%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM792^4 : TPTP v9.2.0. Released v7.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n006.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 02:12:12 PM UTC 2025 % Result : Theorem 38.72s 38.79s % Output : Proof 38.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM792^4 : TPTP v9.2.0. Released v7.1.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n006.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Oct 8 23:08:38 EDT 2025 % 0.14/0.35 % CPUTime : % 38.72/38.79 % SZS status Theorem % 38.72/38.79 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 % 38.72/38.79 % Inferences: 2793 % 38.72/38.79 % SZS output start Proof % 38.72/38.79 thf(ty_n_eq, type, n_eq : ($i>$i>$o)). % 38.72/38.79 thf(ty_l_some, type, l_some : ($i>($i>$o)>$o)). % 38.72/38.79 thf(ty_eigen__2, type, eigen__2 : $i). % 38.72/38.79 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 38.72/38.79 thf(ty_eigen__1, type, eigen__1 : $i). % 38.72/38.79 thf(ty_frac, type, frac : $i). % 38.72/38.79 thf(ty_eigen__0, type, eigen__0 : $i). % 38.72/38.79 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 38.72/38.79 thf(ty_ect, type, ect : ($i>($i>$i>$o)>$i)). % 38.72/38.79 thf(ty_class, type, class : ($i>$i)). % 38.72/38.79 thf(ty_rt_is, type, rt_is : ($i>$i>$o)). % 38.72/38.79 thf(ty_moref, type, moref : ($i>$i>$o)). % 38.72/38.79 thf(ty_rt_less, type, rt_less : ($i>$i>$o)). % 38.72/38.79 thf(ty_and3, type, and3 : ($o>$o>$o>$o)). % 38.72/38.79 thf(ty_rt_lessis, type, rt_lessis : ($i>$i>$o)). % 38.72/38.79 thf(ty_in, type, in : ($i>$i>$o)). % 38.72/38.79 thf(ty_inf, type, inf : ($i>$i>$o)). % 38.72/38.79 thf(sP1,plain,sP1 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ eigen__2) @ X1) => (((rt_lessis @ X1) @ X2) => ((rt_less @ eigen__2) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 38.72/38.79 thf(sP2,plain,sP2 <=> (((rt_less @ eigen__2) @ eigen__1) => (((rt_lessis @ eigen__1) @ eigen__0) => ((rt_less @ eigen__2) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP2])])). % 38.72/38.79 thf(sP3,plain,sP3 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3))))))) @ ((rt_is @ eigen__0) @ X1)) => ((rt_lessis @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP3])])). % 38.72/38.79 thf(sP4,plain,sP4 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__1))) @ ((inf @ X2) @ (class @ eigen__2))) @ ((moref @ X1) @ X2)))))) => ((rt_less @ eigen__2) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])). % 38.72/38.79 thf(sP5,plain,sP5 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ eigen__2) @ X1) => ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ X1))) @ ((inf @ X3) @ (class @ eigen__2))) @ ((moref @ X2) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 38.72/38.79 thf(sP6,plain,sP6 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => sP2),introduced(definition,[new_symbols(definition,[sP6])])). % 38.72/38.79 thf(sP7,plain,sP7 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))),introduced(definition,[new_symbols(definition,[sP7])])). % 38.72/38.79 thf(sP8,plain,sP8 <=> ((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__1))) @ ((inf @ X2) @ (class @ eigen__2))) @ ((moref @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 38.72/38.79 thf(sP9,plain,sP9 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => sP3),introduced(definition,[new_symbols(definition,[sP9])])). % 38.72/38.79 thf(sP10,plain,sP10 <=> (sP7 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ eigen__2) @ eigen__1) => (((rt_lessis @ eigen__1) @ X1) => ((rt_less @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP10])])). % 38.72/38.79 thf(sP11,plain,sP11 <=> ((rt_less @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP11])])). % 38.72/38.79 thf(sP12,plain,sP12 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => sP1),introduced(definition,[new_symbols(definition,[sP12])])). % 38.72/38.79 thf(sP13,plain,sP13 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4)))))) => ((rt_less @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 38.72/38.79 thf(sP14,plain,sP14 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (sP11 => (((rt_lessis @ eigen__1) @ X1) => ((rt_less @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP14])])). % 38.72/38.79 thf(sP15,plain,sP15 <=> ((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__0))) @ ((inf @ X2) @ (class @ eigen__2))) @ ((moref @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP15])])). % 38.72/38.79 thf(sP16,plain,sP16 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ X1) @ X2) => (((rt_lessis @ X2) @ X3) => ((rt_less @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 38.72/38.79 thf(sP17,plain,sP17 <=> (((rt_less @ eigen__2) @ eigen__0) => sP15),introduced(definition,[new_symbols(definition,[sP17])])). % 38.72/38.79 thf(sP18,plain,sP18 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ eigen__2) @ X1) => ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ X1))) @ ((inf @ X3) @ (class @ eigen__2))) @ ((moref @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 38.72/38.79 thf(sP19,plain,sP19 <=> (sP8 => sP11),introduced(definition,[new_symbols(definition,[sP19])])). % 38.72/38.79 thf(sP20,plain,sP20 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => sP17),introduced(definition,[new_symbols(definition,[sP20])])). % 38.72/38.79 thf(sP21,plain,sP21 <=> ((rt_lessis @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP21])])). % 38.72/38.79 thf(sP22,plain,sP22 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__1))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3)))))) => ((rt_less @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP22])])). % 38.72/38.79 thf(sP23,plain,sP23 <=> ((rt_less @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP23])])). % 38.72/38.79 thf(sP24,plain,sP24 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4))))))) @ ((rt_is @ X1) @ X2)) => ((rt_lessis @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP24])])). % 38.72/38.79 thf(sP25,plain,sP25 <=> ((l_or @ ((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__0))) @ ((inf @ X2) @ (class @ eigen__1))) @ ((moref @ X1) @ X2))))))) @ ((rt_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP25])])). % 38.72/38.79 thf(sP26,plain,sP26 <=> (sP21 => sP23),introduced(definition,[new_symbols(definition,[sP26])])). % 38.72/38.79 thf(sP27,plain,sP27 <=> (sP25 => sP21),introduced(definition,[new_symbols(definition,[sP27])])). % 38.72/38.79 thf(sP28,plain,sP28 <=> (sP7 => sP27),introduced(definition,[new_symbols(definition,[sP28])])). % 38.72/38.79 thf(sP29,plain,sP29 <=> ((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))),introduced(definition,[new_symbols(definition,[sP29])])). % 38.72/38.79 thf(sP30,plain,sP30 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))),introduced(definition,[new_symbols(definition,[sP30])])). % 38.72/38.79 thf(sP31,plain,sP31 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((rt_less @ X1) @ X2) => ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X2))) @ ((inf @ X4) @ (class @ X1))) @ ((moref @ X3) @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 38.72/38.79 thf(sP32,plain,sP32 <=> (sP7 => sP22),introduced(definition,[new_symbols(definition,[sP32])])). % 38.72/38.79 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 38.72/38.79 thf(def_rat,definition,(rat = ((ect @ frac) @ n_eq))). % 38.72/38.79 thf(def_rt_more,definition,(rt_more = (^[X1:$i]:(^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4)))))))))). % 38.72/38.79 thf(def_rt_moreis,definition,(rt_moreis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2)))))). % 38.72/38.79 thf(satz87c,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X2))) @ ((moref @ X4) @ X5))))))) @ ((rt_is @ X1) @ X2)) => (((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X2))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5)))))) => ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5))))))))))))))). % 38.72/38.79 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X2))) @ ((moref @ X4) @ X5))))))) @ ((rt_is @ X1) @ X2)) => (((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X2))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5)))))) => ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5)))))))))))))))),inference(assume_negation,[status(cth)],[satz87c])). % 38.72/38.79 thf(h1,assumption,(~((sP30 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ eigen__0))) @ ((inf @ X4) @ (class @ X1))) @ ((moref @ X3) @ X4))))))) @ ((rt_is @ eigen__0) @ X1)) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4)))))) => ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ eigen__0))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4))))))))))))))),introduced(assumption,[])). % 38.72/38.79 thf(h2,assumption,sP30,introduced(assumption,[])). % 38.72/38.79 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ eigen__0))) @ ((inf @ X4) @ (class @ X1))) @ ((moref @ X3) @ X4))))))) @ ((rt_is @ eigen__0) @ X1)) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4)))))) => ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ eigen__0))) @ ((inf @ X4) @ (class @ X2))) @ ((moref @ X3) @ X4)))))))))))))),introduced(assumption,[])). % 38.72/38.79 thf(h4,assumption,(~((sP7 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (sP25 => (((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__1))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3)))))) => ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3))))))))))))),introduced(assumption,[])). % 38.72/38.79 thf(h5,assumption,sP7,introduced(assumption,[])). % 38.72/38.79 thf(h6,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (sP25 => (((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__1))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3)))))) => ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((moref @ X2) @ X3)))))))))))),introduced(assumption,[])). % 38.72/38.79 thf(h7,assumption,(~((sP29 => (sP25 => (sP8 => sP15))))),introduced(assumption,[])). % 38.72/38.79 thf(h8,assumption,sP29,introduced(assumption,[])). % 38.72/38.79 thf(h9,assumption,(~((sP25 => (sP8 => sP15)))),introduced(assumption,[])). % 38.72/38.79 thf(h10,assumption,sP25,introduced(assumption,[])). % 38.72/38.79 thf(h11,assumption,(~((sP8 => sP15))),introduced(assumption,[])). % 38.72/38.79 thf(h12,assumption,sP8,introduced(assumption,[])). % 38.72/38.79 thf(h13,assumption,(~(sP15)),introduced(assumption,[])). % 38.72/38.79 thf(1,plain,(~(sP14) | sP6),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(2,plain,((~(sP6) | ~(sP30)) | sP2),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(3,plain,((~(sP2) | ~(sP11)) | sP26),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(4,plain,((~(sP26) | ~(sP21)) | sP23),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(5,plain,(~(sP1) | sP10),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(6,plain,((~(sP10) | ~(sP7)) | sP14),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(7,plain,((~(sP12) | ~(sP29)) | sP1),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(8,plain,((~(sP9) | ~(sP30)) | sP3),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(9,plain,(~(sP3) | sP28),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(10,plain,((~(sP28) | ~(sP7)) | sP27),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(11,plain,((~(sP27) | ~(sP25)) | sP21),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(12,plain,((~(sP32) | ~(sP7)) | sP22),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(13,plain,(~(sP22) | sP4),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(14,plain,((~(sP4) | ~(sP29)) | sP19),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(15,plain,((~(sP19) | ~(sP8)) | sP11),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(16,plain,((~(sP5) | ~(sP29)) | sP18),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(17,plain,(~(sP18) | sP20),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(18,plain,((~(sP20) | ~(sP30)) | sP17),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(19,plain,((~(sP17) | ~(sP23)) | sP15),inference(prop_rule,[status(thm)],[])). % 38.72/38.79 thf(20,plain,(~(sP16) | sP12),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(21,plain,(~(sP24) | sP9),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(22,plain,(~(sP31) | sP5),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(23,plain,(~(sP13) | sP32),inference(all_rule,[status(thm)],[])). % 38.72/38.79 thf(satz87b,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ rat))) @ (^[X3:$i]:(((rt_less @ X1) @ X2) => (((rt_lessis @ X2) @ X3) => ((rt_less @ X1) @ X3)))))))))). % 38.72/38.79 thf(24,plain,sP16,inference(preprocess,[status(thm)],[satz87b]). % 38.72/38.79 thf(satz84,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_moreis @ X1) @ X2) => ((rt_lessis @ X2) @ X1))))))). % 38.72/38.79 thf(25,plain,sP24,inference(preprocess,[status(thm)],[satz84]). % 38.72/38.79 thf(satz83,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_less @ X1) @ X2) => ((rt_more @ X2) @ X1))))))). % 38.72/38.79 thf(26,plain,sP31,inference(preprocess,[status(thm)],[satz83]). % 38.72/38.79 thf(satz82,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_more @ X1) @ X2) => ((rt_less @ X2) @ X1))))))). % 38.72/38.79 thf(27,plain,sP13,inference(preprocess,[status(thm)],[satz82]). % 38.72/38.79 thf(28,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,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,h2,h5,h8,h10,h12,h13,24,25,26,27])). % 38.72/38.79 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,28,h12,h13])). % 38.72/38.79 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,29,h10,h11])). % 38.72/38.79 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,30,h8,h9])). % 38.72/38.79 thf(32,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,31,h7])). % 38.72/38.79 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,32,h5,h6])). % 38.72/38.79 thf(34,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,33,h4])). % 38.72/38.79 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,34,h2,h3])). % 38.72/38.79 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,35,h1])). % 38.72/38.79 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X2))) @ ((moref @ X4) @ X5))))))) @ ((rt_is @ X1) @ X2)) => (((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X2))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5)))))) => ((l_some @ frac) @ (^[X4:$i]:((l_some @ frac) @ (^[X5:$i]:(((and3 @ ((inf @ X4) @ (class @ X1))) @ ((inf @ X5) @ (class @ X3))) @ ((moref @ X4) @ X5)))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[36,h0])). % 38.72/38.79 % SZS output end Proof %------------------------------------------------------------------------------