%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n028.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 03:26:31 PM UTC 2025 % Result : Theorem 61.53s 61.73s % Output : Proof 61.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.35 % Computer : n028.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 9 01:16:53 EDT 2025 % 0.14/0.36 % CPUTime : % 61.53/61.73 % SZS status Theorem % 61.53/61.73 % Mode: mode368 % 61.53/61.73 % Inferences: 3544 % 61.53/61.73 % SZS output start Proof % 61.53/61.73 thf(ty_individuals, type, individuals : $tType). % 61.53/61.73 thf(ty_relr, type, relr : ($i>$i>$o)). % 61.53/61.73 thf(ty_eigen__2, type, eigen__2 : $i). % 61.53/61.73 thf(ty_eigen__1, type, eigen__1 : $i). % 61.53/61.73 thf(ty_eigen__0, type, eigen__0 : (individuals>$i>$o)). % 61.53/61.73 thf(ty_reli, type, reli : ($i>$i>$o)). % 61.53/61.73 thf(ty_eigen__3, type, eigen__3 : $i). % 61.53/61.73 thf(ty_eigen__10, type, eigen__10 : individuals). % 61.53/61.73 thf(ty_eigen__8, type, eigen__8 : $i). % 61.53/61.73 thf(ty_eigen__9, type, eigen__9 : $i). % 61.53/61.73 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 61.53/61.73 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 61.53/61.73 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((eigen__0 @ X4) @ X7)))))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:individuals]:(![X7:$i]:(((reli @ X5) @ X7) => ((eigen__0 @ X6) @ X7))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 61.53/61.73 thf(h1, assumption, (![X1:(individuals>$i>$o)>$o]:(![X2:individuals>$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 61.53/61.73 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:individuals>$i>$o]:(~((![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X5) @ X8)))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:individuals]:(![X8:$i]:(((reli @ X6) @ X8) => ((X1 @ X7) @ X8)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 61.53/61.73 thf(h2, assumption, (![X1:individuals>$o]:(![X2:individuals]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])). % 61.53/61.73 thf(eigendef_eigen__10, definition, eigen__10 = (eps__2 @ (^[X1:individuals]:(~((![X2:$i]:(((reli @ eigen__9) @ X2) => ((eigen__0 @ X1) @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 61.53/61.73 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => ((eigen__0 @ X3) @ X4))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 61.53/61.73 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => ((eigen__0 @ X5) @ X6)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 61.53/61.73 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~((((relr @ eigen__8) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => ((eigen__0 @ X2) @ X3))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 61.53/61.73 thf(sP1,plain,sP1 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (X1 @ X4))))) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 61.53/61.73 thf(sP2,plain,sP2 <=> (![X1:individuals]:(![X2:$i]:(((reli @ eigen__9) @ X2) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP2])])). % 61.53/61.73 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((eigen__0 @ X4) @ X7)))))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:individuals]:(![X7:$i]:(((reli @ X5) @ X7) => ((eigen__0 @ X6) @ X7)))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 61.53/61.73 thf(sP4,plain,sP4 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((eigen__0 @ X4) @ X7)))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 61.53/61.73 thf(sP5,plain,sP5 <=> ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))) => (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 61.53/61.73 thf(sP6,plain,sP6 <=> (((relr @ eigen__8) @ eigen__9) => sP2),introduced(definition,[new_symbols(definition,[sP6])])). % 61.53/61.73 thf(sP7,plain,sP7 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 61.53/61.73 thf(sP8,plain,sP8 <=> (((reli @ eigen__2) @ eigen__3) => sP7),introduced(definition,[new_symbols(definition,[sP8])])). % 61.53/61.73 thf(sP9,plain,sP9 <=> ((relr @ eigen__8) @ eigen__9),introduced(definition,[new_symbols(definition,[sP9])])). % 61.53/61.73 thf(sP10,plain,sP10 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP10])])). % 61.53/61.73 thf(sP11,plain,sP11 <=> (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((eigen__0 @ eigen__10) @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])). % 61.53/61.73 thf(sP12,plain,sP12 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6)))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 61.53/61.73 thf(sP13,plain,sP13 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => ((eigen__0 @ X3) @ X4)))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 61.53/61.73 thf(sP14,plain,sP14 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5)))))))) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 61.53/61.73 thf(sP15,plain,sP15 <=> (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => ((eigen__0 @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP15])])). % 61.53/61.73 thf(sP16,plain,sP16 <=> (sP9 => (![X1:$i]:(((reli @ eigen__9) @ X1) => ((eigen__0 @ eigen__10) @ X1)))),introduced(definition,[new_symbols(definition,[sP16])])). % 61.53/61.73 thf(sP17,plain,sP17 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 61.53/61.73 thf(sP18,plain,sP18 <=> (((reli @ eigen__1) @ eigen__2) => ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))) => sP17)),introduced(definition,[new_symbols(definition,[sP18])])). % 61.53/61.73 thf(sP19,plain,sP19 <=> ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))) => sP17),introduced(definition,[new_symbols(definition,[sP19])])). % 61.53/61.73 thf(sP20,plain,sP20 <=> (![X1:individuals]:(![X2:$i]:(((reli @ eigen__8) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__0 @ X1) @ X4)))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 61.53/61.73 thf(sP21,plain,sP21 <=> (![X1:$i]:(((reli @ eigen__9) @ X1) => ((eigen__0 @ eigen__10) @ X1))),introduced(definition,[new_symbols(definition,[sP21])])). % 61.53/61.73 thf(sP22,plain,sP22 <=> (![X1:$i]:(((relr @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => ((eigen__0 @ X3) @ X4)))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 61.53/61.73 thf(sP23,plain,sP23 <=> (![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X5) @ X8)))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:individuals]:(![X8:$i]:(((reli @ X6) @ X8) => ((X1 @ X7) @ X8))))))))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 61.53/61.73 thf(sP24,plain,sP24 <=> (![X1:$i]:(((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => ((eigen__0 @ X5) @ X6))))))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 61.53/61.73 thf(sP25,plain,sP25 <=> (((reli @ eigen__3) @ eigen__8) => sP20),introduced(definition,[new_symbols(definition,[sP25])])). % 61.53/61.73 thf(sP26,plain,sP26 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__0 @ eigen__10) @ X4))))))) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((eigen__0 @ eigen__10) @ X3))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 61.53/61.73 thf(sP27,plain,sP27 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 61.53/61.73 thf(sP28,plain,sP28 <=> ((reli @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP28])])). % 61.53/61.73 thf(sP29,plain,sP29 <=> ((reli @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP29])])). % 61.53/61.73 thf(sP30,plain,sP30 <=> (sP29 => sP22),introduced(definition,[new_symbols(definition,[sP30])])). % 61.53/61.73 thf(sP31,plain,sP31 <=> (sP28 => sP15),introduced(definition,[new_symbols(definition,[sP31])])). % 61.53/61.73 thf(sP32,plain,sP32 <=> (![X1:$i]:(((reli @ eigen__8) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((eigen__0 @ eigen__10) @ X3))))))),introduced(definition,[new_symbols(definition,[sP32])])). % 61.53/61.73 thf(sP33,plain,sP33 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP33])])). % 61.53/61.73 thf(sP34,plain,sP34 <=> (sP13 => sP22),introduced(definition,[new_symbols(definition,[sP34])])). % 61.53/61.73 thf(sP35,plain,sP35 <=> (sP32 => sP11),introduced(definition,[new_symbols(definition,[sP35])])). % 61.53/61.73 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 61.53/61.73 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 61.53/61.73 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 61.53/61.73 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 61.53/61.73 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 61.53/61.73 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 61.53/61.73 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 61.53/61.73 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 61.53/61.73 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 61.53/61.73 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 61.53/61.73 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 61.53/61.73 thf(def_mvalid,definition,(mvalid = (!!))). % 61.53/61.73 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 61.53/61.73 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 61.53/61.73 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 61.53/61.73 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))). % 61.53/61.73 thf(def_cs4_and,definition,(cs4_and = mand)). % 61.53/61.73 thf(def_cs4_or,definition,(cs4_or = mor)). % 61.53/61.73 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))). % 61.53/61.73 thf(def_cs4_true,definition,(cs4_true = mtrue)). % 61.53/61.73 thf(def_cs4_false,definition,(cs4_false = mfalse)). % 61.53/61.73 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))). % 61.53/61.73 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))). % 61.53/61.73 thf(def_cs4_valid,definition,(cs4_valid = mvalid)). % 61.53/61.73 thf(cs4_barcan,conjecture,(![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X5) @ X8)))))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:individuals]:(![X8:$i]:(((reli @ X6) @ X8) => ((X1 @ X7) @ X8)))))))))))))))). % 61.53/61.73 thf(h3,negated_conjecture,(~(sP23)),inference(assume_negation,[status(cth)],[cs4_barcan])). % 61.53/61.73 thf(1,plain,(~(sP11) | sP16),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(2,plain,((~(sP16) | ~(sP9)) | sP21),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(3,plain,(~(sP10) | sP26),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(4,plain,(~(sP26) | sP35),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(5,plain,((~(sP35) | ~(sP32)) | sP11),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(6,plain,(~(sP20) | sP32),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(7,plain,(~(sP7) | sP25),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(8,plain,((~(sP25) | ~(sP28)) | sP20),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(9,plain,(~(sP12) | sP8),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(10,plain,((~(sP8) | ~(sP29)) | sP7),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(11,plain,(~(sP33) | sP4),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(12,plain,(~(sP4) | sP5),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(13,plain,((~(sP5) | ~(sP27)) | sP12),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(14,plain,(sP2 | ~(sP21)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__10])). % 61.53/61.73 thf(15,plain,(sP6 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(16,plain,(sP6 | sP9),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(17,plain,(sP15 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])). % 61.53/61.73 thf(18,plain,(sP31 | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(19,plain,(sP31 | sP28),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(20,plain,(sP13 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 61.53/61.73 thf(21,plain,(~(sP1) | sP14),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(22,plain,(~(sP14) | sP34),inference(all_rule,[status(thm)],[])). % 61.53/61.73 thf(23,plain,((~(sP34) | ~(sP13)) | sP22),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(24,plain,(sP30 | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(25,plain,(sP30 | sP29),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(26,plain,(sP17 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 61.53/61.73 thf(27,plain,(sP19 | ~(sP17)),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(28,plain,(sP19 | sP27),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(29,plain,(sP18 | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 61.53/61.73 thf(30,plain,(sP24 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 61.53/61.73 thf(31,plain,(sP3 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 61.53/61.73 thf(32,plain,(sP23 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 61.53/61.73 thf(refl_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ X1)))). % 61.53/61.73 thf(33,plain,sP10,inference(preprocess,[status(thm)],[refl_axiom_i]). % 61.53/61.73 thf(trans_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ ((mbox @ reli) @ ((mbox @ reli) @ X1)))))). % 61.53/61.73 thf(34,plain,sP33,inference(preprocess,[status(thm)],[trans_axiom_i]). % 61.53/61.73 thf(ax_i_r_commute,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ ((mbox @ relr) @ X1))) @ ((mbox @ relr) @ ((mbox @ reli) @ X1)))))). % 61.53/61.73 thf(35,plain,sP1,inference(preprocess,[status(thm)],[ax_i_r_commute]). % 61.53/61.73 thf(36,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h3])). % 61.53/61.73 thf(37,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[36,h2])). % 61.53/61.73 thf(38,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[37,h1])). % 61.53/61.73 thf(39,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[38,h0])). % 61.53/61.73 thf(0,theorem,(![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X5) @ X8)))))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:individuals]:(![X8:$i]:(((reli @ X6) @ X8) => ((X1 @ X7) @ X8))))))))))))))),inference(contra,[status(thm),contra(discharge,[h3])],[36,h3])). % 61.53/61.73 % SZS output end Proof %------------------------------------------------------------------------------