%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYN367^7 : 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 : n003.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 03:18:08 PM UTC 2025 % Result : Theorem 12.93s 13.29s % Output : Proof 12.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN367^7 : TPTP v9.2.0. Released v5.5.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.35 % Computer : n003.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Wed Oct 8 15:09:53 EDT 2025 % 0.12/0.35 % CPUTime : % 12.93/13.29 % SZS status Theorem % 12.93/13.29 % Mode: mode461 % 12.93/13.29 % Inferences: 694 % 12.93/13.29 % SZS output start Proof % 12.93/13.29 thf(ty_mu, type, mu : $tType). % 12.93/13.29 thf(ty_eigen__6, type, eigen__6 : mu). % 12.93/13.29 thf(ty_p, type, p : ($i>$o)). % 12.93/13.29 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 12.93/13.29 thf(ty_eigen__2, type, eigen__2 : $i). % 12.93/13.29 thf(ty_eigen__7, type, eigen__7 : $i). % 12.93/13.29 thf(ty_eigen__1, type, eigen__1 : $i). % 12.93/13.29 thf(ty_eigen__0, type, eigen__0 : $i). % 12.93/13.29 thf(ty_eigen__4, type, eigen__4 : $i). % 12.93/13.29 thf(ty_eigen__5, type, eigen__5 : $i). % 12.93/13.29 thf(ty_eigen__3, type, eigen__3 : mu). % 12.93/13.29 thf(ty_eigen__8, type, eigen__8 : mu). % 12.93/13.29 thf(ty_eigen__9, type, eigen__9 : $i). % 12.93/13.29 thf(ty_big_q, type, big_q : (mu>$i>$o)). % 12.93/13.29 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 12.93/13.29 thf(ty_big_r, type, big_r : (mu>$i>$o)). % 12.93/13.29 thf(h0, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 12.93/13.29 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:mu]:(~((~(((exists_in_world @ X1) @ eigen__1))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 12.93/13.29 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 12.93/13.29 thf(eigendef_eigen__9, definition, eigen__9 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 12.93/13.29 thf(sP1,plain,sP1 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 12.93/13.29 thf(sP2,plain,sP2 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP2])])). % 12.93/13.29 thf(sP3,plain,sP3 <=> (((rel_s4 @ eigen__1) @ eigen__5) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__5) => (((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_r @ X1) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 12.93/13.29 thf(sP4,plain,sP4 <=> ((exists_in_world @ eigen__6) @ eigen__5),introduced(definition,[new_symbols(definition,[sP4])])). % 12.93/13.29 thf(sP5,plain,sP5 <=> ((rel_s4 @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP5])])). % 12.93/13.29 thf(sP6,plain,sP6 <=> ((rel_s4 @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP6])])). % 12.93/13.29 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 12.93/13.29 thf(sP8,plain,sP8 <=> (((rel_s4 @ eigen__5) @ eigen__7) => ((big_r @ eigen__6) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP8])])). % 12.93/13.29 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 12.93/13.29 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((big_r @ eigen__6) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 12.93/13.29 thf(sP11,plain,sP11 <=> ((rel_s4 @ eigen__1) @ eigen__9),introduced(definition,[new_symbols(definition,[sP11])])). % 12.93/13.29 thf(sP12,plain,sP12 <=> (sP11 => (p @ eigen__9)),introduced(definition,[new_symbols(definition,[sP12])])). % 12.93/13.29 thf(sP13,plain,sP13 <=> ((big_r @ eigen__6) @ eigen__7),introduced(definition,[new_symbols(definition,[sP13])])). % 12.93/13.29 thf(sP14,plain,sP14 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP14])])). % 12.93/13.29 thf(sP15,plain,sP15 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__5) => (((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 12.93/13.29 thf(sP16,plain,sP16 <=> ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_q @ eigen__8) @ X1)))))),introduced(definition,[new_symbols(definition,[sP16])])). % 12.93/13.29 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__1) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP17])])). % 12.93/13.29 thf(sP18,plain,sP18 <=> (sP4 => (((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((big_q @ eigen__6) @ X1)))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~(sP10))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 12.93/13.29 thf(sP19,plain,sP19 <=> (((rel_s4 @ eigen__2) @ eigen__9) => (p @ eigen__9)),introduced(definition,[new_symbols(definition,[sP19])])). % 12.93/13.29 thf(sP20,plain,sP20 <=> ((rel_s4 @ eigen__5) @ eigen__7),introduced(definition,[new_symbols(definition,[sP20])])). % 12.93/13.29 thf(sP21,plain,sP21 <=> (((exists_in_world @ eigen__8) @ eigen__1) => (sP16 => (~((sP9 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__8) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 12.93/13.29 thf(sP22,plain,sP22 <=> ((rel_s4 @ eigen__2) @ eigen__9),introduced(definition,[new_symbols(definition,[sP22])])). % 12.93/13.29 thf(sP23,plain,sP23 <=> ((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_q @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 12.93/13.29 thf(sP24,plain,sP24 <=> (((exists_in_world @ eigen__3) @ eigen__2) => (sP23 => (~((sP7 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_r @ eigen__3) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 12.93/13.29 thf(sP25,plain,sP25 <=> (sP5 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 12.93/13.29 thf(sP26,plain,sP26 <=> ((exists_in_world @ eigen__8) @ eigen__1),introduced(definition,[new_symbols(definition,[sP26])])). % 12.93/13.29 thf(sP27,plain,sP27 <=> (((rel_s4 @ eigen__1) @ eigen__5) => (~((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP27])])). % 12.93/13.29 thf(sP28,plain,sP28 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (((![X3:$i]:(((rel_s4 @ X1) @ X3) => (p @ X3))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3)))))) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 12.93/13.29 thf(sP29,plain,sP29 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP29])])). % 12.93/13.29 thf(sP30,plain,sP30 <=> ((~((((rel_s4 @ eigen__1) @ eigen__2) => (~(sP22))))) => sP11),introduced(definition,[new_symbols(definition,[sP30])])). % 12.93/13.29 thf(sP31,plain,sP31 <=> ((big_q @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP31])])). % 12.93/13.29 thf(sP32,plain,sP32 <=> ((exists_in_world @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP32])])). % 12.93/13.29 thf(sP33,plain,sP33 <=> (((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((big_q @ eigen__6) @ X1)))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~(sP10)))))),introduced(definition,[new_symbols(definition,[sP33])])). % 12.93/13.29 thf(sP34,plain,sP34 <=> (![X1:$i]:((~((((rel_s4 @ eigen__1) @ eigen__2) => (~(((rel_s4 @ eigen__2) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP34])])). % 12.93/13.29 thf(sP35,plain,sP35 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_q @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP35])])). % 12.93/13.29 thf(sP36,plain,sP36 <=> (((rel_s4 @ eigen__1) @ eigen__2) => sP1),introduced(definition,[new_symbols(definition,[sP36])])). % 12.93/13.29 thf(sP37,plain,sP37 <=> ((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~(sP10))),introduced(definition,[new_symbols(definition,[sP37])])). % 12.93/13.29 thf(sP38,plain,sP38 <=> (sP7 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_r @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP38])])). % 12.93/13.29 thf(sP39,plain,sP39 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP39])])). % 12.93/13.29 thf(sP40,plain,sP40 <=> (((rel_s4 @ eigen__1) @ eigen__2) => (~(sP22))),introduced(definition,[new_symbols(definition,[sP40])])). % 12.93/13.29 thf(sP41,plain,sP41 <=> (sP14 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => ((sP29 => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_q @ X1) @ X2)))))) => (~((sP9 => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_r @ X1) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP41])])). % 12.93/13.29 thf(sP42,plain,sP42 <=> (![X1:$i]:(~((![X2:mu]:(~(((exists_in_world @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP42])])). % 12.93/13.29 thf(sP43,plain,sP43 <=> (p @ eigen__9),introduced(definition,[new_symbols(definition,[sP43])])). % 12.93/13.29 thf(sP44,plain,sP44 <=> (sP16 => (~((sP9 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__8) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP44])])). % 12.93/13.29 thf(sP45,plain,sP45 <=> ((rel_s4 @ eigen__1) @ eigen__5),introduced(definition,[new_symbols(definition,[sP45])])). % 12.93/13.29 thf(sP46,plain,sP46 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP46])])). % 12.93/13.29 thf(sP47,plain,sP47 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => ((sP29 => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_q @ X1) @ X2)))))) => (~((sP9 => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP47])])). % 12.93/13.29 thf(sP48,plain,sP48 <=> (sP6 => sP31),introduced(definition,[new_symbols(definition,[sP48])])). % 12.93/13.29 thf(sP49,plain,sP49 <=> (![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP49])])). % 12.93/13.29 thf(sP50,plain,sP50 <=> (sP9 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__8) @ X1)))))),introduced(definition,[new_symbols(definition,[sP50])])). % 12.93/13.29 thf(sP51,plain,sP51 <=> (sP49 => (~((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((big_q @ eigen__6) @ X1)))))),introduced(definition,[new_symbols(definition,[sP51])])). % 12.93/13.29 thf(sP52,plain,sP52 <=> (![X1:mu]:(~(((exists_in_world @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP52])])). % 12.93/13.29 thf(sP53,plain,sP53 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP53])])). % 12.93/13.29 thf(sP54,plain,sP54 <=> (sP23 => (~(sP38))),introduced(definition,[new_symbols(definition,[sP54])])). % 12.93/13.29 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 12.93/13.29 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 12.93/13.29 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 12.93/13.29 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 12.93/13.29 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 12.93/13.29 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 12.93/13.29 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 12.93/13.29 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 12.93/13.29 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 12.93/13.29 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 12.93/13.29 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 12.93/13.29 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 12.93/13.29 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 12.93/13.29 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 12.93/13.29 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 12.93/13.29 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 12.93/13.29 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 12.93/13.29 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 12.93/13.29 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 12.93/13.29 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 12.93/13.29 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 12.93/13.29 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 12.93/13.29 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 12.93/13.29 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 12.93/13.29 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))))))))). % 12.93/13.29 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 12.93/13.29 thf(def_mvalid,definition,(mvalid = (!!))). % 12.93/13.29 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 12.93/13.29 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 12.93/13.29 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 12.93/13.29 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 12.93/13.29 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 12.93/13.29 thf(x2118,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => ((~((~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))))))) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))). % 12.93/13.29 thf(h2,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5)))))))))))))),inference(assume_negation,[status(cth)],[x2118])). % 12.93/13.29 thf(h3,assumption,(~((![X1:$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) => (p @ X4))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4)))))) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (p @ X5))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4))))))))))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4))))))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h4,assumption,(~((((rel_s4 @ eigen__0) @ eigen__1) => (sP28 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3)))))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h5,assumption,((rel_s4 @ eigen__0) @ eigen__1),introduced(assumption,[])). % 12.93/13.29 thf(h6,assumption,(~((sP28 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h7,assumption,sP28,introduced(assumption,[])). % 12.93/13.29 thf(h8,assumption,(~(((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3)))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h9,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h10,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))))),introduced(assumption,[])). % 12.93/13.29 thf(h11,assumption,(~((sP46 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_q @ X1) @ X2)))))))),introduced(assumption,[])). % 12.93/13.29 thf(h12,assumption,sP46,introduced(assumption,[])). % 12.93/13.29 thf(h13,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_q @ X1) @ X2))))))),introduced(assumption,[])). % 12.93/13.29 thf(h14,assumption,(~((sP32 => sP35))),introduced(assumption,[])). % 12.93/13.29 thf(h15,assumption,sP32,introduced(assumption,[])). % 12.93/13.29 thf(h16,assumption,(~(sP35)),introduced(assumption,[])). % 12.93/13.29 thf(h17,assumption,(~(sP48)),introduced(assumption,[])). % 12.93/13.29 thf(h18,assumption,sP6,introduced(assumption,[])). % 12.93/13.29 thf(h19,assumption,(~(sP31)),introduced(assumption,[])). % 12.93/13.29 thf(h20,assumption,(~((sP45 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__5) => (![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_r @ X1) @ X2)))))))),introduced(assumption,[])). % 12.93/13.29 thf(h21,assumption,sP45,introduced(assumption,[])). % 12.93/13.29 thf(h22,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__5) => (![X2:$i]:(((rel_s4 @ eigen__5) @ X2) => ((big_r @ X1) @ X2))))))),introduced(assumption,[])). % 12.93/13.29 thf(h23,assumption,(~((sP4 => sP10))),introduced(assumption,[])). % 12.93/13.29 thf(h24,assumption,sP4,introduced(assumption,[])). % 12.93/13.29 thf(h25,assumption,(~(sP10)),introduced(assumption,[])). % 12.93/13.29 thf(h26,assumption,(~(sP8)),introduced(assumption,[])). % 12.93/13.29 thf(h27,assumption,sP20,introduced(assumption,[])). % 12.93/13.29 thf(h28,assumption,(~(sP13)),introduced(assumption,[])). % 12.93/13.29 thf(1,plain,(~(sP10) | sP8),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(2,plain,((~(sP8) | ~(sP20)) | sP13),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(3,plain,(~(sP35) | sP48),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(4,plain,((~(sP48) | ~(sP6)) | sP31),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(5,plain,(sP38 | sP7),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(6,plain,(sP23 | sP35),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(7,plain,(sP37 | sP10),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(8,plain,(sP51 | sP49),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(9,plain,(~(sP17) | sP34),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(10,plain,(~(sP34) | sP30),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(11,plain,((~(sP30) | sP40) | sP11),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(12,plain,((~(sP40) | ~(sP46)) | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(13,plain,(~(sP7) | sP25),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(14,plain,((~(sP25) | ~(sP5)) | ~(sP53)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(15,plain,(~(sP29) | sP12),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(16,plain,((~(sP12) | ~(sP11)) | sP43),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(17,plain,(sP19 | ~(sP43)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(18,plain,(sP19 | sP22),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(19,plain,(sP53 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9])). % 12.93/13.29 thf(20,plain,(~(sP9) | sP27),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(21,plain,((~(sP27) | ~(sP45)) | ~(sP49)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(22,plain,(sP50 | sP9),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(23,plain,(sP16 | sP29),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(24,plain,((~(sP41) | ~(sP14)) | sP47),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(25,plain,(~(sP47) | sP21),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(26,plain,((~(sP21) | ~(sP26)) | sP44),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(27,plain,((~(sP44) | ~(sP16)) | ~(sP50)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(28,plain,(sP52 | sP26),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 12.93/13.29 thf(29,plain,(~(sP42) | ~(sP52)),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(30,plain,(~(sP2) | sP14),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(31,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(32,plain,(~(sP39) | sP17),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(33,plain,(~(sP28) | sP3),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(34,plain,((~(sP3) | ~(sP45)) | sP15),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(35,plain,(~(sP15) | sP18),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(36,plain,((~(sP18) | ~(sP4)) | sP33),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(37,plain,((~(sP33) | ~(sP51)) | ~(sP37)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(38,plain,(~(sP28) | sP41),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(39,plain,(~(sP28) | sP36),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(40,plain,((~(sP36) | ~(sP46)) | sP1),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(41,plain,(~(sP1) | sP24),inference(all_rule,[status(thm)],[])). % 12.93/13.29 thf(42,plain,((~(sP24) | ~(sP32)) | sP54),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(43,plain,((~(sP54) | ~(sP23)) | ~(sP38)),inference(prop_rule,[status(thm)],[])). % 12.93/13.29 thf(a2,axiom,(mtransitive @ rel_s4)). % 12.93/13.29 thf(44,plain,sP39,inference(preprocess,[status(thm)],[a2]). % 12.93/13.29 thf(a1,axiom,(mreflexive @ rel_s4)). % 12.93/13.29 thf(45,plain,sP2,inference(preprocess,[status(thm)],[a1]). % 12.93/13.29 thf(nonempty_ax,axiom,sP42). % 12.93/13.29 thf(46,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,h7,h12,h15,h18,h19,h21,h24,h27,h28,44,45,nonempty_ax])). % 12.93/13.29 thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,46,h27,h28])). % 12.93/13.29 thf(48,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[h25,47,h26])). % 12.93/13.29 thf(49,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,48,h24,h25])). % 12.93/13.29 thf(50,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h22,49,h23])). % 12.93/13.29 thf(51,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,50,h21,h22])). % 12.93/13.29 thf(52,plain,$false,inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h10,51,h20])). % 12.93/13.29 thf(53,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,52,h18,h19])). % 12.93/13.29 thf(54,plain,$false,inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,53,h17])). % 12.93/13.29 thf(55,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,54,h15,h16])). % 12.93/13.29 thf(56,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,55,h14])). % 12.93/13.29 thf(57,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,56,h12,h13])). % 12.93/13.29 thf(58,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,57,h11])). % 12.93/13.29 thf(59,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,58,h9,h10])). % 12.93/13.29 thf(60,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,59,h7,h8])). % 12.93/13.29 thf(61,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,60,h5,h6])). % 12.93/13.29 thf(62,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,61,h4])). % 12.93/13.29 thf(63,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,62,h3])). % 12.93/13.29 thf(64,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[63,h1])). % 12.93/13.29 thf(65,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[64,h0])). % 12.93/13.29 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) => (p @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))))))) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5)))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[63,h2])). % 12.93/13.29 % SZS output end Proof %------------------------------------------------------------------------------