%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM750^4 : 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 : n008.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 02:12:02 PM UTC 2025 % Result : Theorem 0.45s 0.66s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM750^4 : TPTP v9.2.0. Released v7.1.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n008.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 : Wed Oct 8 22:38:53 EDT 2025 % 0.13/0.34 % CPUTime : % 0.45/0.66 % SZS status Theorem % 0.45/0.66 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 % 0.45/0.66 % Inferences: 49 % 0.45/0.66 % SZS output start Proof % 0.45/0.66 thf(ty_nat, type, nat : $i). % 0.45/0.66 thf(ty_eigen__2, type, eigen__2 : $i). % 0.45/0.66 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 0.45/0.66 thf(ty_num, type, num : ($i>$i)). % 0.45/0.66 thf(ty_eigen__1, type, eigen__1 : $i). % 0.45/0.66 thf(ty_eigen__0, type, eigen__0 : $i). % 0.45/0.66 thf(ty_n_fr, type, n_fr : ($i>$i>$i)). % 0.45/0.66 thf(ty_den, type, den : ($i>$i)). % 0.45/0.66 thf(ty_n_ts, type, n_ts : ($i>$i>$i)). % 0.45/0.66 thf(ty_pair1type, type, pair1type : ($i>$i)). % 0.45/0.66 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 0.45/0.66 thf(ty_in, type, in : ($i>$i>$o)). % 0.45/0.66 thf(ty_n_pl, type, n_pl : ($i>$i>$i)). % 0.45/0.66 thf(sP1,plain,sP1 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ eigen__2)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ eigen__2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.45/0.66 thf(sP2,plain,sP2 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.45/0.66 thf(sP3,plain,sP3 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (![X4:$i]:(((is_of @ X4) @ (^[X5:$i]:((in @ X5) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X3)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X3))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X4)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X4))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3)))))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.45/0.66 thf(sP4,plain,sP4 <=> ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.45/0.66 thf(sP5,plain,sP5 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.45/0.66 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP4 => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.45/0.66 thf(sP7,plain,sP7 <=> ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ eigen__2)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ eigen__2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.45/0.66 thf(sP8,plain,sP8 <=> (sP4 => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) => sP7)),introduced(definition,[new_symbols(definition,[sP8])])). % 0.45/0.66 thf(sP9,plain,sP9 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.45/0.66 thf(sP10,plain,sP10 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.45/0.66 thf(sP11,plain,sP11 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP4 => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X2)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1)))))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.45/0.66 thf(sP12,plain,sP12 <=> (sP10 => sP11),introduced(definition,[new_symbols(definition,[sP12])])). % 0.45/0.66 thf(sP13,plain,sP13 <=> (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) => sP7),introduced(definition,[new_symbols(definition,[sP13])])). % 0.45/0.66 thf(sP14,plain,sP14 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP6),introduced(definition,[new_symbols(definition,[sP14])])). % 0.45/0.66 thf(sP15,plain,sP15 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ X1))))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.45/0.66 thf(sP16,plain,sP16 <=> ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__2))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.45/0.66 thf(sP17,plain,sP17 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2)))))))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.45/0.66 thf(sP18,plain,sP18 <=> ((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.45/0.66 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 0.45/0.66 thf(def_frac,definition,(frac = (pair1type @ nat))). % 0.45/0.66 thf(def_n_eq,definition,(n_eq = (^[X1:$i]:(^[X2:$i]:((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))))))). % 0.45/0.66 thf(def_n_pf,definition,(n_pf = (^[X1:$i]:(^[X2:$i]:((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X2))))))). % 0.45/0.66 thf(satz62b,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3)))))))))))))). % 0.45/0.66 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))))))))))))),inference(assume_negation,[status(cth)],[satz62b])). % 0.45/0.66 thf(h1,assumption,(~((sP9 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X2)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2)))))))))))))),introduced(assumption,[])). % 0.45/0.66 thf(h2,assumption,sP9,introduced(assumption,[])). % 0.45/0.66 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X2)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X2))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X2))))))))))))),introduced(assumption,[])). % 0.45/0.66 thf(h4,assumption,(~((sP10 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP4 => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1)))))))))))),introduced(assumption,[])). % 0.45/0.66 thf(h5,assumption,sP10,introduced(assumption,[])). % 0.45/0.66 thf(h6,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP4 => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1)))) @ ((n_ts @ (den @ eigen__1)) @ (den @ X1))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) @ ((n_ts @ (den @ eigen__0)) @ (den @ X1))))))))))),introduced(assumption,[])). % 0.45/0.66 thf(h7,assumption,(~((sP18 => (sP4 => sP7)))),introduced(assumption,[])). % 0.45/0.66 thf(h8,assumption,sP18,introduced(assumption,[])). % 0.45/0.66 thf(h9,assumption,(~((sP4 => sP7))),introduced(assumption,[])). % 0.45/0.66 thf(h10,assumption,sP4,introduced(assumption,[])). % 0.45/0.66 thf(h11,assumption,(~(sP7)),introduced(assumption,[])). % 0.45/0.66 thf(1,plain,(~(sP15) | sP2),inference(all_rule,[status(thm)],[])). % 0.45/0.66 thf(2,plain,((~(sP2) | ~(sP18)) | sP16),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(3,plain,(~(sP3) | sP5),inference(all_rule,[status(thm)],[])). % 0.45/0.66 thf(4,plain,((~(sP5) | ~(sP9)) | sP17),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(5,plain,(~(sP17) | sP12),inference(all_rule,[status(thm)],[])). % 0.45/0.66 thf(6,plain,((~(sP12) | ~(sP10)) | sP11),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(7,plain,(~(sP11) | sP14),inference(all_rule,[status(thm)],[])). % 0.45/0.66 thf(8,plain,((~(sP14) | ~(sP18)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(9,plain,(~(sP6) | sP1),inference(all_rule,[status(thm)],[])). % 0.45/0.66 thf(10,plain,((~(sP1) | ~(sP18)) | sP8),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(11,plain,((~(sP8) | ~(sP4)) | sP13),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(12,plain,((~(sP13) | ~(sP16)) | sP7),inference(prop_rule,[status(thm)],[])). % 0.45/0.66 thf(satz56,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ frac))) @ (^[X3:$i]:((all_of @ (^[X4:$i]:((in @ X4) @ frac))) @ (^[X4:$i]:(((n_eq @ X1) @ X2) => (((n_eq @ X3) @ X4) => ((n_eq @ ((n_pf @ X1) @ X3)) @ ((n_pf @ X2) @ X4))))))))))))). % 0.45/0.66 thf(13,plain,sP3,inference(preprocess,[status(thm)],[satz56]). % 0.45/0.66 thf(satz37,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((n_eq @ X1) @ X1)))). % 0.45/0.66 thf(14,plain,sP15,inference(preprocess,[status(thm)],[satz37]). % 0.45/0.66 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h5,h8,h10,h11,13,14])). % 0.45/0.66 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,15,h10,h11])). % 0.45/0.66 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,16,h8,h9])). % 0.45/0.66 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,17,h7])). % 0.45/0.66 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,18,h5,h6])). % 0.45/0.66 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,19,h4])). % 0.45/0.66 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3])). % 0.45/0.66 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1])). % 0.45/0.66 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3)))))) @ ((n_ts @ (num @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))) @ ((n_ts @ (den @ X2)) @ (den @ X3))))) @ (den @ ((n_fr @ ((n_pl @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1)))) @ ((n_ts @ (den @ X1)) @ (den @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[22,h0])). % 0.45/0.66 % SZS output end Proof %------------------------------------------------------------------------------