%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO444^1 : 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 : n027.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 0.35s 0.63s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO444^1 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n027.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 9 00:27:53 EDT 2025 % 0.12/0.34 % CPUTime : % 0.35/0.63 % SZS status Theorem % 0.35/0.63 % Mode: mode213 % 0.35/0.63 % Inferences: 2186 % 0.35/0.63 % SZS output start Proof % 0.35/0.63 thf(ty_p, type, p : ($i>$o)). % 0.35/0.63 thf(ty_eigen__2, type, eigen__2 : $i). % 0.35/0.63 thf(ty_q, type, q : ($i>$o)). % 0.35/0.63 thf(ty_eigen__1, type, eigen__1 : $i). % 0.35/0.63 thf(ty_eigen__0, type, eigen__0 : $i). % 0.35/0.63 thf(ty_eigen__4, type, eigen__4 : $i). % 0.35/0.63 thf(ty_eigen__5, type, eigen__5 : $i). % 0.35/0.63 thf(ty_eigen__3, type, eigen__3 : $i). % 0.35/0.63 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 0.35/0.63 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.35/0.63 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__1) @ X1) => (~((q @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.35/0.63 thf(sP1,plain,sP1 <=> (p @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.35/0.63 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.35/0.63 thf(sP3,plain,sP3 <=> ((~((((rel_s5 @ eigen__0) @ eigen__1) => (~(((rel_s5 @ eigen__1) @ eigen__2)))))) => ((rel_s5 @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.35/0.63 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.35/0.63 thf(sP5,plain,sP5 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.35/0.63 thf(sP6,plain,sP6 <=> (q @ eigen__4),introduced(definition,[new_symbols(definition,[sP6])])). % 0.35/0.63 thf(sP7,plain,sP7 <=> (((rel_s5 @ eigen__0) @ eigen__3) => (~((p @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.35/0.63 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.35/0.63 thf(sP9,plain,sP9 <=> (p @ eigen__3),introduced(definition,[new_symbols(definition,[sP9])])). % 0.35/0.63 thf(sP10,plain,sP10 <=> ((~((((rel_s5 @ eigen__5) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__4)))))) => ((rel_s5 @ eigen__5) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.35/0.63 thf(sP11,plain,sP11 <=> (![X1:$i]:((~((((rel_s5 @ eigen__5) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.35/0.63 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.35/0.63 thf(sP13,plain,sP13 <=> ((rel_s5 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP13])])). % 0.35/0.63 thf(sP14,plain,sP14 <=> (((rel_s5 @ eigen__0) @ eigen__1) => (~(((rel_s5 @ eigen__1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.35/0.63 thf(sP15,plain,sP15 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP15])])). % 0.35/0.63 thf(sP16,plain,sP16 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP16])])). % 0.35/0.63 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.35/0.63 thf(sP18,plain,sP18 <=> (((rel_s5 @ eigen__5) @ eigen__0) => (~(sP13))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.35/0.63 thf(sP19,plain,sP19 <=> (((rel_s5 @ eigen__5) @ eigen__4) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.35/0.63 thf(sP20,plain,sP20 <=> (((rel_s5 @ eigen__1) @ eigen__2) => (~((q @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.35/0.63 thf(sP21,plain,sP21 <=> (q @ eigen__2),introduced(definition,[new_symbols(definition,[sP21])])). % 0.35/0.63 thf(sP22,plain,sP22 <=> (sP1 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.35/0.63 thf(sP23,plain,sP23 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP23])])). % 0.35/0.63 thf(sP24,plain,sP24 <=> (sP15 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP24])])). % 0.35/0.63 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.35/0.63 thf(sP26,plain,sP26 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__5) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__5) @ X2)))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.35/0.63 thf(sP27,plain,sP27 <=> ((rel_s5 @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP27])])). % 0.35/0.63 thf(sP28,plain,sP28 <=> ((rel_s5 @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP28])])). % 0.35/0.63 thf(sP29,plain,sP29 <=> ((rel_s5 @ eigen__5) @ eigen__0),introduced(definition,[new_symbols(definition,[sP29])])). % 0.35/0.63 thf(sP30,plain,sP30 <=> (sP23 => sP22),introduced(definition,[new_symbols(definition,[sP30])])). % 0.35/0.63 thf(sP31,plain,sP31 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.35/0.63 thf(sP32,plain,sP32 <=> (![X1:$i]:((~((sP23 => (~(((rel_s5 @ eigen__1) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP32])])). % 0.35/0.63 thf(sP33,plain,sP33 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((p @ X1) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP33])])). % 0.35/0.63 thf(sP34,plain,sP34 <=> ((rel_s5 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP34])])). % 0.35/0.63 thf(sP35,plain,sP35 <=> (sP28 => sP29),introduced(definition,[new_symbols(definition,[sP35])])). % 0.35/0.63 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.35/0.63 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.35/0.63 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.35/0.63 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.35/0.63 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.35/0.63 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.35/0.63 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.35/0.63 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.35/0.63 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.35/0.63 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.35/0.63 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.35/0.63 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.35/0.63 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.35/0.63 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.35/0.63 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.35/0.63 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.35/0.63 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.35/0.63 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.35/0.63 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.35/0.63 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.35/0.63 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.35/0.63 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.35/0.63 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)))))))). % 0.35/0.63 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.35/0.63 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.35/0.63 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 0.35/0.63 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.35/0.63 thf(def_mvalid,definition,(mvalid = (!!))). % 0.35/0.63 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.35/0.63 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.35/0.63 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.35/0.63 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 0.35/0.63 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 0.35/0.63 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3)))))))))))))) => ((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2))))))))))))) => (~(((~((~(((~((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3)))))))))))))))))). % 0.35/0.63 thf(h1,negated_conjecture,(~((![X1:$i]:(~((((![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))))))))) => (~((((~((![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))))))))))))))))))),inference(assume_negation,[status(cth)],[prove])). % 0.35/0.63 thf(h2,assumption,((sP33 => ((~(sP4)) => (~(sP25)))) => (~((((~(sP4)) => (~(sP25))) => sP33)))),introduced(assumption,[])). % 0.35/0.63 thf(h3,assumption,(~((sP33 => ((~(sP4)) => (~(sP25)))))),introduced(assumption,[])). % 0.35/0.63 thf(h4,assumption,(~((((~(sP4)) => (~(sP25))) => sP33))),introduced(assumption,[])). % 0.35/0.63 thf(h5,assumption,sP33,introduced(assumption,[])). % 0.35/0.63 thf(h6,assumption,(~(((~(sP4)) => (~(sP25))))),introduced(assumption,[])). % 0.35/0.63 thf(h7,assumption,(~(sP4)),introduced(assumption,[])). % 0.35/0.63 thf(h8,assumption,sP25,introduced(assumption,[])). % 0.35/0.63 thf(h9,assumption,(~((sP23 => (~(sP1))))),introduced(assumption,[])). % 0.35/0.63 thf(h10,assumption,sP23,introduced(assumption,[])). % 0.35/0.63 thf(h11,assumption,sP1,introduced(assumption,[])). % 0.35/0.63 thf(1,plain,(~(sP17) | sP31),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(2,plain,(~(sP31) | sP32),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(3,plain,(~(sP32) | sP3),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(4,plain,((~(sP3) | sP14) | sP15),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(5,plain,((~(sP14) | ~(sP23)) | ~(sP34)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(6,plain,(~(sP25) | sP24),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(7,plain,((~(sP24) | ~(sP15)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(8,plain,(sP20 | sP21),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(9,plain,(sP20 | sP34),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(10,plain,(sP8 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 0.35/0.63 thf(11,plain,(~(sP33) | sP30),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(12,plain,((~(sP30) | ~(sP23)) | sP22),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(13,plain,((~(sP22) | ~(sP1)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(a2,axiom,(mtransitive @ rel_s5)). % 0.35/0.63 thf(14,plain,sP17,inference(preprocess,[status(thm)],[a2]). % 0.35/0.63 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h5,h10,h11,h8])). % 0.35/0.63 thf(16,plain,$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])). % 0.35/0.63 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,16,h9])). % 0.35/0.63 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,17,h7,h8])). % 0.35/0.63 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6])). % 0.35/0.63 thf(h12,assumption,((~(sP4)) => (~(sP25))),introduced(assumption,[])). % 0.35/0.63 thf(h13,assumption,(~(sP33)),introduced(assumption,[])). % 0.35/0.63 thf(h14,assumption,sP4,introduced(assumption,[])). % 0.35/0.63 thf(h15,assumption,(~(sP25)),introduced(assumption,[])). % 0.35/0.63 thf(h16,assumption,(~((sP16 => (sP9 => (~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((q @ X1))))))))))),introduced(assumption,[])). % 0.35/0.63 thf(h17,assumption,sP16,introduced(assumption,[])). % 0.35/0.63 thf(h18,assumption,(~((sP9 => (~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((q @ X1)))))))))),introduced(assumption,[])). % 0.35/0.63 thf(h19,assumption,sP9,introduced(assumption,[])). % 0.35/0.63 thf(h20,assumption,(![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((q @ X1))))),introduced(assumption,[])). % 0.35/0.63 thf(20,plain,(~(sP4) | sP7),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(21,plain,((~(sP7) | ~(sP16)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(22,plain,$false,inference(prop_unsat,[status(thm),assumptions([h19,h20,h17,h18,h16,h14,h12,h13,h4,h2,h1,h0])],[20,21,h14,h17,h19])). % 0.35/0.63 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h14,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,22,h19,h20])). % 0.35/0.63 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h14,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,23,h17,h18])). % 0.35/0.63 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h12,h13,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h13,24,h16])). % 0.35/0.63 thf(h21,assumption,(~((sP13 => (~(sP6))))),introduced(assumption,[])). % 0.35/0.63 thf(h22,assumption,sP13,introduced(assumption,[])). % 0.35/0.63 thf(h23,assumption,sP6,introduced(assumption,[])). % 0.35/0.63 thf(h24,assumption,(~((sP28 => ((p @ eigen__5) => (~(sP2)))))),introduced(assumption,[])). % 0.35/0.63 thf(h25,assumption,sP28,introduced(assumption,[])). % 0.35/0.63 thf(h26,assumption,(~(((p @ eigen__5) => (~(sP2))))),introduced(assumption,[])). % 0.35/0.63 thf(h27,assumption,(p @ eigen__5),introduced(assumption,[])). % 0.35/0.63 thf(h28,assumption,sP2,introduced(assumption,[])). % 0.35/0.63 thf(26,plain,(~(sP5) | sP35),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(27,plain,((~(sP35) | ~(sP28)) | sP29),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(28,plain,(~(sP12) | sP5),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(29,plain,(~(sP26) | sP11),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(30,plain,(~(sP11) | sP10),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(31,plain,((~(sP10) | sP18) | sP27),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(32,plain,((~(sP18) | ~(sP29)) | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(33,plain,(~(sP17) | sP26),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(34,plain,(~(sP2) | sP19),inference(all_rule,[status(thm)],[])). % 0.35/0.63 thf(35,plain,((~(sP19) | ~(sP27)) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 0.35/0.63 thf(a3,axiom,(msymmetric @ rel_s5)). % 0.35/0.63 thf(36,plain,sP12,inference(preprocess,[status(thm)],[a3]). % 0.35/0.63 thf(37,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h25,h26,h24,h22,h23,h21,h15,h12,h13,h4,h2,h1,h0])],[26,27,28,29,30,31,32,33,34,35,14,36,h22,h23,h25,h28])). % 0.35/0.63 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h25,h26,h24,h22,h23,h21,h15,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,37,h27,h28])). % 0.35/0.63 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h21,h15,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,38,h25,h26])). % 0.35/0.63 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h22,h23,h21,h15,h12,h13,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__5)],[h13,39,h24])). % 0.35/0.63 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h15,h12,h13,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,40,h22,h23])). % 0.35/0.63 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h15,h12,h13,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__4)],[h15,41,h21])). % 0.35/0.63 thf(43,plain,$false,inference(tab_imp,[status(thm),assumptions([h12,h13,h4,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h12,25,42,h14,h15])). % 0.35/0.63 thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,43,h12,h13])). % 0.35/0.63 thf(45,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,19,44,h3,h4])). % 0.35/0.63 thf(46,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,45,h2])). % 0.35/0.63 thf(47,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[46,h0])). % 0.35/0.63 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((![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))))))))))))) => (~(((~((~(((~((~((~((![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))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[46,h1])). % 0.35/0.63 % SZS output end Proof %------------------------------------------------------------------------------