%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO430^1 : 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 : n011.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 03:25:34 PM UTC 2025 % Result : Theorem 0.19s 0.38s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO430^1 : TPTP v9.2.0. Released v4.0.0. % 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.33 % Computer : n011.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 9 00:35:23 EDT 2025 % 0.13/0.34 % CPUTime : % 0.19/0.38 % SZS status Theorem % 0.19/0.38 % Mode: mode213 % 0.19/0.38 % Inferences: 217 % 0.19/0.38 % SZS output start Proof % 0.19/0.38 thf(ty_p, type, p : ($i>$o)). % 0.19/0.38 thf(ty_eigen__2, type, eigen__2 : $i). % 0.19/0.38 thf(ty_eigen__7, type, eigen__7 : $i). % 0.19/0.38 thf(ty_eigen__1, type, eigen__1 : $i). % 0.19/0.38 thf(ty_eigen__0, type, eigen__0 : $i). % 0.19/0.38 thf(ty_eigen__5, type, eigen__5 : $i). % 0.19/0.38 thf(ty_rel_b, type, rel_b : ($i>$i>$o)). % 0.19/0.38 thf(ty_eigen__3, type, eigen__3 : $i). % 0.19/0.38 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.19/0.38 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_b @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.19/0.38 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((((rel_b @ eigen__5) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__7])])). % 0.19/0.38 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((rel_b @ eigen__3) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 0.19/0.38 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_b @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.19/0.38 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel_b @ eigen__1) @ X1) => ((rel_b @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.19/0.38 thf(sP3,plain,sP3 <=> (p @ eigen__5),introduced(definition,[new_symbols(definition,[sP3])])). % 0.19/0.38 thf(sP4,plain,sP4 <=> (((rel_b @ eigen__0) @ eigen__1) => (~((![X1:$i]:(((rel_b @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.19/0.38 thf(sP5,plain,sP5 <=> (![X1:$i]:(((rel_b @ eigen__5) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.19/0.38 thf(sP6,plain,sP6 <=> ((rel_b @ eigen__3) @ eigen__5),introduced(definition,[new_symbols(definition,[sP6])])). % 0.19/0.38 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_b @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.19/0.38 thf(sP8,plain,sP8 <=> ((rel_b @ eigen__7) @ eigen__5),introduced(definition,[new_symbols(definition,[sP8])])). % 0.19/0.38 thf(sP9,plain,sP9 <=> (sP8 => sP3),introduced(definition,[new_symbols(definition,[sP9])])). % 0.19/0.38 thf(sP10,plain,sP10 <=> (sP6 => sP3),introduced(definition,[new_symbols(definition,[sP10])])). % 0.19/0.38 thf(sP11,plain,sP11 <=> (sP6 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.19/0.38 thf(sP12,plain,sP12 <=> (![X1:$i]:(((rel_b @ eigen__5) @ X1) => ((rel_b @ X1) @ eigen__5))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.19/0.38 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_b @ eigen__3) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.19/0.38 thf(sP14,plain,sP14 <=> (![X1:$i]:(((rel_b @ eigen__7) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.19/0.38 thf(sP15,plain,sP15 <=> ((rel_b @ eigen__5) @ eigen__7),introduced(definition,[new_symbols(definition,[sP15])])). % 0.19/0.38 thf(sP16,plain,sP16 <=> (sP15 => (~(sP14))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.19/0.38 thf(sP17,plain,sP17 <=> (![X1:$i]:(((rel_b @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.19/0.38 thf(sP18,plain,sP18 <=> (((rel_b @ eigen__1) @ eigen__2) => ((rel_b @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP18])])). % 0.19/0.38 thf(sP19,plain,sP19 <=> ((rel_b @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP19])])). % 0.19/0.38 thf(sP20,plain,sP20 <=> ((rel_b @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP20])])). % 0.19/0.38 thf(sP21,plain,sP21 <=> (![X1:$i]:(((rel_b @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.19/0.38 thf(sP22,plain,sP22 <=> ((rel_b @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP22])])). % 0.19/0.38 thf(sP23,plain,sP23 <=> ((rel_b @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP23])])). % 0.19/0.38 thf(sP24,plain,sP24 <=> (![X1:$i]:(((rel_b @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (p @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 0.19/0.38 thf(sP25,plain,sP25 <=> (sP20 => (~(sP7))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.19/0.38 thf(sP26,plain,sP26 <=> (sP23 => (~((![X1:$i]:(((rel_b @ eigen__3) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.19/0.38 thf(sP27,plain,sP27 <=> (sP19 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP27])])). % 0.19/0.38 thf(sP28,plain,sP28 <=> (![X1:$i]:(((rel_b @ eigen__3) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.19/0.38 thf(sP29,plain,sP29 <=> (![X1:$i]:(![X2:$i]:(((rel_b @ X1) @ X2) => ((rel_b @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP29])])). % 0.19/0.38 thf(sP30,plain,sP30 <=> (sP15 => sP8),introduced(definition,[new_symbols(definition,[sP30])])). % 0.19/0.38 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.19/0.38 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.19/0.38 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.19/0.38 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.19/0.38 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.19/0.38 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.19/0.38 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.19/0.38 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.19/0.38 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.19/0.38 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.19/0.38 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.19/0.38 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.19/0.38 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.19/0.38 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.19/0.38 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.19/0.38 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.19/0.38 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.19/0.38 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.19/0.38 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.19/0.38 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.19/0.38 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.19/0.38 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.19/0.38 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.19/0.38 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.19/0.38 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.19/0.38 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))))))))). % 0.19/0.38 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.19/0.38 thf(def_mvalid,definition,(mvalid = (!!))). % 0.19/0.38 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.19/0.38 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.19/0.38 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.19/0.38 thf(def_mbox_b,definition,(mbox_b = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_b @ X2) @ X3) => (X1 @ X3))))))). % 0.19/0.38 thf(def_mdia_b,definition,(mdia_b = (^[X1:$i>$o]:(mnot @ (mbox_b @ (mnot @ X1)))))). % 0.19/0.38 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5)))))))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5))))))))))))))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))))))))))). % 0.19/0.38 thf(h1,negated_conjecture,(~((![X1:$i]:(~((((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5)))))))))))))))))) => (~(((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5))))))))))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3)))))))))))))))))),inference(assume_negation,[status(cth)],[prove])). % 0.19/0.38 thf(h2,assumption,(((~(sP21)) => (~(sP24))) => (~(((~(sP24)) => (~(sP21)))))),introduced(assumption,[])). % 0.19/0.38 thf(h3,assumption,(~(((~(sP21)) => (~(sP24))))),introduced(assumption,[])). % 0.19/0.38 thf(h4,assumption,(~(((~(sP24)) => (~(sP21))))),introduced(assumption,[])). % 0.19/0.38 thf(h5,assumption,(~(sP21)),introduced(assumption,[])). % 0.19/0.38 thf(h6,assumption,sP24,introduced(assumption,[])). % 0.19/0.38 thf(h7,assumption,(~((sP22 => (~(sP1))))),introduced(assumption,[])). % 0.19/0.38 thf(h8,assumption,sP22,introduced(assumption,[])). % 0.19/0.38 thf(h9,assumption,sP1,introduced(assumption,[])). % 0.19/0.38 thf(1,plain,(~(sP29) | sP2),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(2,plain,(~(sP2) | sP18),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(3,plain,((~(sP18) | ~(sP20)) | sP19),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(4,plain,(~(sP7) | sP27),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(5,plain,((~(sP27) | ~(sP19)) | ~(sP1)),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(6,plain,(sP25 | sP7),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(7,plain,(sP25 | sP20),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(8,plain,(sP17 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 0.19/0.38 thf(9,plain,(~(sP24) | sP4),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(10,plain,((~(sP4) | ~(sP22)) | ~(sP17)),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(a2,axiom,(msymmetric @ rel_b)). % 0.19/0.38 thf(11,plain,sP29,inference(preprocess,[status(thm)],[a2]). % 0.19/0.38 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h8,h9,h6])). % 0.19/0.38 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,12,h8,h9])). % 0.19/0.38 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h5,13,h7])). % 0.19/0.38 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,14,h5,h6])). % 0.19/0.38 thf(h10,assumption,(~(sP24)),introduced(assumption,[])). % 0.19/0.38 thf(h11,assumption,sP21,introduced(assumption,[])). % 0.19/0.38 thf(h12,assumption,(~((sP23 => (~(sP13))))),introduced(assumption,[])). % 0.19/0.38 thf(h13,assumption,sP23,introduced(assumption,[])). % 0.19/0.38 thf(h14,assumption,sP13,introduced(assumption,[])). % 0.19/0.38 thf(16,plain,(~(sP12) | sP30),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(17,plain,((~(sP30) | ~(sP15)) | sP8),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(18,plain,(~(sP29) | sP12),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(19,plain,(~(sP14) | sP9),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(20,plain,((~(sP9) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(21,plain,(sP16 | sP14),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(22,plain,(sP16 | sP15),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(23,plain,(sP5 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])). % 0.19/0.38 thf(24,plain,(~(sP13) | sP11),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(25,plain,((~(sP11) | ~(sP6)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(26,plain,(sP10 | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(27,plain,(sP10 | sP6),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(28,plain,(sP28 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 0.19/0.38 thf(29,plain,(~(sP21) | sP26),inference(all_rule,[status(thm)],[])). % 0.19/0.38 thf(30,plain,((~(sP26) | ~(sP23)) | ~(sP28)),inference(prop_rule,[status(thm)],[])). % 0.19/0.38 thf(31,plain,$false,inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h4,h2,h1,h0])],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,11,h13,h14,h11])). % 0.19/0.38 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,31,h13,h14])). % 0.19/0.38 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h11,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h10,32,h12])). % 0.19/0.38 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h4,33,h10,h11])). % 0.19/0.38 thf(35,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,15,34,h3,h4])). % 0.19/0.38 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,35,h2])). % 0.19/0.38 thf(37,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0])). % 0.19/0.38 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3))))))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5)))))))))))))))))))))) => (~(((~((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => (~((![X5:$i]:(((rel_b @ X4) @ X5) => (p @ X5))))))))))))))))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (p @ X3)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[36,h1])). % 0.19/0.38 % SZS output end Proof %------------------------------------------------------------------------------