%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO932^9 : 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 : n002.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 03:26:37 PM UTC 2025 % Result : Theorem 5.00s 5.23s % Output : Proof 5.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO932^9 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 9 00:27:53 EDT 2025 % 0.13/0.34 % CPUTime : % 5.00/5.23 % SZS status Theorem % 5.00/5.23 % Mode: mode495 % 5.00/5.23 % Inferences: 55 % 5.00/5.23 % SZS output start Proof % 5.00/5.23 thf(ty_individuals, type, individuals : $tType). % 5.00/5.23 thf(ty_eigen__6, type, eigen__6 : $i). % 5.00/5.23 thf(ty_relr, type, relr : ($i>$i>$o)). % 5.00/5.23 thf(ty_eigen__2, type, eigen__2 : $i). % 5.00/5.23 thf(ty_eigen__7, type, eigen__7 : $i). % 5.00/5.23 thf(ty_eigen__1, type, eigen__1 : $i). % 5.00/5.23 thf(ty_eigen__0, type, eigen__0 : (individuals>$i>$o)). % 5.00/5.23 thf(ty_eigen__4, type, eigen__4 : individuals). % 5.00/5.23 thf(ty_eigen__5, type, eigen__5 : $i). % 5.00/5.23 thf(ty_reli, type, reli : ($i>$i>$o)). % 5.00/5.23 thf(ty_eigen__3, type, eigen__3 : $i). % 5.00/5.23 thf(sP1,plain,sP1 <=> (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => ((eigen__0 @ X3) @ X4)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 5.00/5.23 thf(sP2,plain,sP2 <=> (![X1:$i]:(((reli @ eigen__6) @ X1) => ((eigen__0 @ eigen__4) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])). % 5.00/5.23 thf(sP3,plain,sP3 <=> ((reli @ eigen__6) @ eigen__7),introduced(definition,[new_symbols(definition,[sP3])])). % 5.00/5.23 thf(sP4,plain,sP4 <=> ((reli @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])). % 5.00/5.23 thf(sP5,plain,sP5 <=> (((reli @ eigen__3) @ eigen__5) => sP1),introduced(definition,[new_symbols(definition,[sP5])])). % 5.00/5.23 thf(sP6,plain,sP6 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 5.00/5.23 thf(sP7,plain,sP7 <=> (![X1:$i]:((![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)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:individuals]:(![X7:$i]:(((reli @ X5) @ X7) => ((eigen__0 @ X6) @ X7)))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 5.00/5.23 thf(sP8,plain,sP8 <=> (((relr @ eigen__5) @ eigen__6) => (![X1:$i]:(((reli @ eigen__6) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => ((eigen__0 @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 5.00/5.23 thf(sP9,plain,sP9 <=> (sP3 => ((eigen__0 @ eigen__4) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP9])])). % 5.00/5.23 thf(sP10,plain,sP10 <=> (![X1:$i]:(((reli @ eigen__6) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => ((eigen__0 @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP10])])). % 5.00/5.23 thf(sP11,plain,sP11 <=> (sP10 => (![X1:individuals]:(![X2:$i]:(((reli @ eigen__6) @ X2) => ((eigen__0 @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])). % 5.00/5.23 thf(sP12,plain,sP12 <=> ((eigen__0 @ eigen__4) @ eigen__7),introduced(definition,[new_symbols(definition,[sP12])])). % 5.00/5.23 thf(sP13,plain,sP13 <=> ((![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)))))))))) => (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => ((eigen__0 @ X5) @ X6))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 5.00/5.23 thf(sP14,plain,sP14 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => ((eigen__0 @ X3) @ X4)))))) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => ((eigen__0 @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP14])])). % 5.00/5.23 thf(sP15,plain,sP15 <=> ((reli @ eigen__3) @ eigen__5),introduced(definition,[new_symbols(definition,[sP15])])). % 5.00/5.23 thf(sP16,plain,sP16 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:individuals]:(![X5:$i]:(((reli @ X3) @ X5) => ((eigen__0 @ X4) @ X5)))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 5.00/5.23 thf(sP17,plain,sP17 <=> (![X1:individuals]:(![X2:$i]:(((reli @ eigen__6) @ X2) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP17])])). % 5.00/5.23 thf(sP18,plain,sP18 <=> (sP4 => sP6),introduced(definition,[new_symbols(definition,[sP18])])). % 5.00/5.23 thf(sP19,plain,sP19 <=> (![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,[sP19])])). % 5.00/5.23 thf(sP20,plain,sP20 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP20])])). % 5.00/5.23 thf(sP21,plain,sP21 <=> ((relr @ eigen__5) @ eigen__6),introduced(definition,[new_symbols(definition,[sP21])])). % 5.00/5.23 thf(sP22,plain,sP22 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => ((eigen__0 @ X5) @ X6)))))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 5.00/5.23 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 5.00/5.23 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 5.00/5.23 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 5.00/5.23 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 5.00/5.23 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 5.00/5.23 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 5.00/5.23 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 5.00/5.23 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 5.00/5.23 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 5.00/5.23 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 5.00/5.23 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 5.00/5.23 thf(def_mvalid,definition,(mvalid = (!!))). % 5.00/5.23 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 5.00/5.23 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 5.00/5.23 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 5.00/5.23 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))). % 5.00/5.23 thf(def_cs4_and,definition,(cs4_and = mand)). % 5.00/5.23 thf(def_cs4_or,definition,(cs4_or = mor)). % 5.00/5.23 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))). % 5.00/5.23 thf(def_cs4_true,definition,(cs4_true = mtrue)). % 5.00/5.23 thf(def_cs4_false,definition,(cs4_false = mfalse)). % 5.00/5.23 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))). % 5.00/5.23 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))). % 5.00/5.23 thf(def_cs4_valid,definition,(cs4_valid = mvalid)). % 5.00/5.23 thf(cs4_cbarcan,conjecture,(![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![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)))))))))))))) => (![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)))))))))))))))). % 5.00/5.23 thf(h0,negated_conjecture,(~((![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![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)))))))))) => (![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))))))))))))))))),inference(assume_negation,[status(cth)],[cs4_cbarcan])). % 5.00/5.23 thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![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)))))))))) => (![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(assumption,[])). % 5.00/5.23 thf(h2,assumption,(~((![X1:$i]:(((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => ((eigen__0 @ X5) @ X6)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:individuals]:(![X4:$i]:(((reli @ X2) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__0 @ X3) @ X6))))))))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h3,assumption,(~((((reli @ eigen__1) @ eigen__2) => (sP16 => (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h4,assumption,((reli @ eigen__1) @ eigen__2),introduced(assumption,[])). % 5.00/5.23 thf(h5,assumption,(~((sP16 => (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5))))))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h6,assumption,sP16,introduced(assumption,[])). % 5.00/5.23 thf(h7,assumption,(~((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:individuals]:(![X3:$i]:(((reli @ X1) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__0 @ X2) @ X5)))))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h8,assumption,(~((sP4 => (![X1:individuals]:(![X2:$i]:(((reli @ eigen__3) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__0 @ X1) @ X4))))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h9,assumption,sP4,introduced(assumption,[])). % 5.00/5.23 thf(h10,assumption,(~((![X1:individuals]:(![X2:$i]:(((reli @ eigen__3) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__0 @ X1) @ X4)))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h11,assumption,(~((![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((eigen__0 @ eigen__4) @ X3))))))))),introduced(assumption,[])). % 5.00/5.23 thf(h12,assumption,(~((sP15 => (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((eigen__0 @ eigen__4) @ X2)))))))),introduced(assumption,[])). % 5.00/5.23 thf(h13,assumption,sP15,introduced(assumption,[])). % 5.00/5.23 thf(h14,assumption,(~((![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((eigen__0 @ eigen__4) @ X2))))))),introduced(assumption,[])). % 5.00/5.23 thf(h15,assumption,(~((sP21 => sP2))),introduced(assumption,[])). % 5.00/5.23 thf(h16,assumption,sP21,introduced(assumption,[])). % 5.00/5.23 thf(h17,assumption,(~(sP2)),introduced(assumption,[])). % 5.00/5.23 thf(h18,assumption,(~(sP9)),introduced(assumption,[])). % 5.00/5.23 thf(h19,assumption,sP3,introduced(assumption,[])). % 5.00/5.23 thf(h20,assumption,(~(sP12)),introduced(assumption,[])). % 5.00/5.23 thf(1,plain,(~(sP20) | sP14),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(2,plain,(~(sP14) | sP11),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(3,plain,((~(sP11) | ~(sP10)) | sP17),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(4,plain,(~(sP22) | sP18),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(5,plain,((~(sP18) | ~(sP4)) | sP6),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(6,plain,(~(sP6) | sP5),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(7,plain,((~(sP5) | ~(sP15)) | sP1),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(8,plain,(~(sP19) | sP7),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(9,plain,(~(sP7) | sP13),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(10,plain,((~(sP13) | ~(sP16)) | sP22),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(11,plain,(~(sP17) | sP2),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(12,plain,(~(sP2) | sP9),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(13,plain,((~(sP9) | ~(sP3)) | sP12),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(14,plain,(~(sP1) | sP8),inference(all_rule,[status(thm)],[])). % 5.00/5.23 thf(15,plain,((~(sP8) | ~(sP21)) | sP10),inference(prop_rule,[status(thm)],[])). % 5.00/5.23 thf(trans_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ ((mbox @ reli) @ ((mbox @ reli) @ X1)))))). % 5.00/5.23 thf(16,plain,sP19,inference(preprocess,[status(thm)],[trans_axiom_i]). % 5.00/5.23 thf(refl_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ X1)))). % 5.00/5.23 thf(17,plain,sP20,inference(preprocess,[status(thm)],[refl_axiom_i]). % 5.00/5.23 thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h6,h9,h13,h16,h19,h20,16,17])). % 5.00/5.23 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,18,h19,h20])). % 5.00/5.23 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__7)],[h17,19,h18])). % 5.00/5.23 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,20,h16,h17])). % 5.00/5.23 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__6)],[h14,21,h15])). % 5.00/5.23 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,22,h13,h14])). % 5.00/5.23 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__5)],[h11,23,h12])). % 5.00/5.23 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,24,h11])). % 5.00/5.23 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,25,h9,h10])). % 5.00/5.23 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,26,h8])). % 5.00/5.23 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,27,h6,h7])). % 5.00/5.23 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,28,h4,h5])). % 5.00/5.23 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,29,h3])). % 5.00/5.23 thf(31,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,30,h2])). % 5.00/5.23 thf(32,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,31,h1])). % 5.00/5.23 thf(0,theorem,(![X1:individuals>$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:individuals]:(![X8:$i]:(((reli @ X6) @ X8) => ((X1 @ X7) @ X8)))))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:individuals]:(![X6:$i]:(((reli @ X4) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X5) @ X8))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[32,h0])). % 5.00/5.23 % SZS output end Proof %------------------------------------------------------------------------------