP10),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(21,plain,(~(sP47) | sP71),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(22,plain,(~(sP70) | sP4),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(23,plain,(~(sP1) | sP32),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(24,plain,(~(sP49) | sP70),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(25,plain,(~(sP49) | sP47),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(26,plain,(~(sP41) | sP48),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(a2,axiom,(mtransitive @ rel_s4)). % 82.07/82.28 thf(27,plain,sP49,inference(preprocess,[status(thm)],[a2]). % 82.07/82.28 thf(a1,axiom,(mreflexive @ rel_s4)). % 82.07/82.28 thf(28,plain,sP1,inference(preprocess,[status(thm)],[a1]). % 82.07/82.28 thf(29,plain,$false,inference(prop_unsat,[status(thm),assumptions([h23,h24,h22,h20,h21,h19,h17,h18,h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,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,h7,h12,h14,h17,h20,h23,h24,27,28])). % 82.07/82.28 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h20,h21,h19,h17,h18,h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,29,h23,h24])). % 82.07/82.28 thf(31,plain,$false,inference(tab_negall,[status(thm),assumptions([h20,h21,h19,h17,h18,h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__5)],[h21,30,h22])). % 82.07/82.28 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,31,h20,h21])). % 82.07/82.28 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h18,32,h19])). % 82.07/82.28 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,33,h17,h18])). % 82.07/82.28 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,34,h16])). % 82.07/82.28 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,35,h14,h15])). % 82.07/82.28 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,36,h12,h13])). % 82.07/82.28 thf(38,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,37,h11])). % 82.07/82.28 thf(h25,assumption,(~((sP33 => (sP2 => (![X1:$i]:(((rel_s4 @ eigen__62) @ X1) => (p @ X1))))))),introduced(assumption,[])). % 82.07/82.28 thf(h26,assumption,sP33,introduced(assumption,[])). % 82.07/82.28 thf(h27,assumption,(~((sP2 => (![X1:$i]:(((rel_s4 @ eigen__62) @ X1) => (p @ X1)))))),introduced(assumption,[])). % 82.07/82.28 thf(h28,assumption,sP2,introduced(assumption,[])). % 82.07/82.28 thf(h29,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__62) @ X1) => (p @ X1))))),introduced(assumption,[])). % 82.07/82.28 thf(h30,assumption,(~((sP55 => sP52))),introduced(assumption,[])). % 82.07/82.28 thf(h31,assumption,sP55,introduced(assumption,[])). % 82.07/82.28 thf(h32,assumption,(~(sP52)),introduced(assumption,[])). % 82.07/82.28 thf(39,plain,((~(sP35) | ~(sP40)) | sP27),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(40,plain,((~(sP20) | ~(sP33)) | ~(sP55)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(41,plain,(~(sP36) | sP35),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(42,plain,((~(sP11) | sP20) | sP40),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(43,plain,((~(sP19) | ~(sP18)) | ~(sP40)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(44,plain,((~(sP26) | ~(sP57)) | ~(sP63)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(45,plain,(sP17 | sP36),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(46,plain,((~(sP53) | ~(sP31)) | sP52),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(47,plain,((~(sP50) | sP26) | sP18),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(48,plain,((~(sP9) | sP19) | sP38),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(49,plain,(~(sP66) | sP11),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(50,plain,((~(sP16) | ~(sP18)) | ~(sP17)),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(51,plain,((~(sP61) | ~(sP38)) | sP23),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(52,plain,(~(sP46) | sP53),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(53,plain,((~(sP27) | ~(sP23)) | sP46),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(54,plain,(~(sP7) | sP9),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(55,plain,(~(sP6) | sP50),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(56,plain,(~(sP14) | sP61),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(57,plain,(~(sP58) | sP16),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(58,plain,((~(sP37) | ~(sP3)) | sP58),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(59,plain,((~(sP65) | ~(sP55)) | sP14),inference(prop_rule,[status(thm)],[])). % 82.07/82.28 thf(60,plain,(~(sP47) | sP66),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(61,plain,(~(sP29) | sP6),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(62,plain,(~(sP29) | sP7),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(63,plain,(~(sP67) | sP29),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(64,plain,(sP22 | sP57),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__64])). % 82.07/82.28 thf(65,plain,(~(sP51) | ~(sP22)),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(66,plain,(~(sP1) | sP31),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(67,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(68,plain,(~(sP49) | sP47),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(69,plain,(~(sP2) | sP65),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(70,plain,(~(sP41) | sP37),inference(all_rule,[status(thm)],[])). % 82.07/82.28 thf(cumulative_ax,axiom,sP67). % 82.07/82.28 thf(nonempty_ax,axiom,sP51). % 82.07/82.28 thf(71,plain,$false,inference(prop_unsat,[status(thm),assumptions([h31,h32,h30,h28,h29,h26,h27,h25,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,h5,h7,h26,h28,h31,h32,cumulative_ax,27,28,nonempty_ax])). % 82.07/82.28 thf(72,plain,$false,inference(tab_negimp,[status(thm),assumptions([h30,h28,h29,h26,h27,h25,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,71,h31,h32])). % 82.07/82.28 thf(73,plain,$false,inference(tab_negall,[status(thm),assumptions([h28,h29,h26,h27,h25,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__63)],[h29,72,h30])). % 82.07/82.28 thf(74,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h27,h25,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,73,h28,h29])). % 82.07/82.28 thf(75,plain,$false,inference(tab_negimp,[status(thm),assumptions([h25,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,74,h26,h27])). % 82.07/82.28 thf(76,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__62)],[h10,75,h25])). % 82.07/82.28 thf(77,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,38,76,h9,h10])). % 82.07/82.28 thf(78,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,77,h7,h8])). % 82.07/82.28 thf(79,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,78,h5,h6])). % 82.07/82.28 thf(80,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,79,h4])). % 82.07/82.28 thf(81,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,80,h3])). % 82.07/82.28 thf(82,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[81,h1])). % 82.07/82.28 thf(83,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[82,h0])). % 82.07/82.28 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_f @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_f @ X5) @ X6))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[81,h2])). % 82.07/82.28 % SZS output end Proof %------------------------------------------------------------------------------