%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO447^1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 03:25:36 PM UTC 2025 % Result : Theorem 0.18s 0.58s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SYO447^1 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.31 % Computer : n001.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Thu Oct 9 01:25:53 EDT 2025 % 0.12/0.32 % CPUTime : % 0.18/0.58 % SZS status Theorem % 0.18/0.58 % Mode: mode213 % 0.18/0.58 % Inferences: 2049 % 0.18/0.58 % SZS output start Proof % 0.18/0.58 thf(ty_p, type, p : ($i>$o)). % 0.18/0.58 thf(ty_eigen__2, type, eigen__2 : $i). % 0.18/0.58 thf(ty_q, type, q : ($i>$o)). % 0.18/0.58 thf(ty_eigen__1, type, eigen__1 : $i). % 0.18/0.58 thf(ty_eigen__0, type, eigen__0 : $i). % 0.18/0.58 thf(ty_eigen__4, type, eigen__4 : $i). % 0.18/0.58 thf(ty_eigen__3, type, eigen__3 : $i). % 0.18/0.58 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 0.18/0.58 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.18/0.58 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__1) @ X1) => (q @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.18/0.58 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.18/0.58 thf(sP2,plain,sP2 <=> ((rel_s5 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP2])])). % 0.18/0.58 thf(sP3,plain,sP3 <=> ((rel_s5 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP3])])). % 0.18/0.58 thf(sP4,plain,sP4 <=> ((~((((rel_s5 @ eigen__0) @ eigen__1) => (~(sP2))))) => ((rel_s5 @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP4])])). % 0.18/0.58 thf(sP5,plain,sP5 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP5])])). % 0.18/0.58 thf(sP6,plain,sP6 <=> (((rel_s5 @ eigen__3) @ eigen__0) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.18/0.58 thf(sP7,plain,sP7 <=> (q @ eigen__4),introduced(definition,[new_symbols(definition,[sP7])])). % 0.18/0.58 thf(sP8,plain,sP8 <=> (sP5 => (~((p @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.18/0.58 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.18/0.58 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.18/0.58 thf(sP11,plain,sP11 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.18/0.58 thf(sP12,plain,sP12 <=> ((rel_s5 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP12])])). % 0.18/0.58 thf(sP13,plain,sP13 <=> (((rel_s5 @ eigen__0) @ eigen__1) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.18/0.58 thf(sP14,plain,sP14 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP14])])). % 0.18/0.58 thf(sP15,plain,sP15 <=> (p @ eigen__3),introduced(definition,[new_symbols(definition,[sP15])])). % 0.18/0.58 thf(sP16,plain,sP16 <=> (![X1:$i]:((~((((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.18/0.58 thf(sP17,plain,sP17 <=> ((~(sP6)) => sP12),introduced(definition,[new_symbols(definition,[sP17])])). % 0.18/0.58 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.18/0.58 thf(sP19,plain,sP19 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__3) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.18/0.58 thf(sP20,plain,sP20 <=> (sP2 => (q @ eigen__2)),introduced(definition,[new_symbols(definition,[sP20])])). % 0.18/0.58 thf(sP21,plain,sP21 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.18/0.58 thf(sP22,plain,sP22 <=> ((p @ eigen__1) => (~((![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (q @ X1)))))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.18/0.58 thf(sP23,plain,sP23 <=> ((rel_s5 @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP23])])). % 0.18/0.58 thf(sP24,plain,sP24 <=> (q @ eigen__2),introduced(definition,[new_symbols(definition,[sP24])])). % 0.18/0.58 thf(sP25,plain,sP25 <=> (p @ eigen__1),introduced(definition,[new_symbols(definition,[sP25])])). % 0.18/0.58 thf(sP26,plain,sP26 <=> (sP14 => sP24),introduced(definition,[new_symbols(definition,[sP26])])). % 0.18/0.58 thf(sP27,plain,sP27 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((p @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 0.18/0.58 thf(sP28,plain,sP28 <=> (sP5 => sP23),introduced(definition,[new_symbols(definition,[sP28])])). % 0.18/0.58 thf(sP29,plain,sP29 <=> (sP12 => sP7),introduced(definition,[new_symbols(definition,[sP29])])). % 0.18/0.58 thf(sP30,plain,sP30 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.18/0.58 thf(sP31,plain,sP31 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.18/0.58 thf(sP32,plain,sP32 <=> (((rel_s5 @ eigen__0) @ eigen__1) => sP22),introduced(definition,[new_symbols(definition,[sP32])])). % 0.18/0.58 thf(sP33,plain,sP33 <=> (![X1:$i]:((~((((rel_s5 @ eigen__0) @ eigen__1) => (~(((rel_s5 @ eigen__1) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP33])])). % 0.18/0.58 thf(sP34,plain,sP34 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP34])])). % 0.18/0.58 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.18/0.58 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.18/0.58 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.18/0.58 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.18/0.58 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.18/0.58 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.18/0.58 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.18/0.58 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.18/0.58 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.18/0.58 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.18/0.58 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.18/0.58 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.18/0.58 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.18/0.58 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.18/0.58 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.18/0.58 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.18/0.58 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.18/0.58 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.18/0.58 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.18/0.58 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.18/0.58 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.18/0.58 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.18/0.58 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.18/0.58 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.18/0.58 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.18/0.58 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))))))))). % 0.18/0.58 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.18/0.58 thf(def_mvalid,definition,(mvalid = (!!))). % 0.18/0.58 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.18/0.58 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.18/0.58 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.18/0.58 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 0.18/0.58 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 0.18/0.58 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~(((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3))))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~(((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))))))))))). % 0.18/0.58 thf(h1,negated_conjecture,(~((![X1:$i]:(~((((~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((p @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3))))))))))) => (~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((p @ X2) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))) => (~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2))))))))))))))))),inference(assume_negation,[status(cth)],[prove])). % 0.18/0.58 thf(h2,assumption,(((~(((~(sP21)) => (~(sP1))))) => (~(sP27))) => (~(((~(sP27)) => (~(((~(sP21)) => (~(sP1))))))))),introduced(assumption,[])). % 0.18/0.58 thf(h3,assumption,(~(((~(((~(sP21)) => (~(sP1))))) => (~(sP27))))),introduced(assumption,[])). % 0.18/0.58 thf(h4,assumption,(~(((~(sP27)) => (~(((~(sP21)) => (~(sP1)))))))),introduced(assumption,[])). % 0.18/0.58 thf(h5,assumption,(~(((~(sP21)) => (~(sP1))))),introduced(assumption,[])). % 0.18/0.58 thf(h6,assumption,sP27,introduced(assumption,[])). % 0.18/0.58 thf(h7,assumption,(~(sP21)),introduced(assumption,[])). % 0.18/0.58 thf(h8,assumption,sP1,introduced(assumption,[])). % 0.18/0.58 thf(h9,assumption,(~((sP34 => (~(sP25))))),introduced(assumption,[])). % 0.18/0.58 thf(h10,assumption,sP34,introduced(assumption,[])). % 0.18/0.58 thf(h11,assumption,sP25,introduced(assumption,[])). % 0.18/0.58 thf(1,plain,(~(sP18) | sP31),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(2,plain,(~(sP31) | sP33),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(3,plain,(~(sP33) | sP4),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(4,plain,((~(sP4) | sP13) | sP14),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(5,plain,((~(sP13) | ~(sP34)) | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(6,plain,(~(sP1) | sP26),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(7,plain,((~(sP26) | ~(sP14)) | sP24),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(8,plain,(sP20 | ~(sP24)),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(9,plain,(sP20 | sP2),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(10,plain,(sP30 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 0.18/0.58 thf(11,plain,(~(sP27) | sP32),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(12,plain,((~(sP32) | ~(sP34)) | sP22),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(13,plain,((~(sP22) | ~(sP25)) | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(a2,axiom,(mtransitive @ rel_s5)). % 0.18/0.58 thf(14,plain,sP18,inference(preprocess,[status(thm)],[a2]). % 0.18/0.58 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h10,h11,h8,h6])). % 0.18/0.58 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,15,h10,h11])). % 0.18/0.58 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,16,h9])). % 0.18/0.58 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,17,h7,h8])). % 0.18/0.58 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6])). % 0.18/0.58 thf(h12,assumption,(~(sP27)),introduced(assumption,[])). % 0.18/0.58 thf(h13,assumption,((~(sP21)) => (~(sP1))),introduced(assumption,[])). % 0.18/0.58 thf(h14,assumption,(~((sP5 => (sP15 => (~(sP10)))))),introduced(assumption,[])). % 0.18/0.58 thf(h15,assumption,sP5,introduced(assumption,[])). % 0.18/0.58 thf(h16,assumption,(~((sP15 => (~(sP10))))),introduced(assumption,[])). % 0.18/0.58 thf(h17,assumption,sP15,introduced(assumption,[])). % 0.18/0.58 thf(h18,assumption,sP10,introduced(assumption,[])). % 0.18/0.58 thf(h19,assumption,sP21,introduced(assumption,[])). % 0.18/0.58 thf(h20,assumption,(~(sP1)),introduced(assumption,[])). % 0.18/0.58 thf(20,plain,(~(sP21) | sP8),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(21,plain,((~(sP8) | ~(sP5)) | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(22,plain,$false,inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h15,h16,h14,h12,h13,h4,h2,h1,h0])],[20,21,h15,h17,h19])). % 0.18/0.58 thf(h21,assumption,(~((sP3 => sP7))),introduced(assumption,[])). % 0.18/0.58 thf(h22,assumption,sP3,introduced(assumption,[])). % 0.18/0.58 thf(h23,assumption,(~(sP7)),introduced(assumption,[])). % 0.18/0.58 thf(23,plain,(~(sP9) | sP28),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(24,plain,((~(sP28) | ~(sP5)) | sP23),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(25,plain,(~(sP11) | sP9),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(26,plain,(~(sP19) | sP16),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(27,plain,(~(sP16) | sP17),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(28,plain,((~(sP17) | sP6) | sP12),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(29,plain,((~(sP6) | ~(sP23)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(30,plain,(~(sP18) | sP19),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(31,plain,(~(sP10) | sP29),inference(all_rule,[status(thm)],[])). % 0.18/0.58 thf(32,plain,((~(sP29) | ~(sP12)) | sP7),inference(prop_rule,[status(thm)],[])). % 0.18/0.58 thf(a3,axiom,(msymmetric @ rel_s5)). % 0.18/0.58 thf(33,plain,sP11,inference(preprocess,[status(thm)],[a3]). % 0.18/0.58 thf(34,plain,$false,inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h20,h17,h18,h15,h16,h14,h12,h13,h4,h2,h1,h0])],[23,24,25,26,27,28,29,30,31,32,14,33,h15,h18,h22,h23])). % 0.18/0.58 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h20,h17,h18,h15,h16,h14,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,34,h22,h23])). % 0.18/0.58 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h20,h17,h18,h15,h16,h14,h12,h13,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__4)],[h20,35,h21])). % 0.18/0.58 thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h4,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h13,22,36,h19,h20])). % 0.18/0.58 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,37,h17,h18])). % 0.18/0.58 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,38,h15,h16])). % 0.18/0.58 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h12,39,h14])). % 0.18/0.58 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,40,h12,h13])). % 0.18/0.58 thf(42,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,19,41,h3,h4])). % 0.18/0.58 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,42,h2])). % 0.18/0.58 thf(44,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[43,h0])). % 0.18/0.58 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~(((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3))))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((~(((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[43,h1])). % 0.18/0.58 % SZS output end Proof %------------------------------------------------------------------------------