%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL692^1 : TPTP v9.3.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:27 PM UTC 2026 % Result : Theorem 13.07s 13.37s % Output : Proof 13.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL692^1 : TPTP v9.3.1. Released v3.7.0. % 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.35 % Computer : n016.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 19:05:00 UTC 2026 % 0.09/0.36 % CPUTime : % 13.07/13.37 % SZS status Theorem % 13.07/13.37 % Mode: mode454 % 13.07/13.37 % Inferences: 42 % 13.07/13.37 % SZS output start Proof % 13.07/13.37 thf(ty_relr, type, relr : ($i>$i>$o)). % 13.07/13.37 thf(ty_eigen__2, type, eigen__2 : $i). % 13.07/13.37 thf(ty_eigen__1, type, eigen__1 : $i). % 13.07/13.37 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 13.07/13.37 thf(ty_reli, type, reli : ($i>$i>$o)). % 13.07/13.37 thf(ty_eigen__3, type, eigen__3 : $i). % 13.07/13.37 thf(ty_eigen__8, type, eigen__8 : $i). % 13.07/13.37 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.07/13.37 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 13.07/13.37 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.07/13.37 thf(h1, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 13.07/13.37 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.07/13.37 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4)))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 13.07/13.37 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 13.07/13.37 thf(sP1,plain,sP1 <=> (![X1:$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])])). % 13.07/13.37 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))))) => (![X1:$i]:(((relr @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.07/13.37 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7))))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.07/13.37 thf(sP4,plain,sP4 <=> (((reli @ eigen__3) @ eigen__8) => (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.07/13.37 thf(sP5,plain,sP5 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.07/13.37 thf(sP6,plain,sP6 <=> (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.07/13.37 thf(sP7,plain,sP7 <=> (![X1:$i]:((![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 13.07/13.37 thf(sP8,plain,sP8 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.07/13.37 thf(sP9,plain,sP9 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.07/13.37 thf(sP10,plain,sP10 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 13.07/13.37 thf(sP11,plain,sP11 <=> (sP6 => (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 13.07/13.37 thf(sP12,plain,sP12 <=> (((reli @ eigen__1) @ eigen__2) => ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))) => sP10)),introduced(definition,[new_symbols(definition,[sP12])])). % 13.07/13.37 thf(sP13,plain,sP13 <=> ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))) => sP10),introduced(definition,[new_symbols(definition,[sP13])])). % 13.07/13.37 thf(sP14,plain,sP14 <=> (![X1:$i]:(((relr @ eigen__8) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 13.07/13.37 thf(sP15,plain,sP15 <=> ((reli @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP15])])). % 13.07/13.37 thf(sP16,plain,sP16 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((relr @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 13.07/13.37 thf(sP17,plain,sP17 <=> (sP15 => (![X1:$i]:(((relr @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 13.07/13.37 thf(sP18,plain,sP18 <=> (![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8)))))))))))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.07/13.37 thf(sP19,plain,sP19 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 13.07/13.37 thf(sP20,plain,sP20 <=> (![X1:$i]:(((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 13.07/13.37 thf(sP21,plain,sP21 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 13.07/13.37 thf(sP22,plain,sP22 <=> ((reli @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP22])])). % 13.07/13.37 thf(sP23,plain,sP23 <=> (sP15 => sP19),introduced(definition,[new_symbols(definition,[sP23])])). % 13.07/13.37 thf(sP24,plain,sP24 <=> (sP22 => sP6),introduced(definition,[new_symbols(definition,[sP24])])). % 13.07/13.37 thf(sP25,plain,sP25 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))))) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))))))),introduced(definition,[new_symbols(definition,[sP25])])). % 13.07/13.37 thf(sP26,plain,sP26 <=> (![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,[sP26])])). % 13.07/13.37 thf(sP27,plain,sP27 <=> (![X1:$i]:(((relr @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 13.07/13.37 thf(sP28,plain,sP28 <=> (sP21 => sP8),introduced(definition,[new_symbols(definition,[sP28])])). % 13.07/13.37 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 13.07/13.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.07/13.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.07/13.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.07/13.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 13.07/13.37 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.07/13.37 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 13.07/13.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.07/13.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 13.07/13.37 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 13.07/13.37 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 13.07/13.37 thf(def_mvalid,definition,(mvalid = (!!))). % 13.07/13.37 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.07/13.37 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.07/13.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.07/13.37 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))). % 13.07/13.37 thf(def_cs4_and,definition,(cs4_and = mand)). % 13.07/13.37 thf(def_cs4_or,definition,(cs4_or = mor)). % 13.07/13.37 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))). % 13.07/13.37 thf(def_cs4_true,definition,(cs4_true = mtrue)). % 13.07/13.37 thf(def_cs4_false,definition,(cs4_false = mfalse)). % 13.07/13.37 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))). % 13.07/13.37 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))). % 13.07/13.37 thf(def_cs4_valid,definition,(cs4_valid = mvalid)). % 13.07/13.37 thf(cs4_trans,conjecture,(![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))))))))))))). % 13.07/13.37 thf(h2,negated_conjecture,(~(sP18)),inference(assume_negation,[status(cth)],[cs4_trans])). % 13.07/13.37 thf(1,plain,(~(sP7) | sP11),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(2,plain,((~(sP11) | ~(sP6)) | sP14),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(3,plain,(~(sP19) | sP24),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(4,plain,((~(sP24) | ~(sP22)) | sP6),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(5,plain,(sP4 | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(6,plain,(sP4 | sP22),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(7,plain,(sP5 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 13.07/13.37 thf(8,plain,(~(sP8) | sP23),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(9,plain,((~(sP23) | ~(sP15)) | sP19),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(10,plain,(~(sP16) | sP7),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(11,plain,(~(sP1) | sP25),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(12,plain,(~(sP25) | sP2),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(13,plain,((~(sP2) | ~(sP5)) | sP27),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(14,plain,(sP17 | ~(sP27)),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(15,plain,(sP17 | sP15),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(16,plain,(sP10 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 13.07/13.37 thf(17,plain,(~(sP26) | sP9),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(18,plain,(~(sP9) | sP28),inference(all_rule,[status(thm)],[])). % 13.07/13.37 thf(19,plain,((~(sP28) | ~(sP21)) | sP8),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(20,plain,(sP13 | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(21,plain,(sP13 | sP21),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(22,plain,(sP12 | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 13.07/13.37 thf(23,plain,(sP20 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 13.07/13.37 thf(24,plain,(sP3 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.07/13.37 thf(25,plain,(sP18 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 13.07/13.37 thf(trans_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ ((mbox @ reli) @ ((mbox @ reli) @ X1)))))). % 13.07/13.37 thf(26,plain,sP26,inference(preprocess,[status(thm)],[trans_axiom_i]). % 13.07/13.37 thf(trans_axiom_r,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ relr) @ X1)) @ ((mbox @ relr) @ ((mbox @ relr) @ X1)))))). % 13.07/13.37 thf(27,plain,sP16,inference(preprocess,[status(thm)],[trans_axiom_r]). % 13.07/13.37 thf(ax_i_r_commute,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ ((mbox @ relr) @ X1))) @ ((mbox @ relr) @ ((mbox @ reli) @ X1)))))). % 13.07/13.37 thf(28,plain,sP1,inference(preprocess,[status(thm)],[ax_i_r_commute]). % 13.07/13.37 thf(29,plain,$false,inference(prop_unsat,[status(thm),assumptions([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,h2])). % 13.07/13.37 thf(30,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[29,h1])). % 13.07/13.37 thf(31,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[30,h0])). % 13.07/13.37 thf(0,theorem,(![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[29,h2])). % 13.07/13.37 % SZS output end Proof %------------------------------------------------------------------------------