%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM789^4 : 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 : n001.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 02:12:11 PM UTC 2025 % Result : Theorem 139.77s 139.57s % Output : Proof 139.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM789^4 : TPTP v9.2.0. Released v7.1.0. % 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n001.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Oct 8 23:12:53 EDT 2025 % 0.12/0.33 % CPUTime : % 139.77/139.57 % SZS status Theorem % 139.77/139.57 % Mode: mode502:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 % 139.77/139.57 % Inferences: 301 % 139.77/139.57 % SZS output start Proof % 139.77/139.57 thf(ty_n_eq, type, n_eq : ($i>$i>$o)). % 139.77/139.57 thf(ty_l_some, type, l_some : ($i>($i>$o)>$o)). % 139.77/139.57 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 139.77/139.57 thf(ty_eigen__1, type, eigen__1 : $i). % 139.77/139.57 thf(ty_frac, type, frac : $i). % 139.77/139.57 thf(ty_eigen__0, type, eigen__0 : $i). % 139.77/139.57 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 139.77/139.57 thf(ty_ect, type, ect : ($i>($i>$i>$o)>$i)). % 139.77/139.57 thf(ty_class, type, class : ($i>$i)). % 139.77/139.57 thf(ty_rt_is, type, rt_is : ($i>$i>$o)). % 139.77/139.57 thf(ty_lessf, type, lessf : ($i>$i>$o)). % 139.77/139.57 thf(ty_and3, type, and3 : ($o>$o>$o>$o)). % 139.77/139.57 thf(ty_imp, type, imp : ($o>$o>$o)). % 139.77/139.57 thf(ty_rt_lessis, type, rt_lessis : ($i>$i>$o)). % 139.77/139.57 thf(ty_in, type, in : ($i>$i>$o)). % 139.77/139.57 thf(ty_inf, type, inf : ($i>$i>$o)). % 139.77/139.57 thf(ty_rt_more, type, rt_more : ($i>$i>$o)). % 139.77/139.57 thf(sP1,plain,sP1 <=> ((imp @ ((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__0))) @ ((inf @ X2) @ (class @ eigen__1))) @ ((lessf @ X1) @ X2))))))) @ $false),introduced(definition,[new_symbols(definition,[sP1])])). % 139.77/139.57 thf(sP2,plain,sP2 <=> (![X1:$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_more @ X1) @ X2) => ((imp @ ((rt_lessis @ X1) @ X2)) @ $false)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 139.77/139.57 thf(sP3,plain,sP3 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((rt_more @ eigen__1) @ X1) => ((imp @ ((rt_lessis @ eigen__1) @ X1)) @ $false)))),introduced(definition,[new_symbols(definition,[sP3])])). % 139.77/139.57 thf(sP4,plain,sP4 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1)) => sP1)),introduced(definition,[new_symbols(definition,[sP4])])). % 139.77/139.57 thf(sP5,plain,sP5 <=> (((rt_lessis @ eigen__1) @ eigen__0) = ((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP5])])). % 139.77/139.57 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((imp @ ((rt_more @ eigen__1) @ X1)) @ $false) => ((rt_lessis @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 139.77/139.57 thf(sP7,plain,sP7 <=> (((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1)) => sP1),introduced(definition,[new_symbols(definition,[sP7])])). % 139.77/139.57 thf(sP8,plain,sP8 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((imp @ ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3))))))) @ $false) => ((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 139.77/139.57 thf(sP9,plain,sP9 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1)) => ((imp @ ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3))))))) @ $false))))),introduced(definition,[new_symbols(definition,[sP9])])). % 139.77/139.57 thf(sP10,plain,sP10 <=> (((rt_more @ eigen__1) @ eigen__0) => ((imp @ ((rt_lessis @ eigen__1) @ eigen__0)) @ $false)),introduced(definition,[new_symbols(definition,[sP10])])). % 139.77/139.57 thf(sP11,plain,sP11 <=> (((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__0))) @ ((inf @ X2) @ (class @ eigen__1))) @ ((lessf @ X1) @ X2)))))) => ((rt_more @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP11])])). % 139.77/139.57 thf(sP12,plain,sP12 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => (sP1 => ((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 139.77/139.57 thf(sP13,plain,sP13 <=> ($false = $false),introduced(definition,[new_symbols(definition,[sP13])])). % 139.77/139.57 thf(sP14,plain,sP14 <=> ((imp @ ((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1))) @ $false),introduced(definition,[new_symbols(definition,[sP14])])). % 139.77/139.57 thf(sP15,plain,sP15 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))),introduced(definition,[new_symbols(definition,[sP15])])). % 139.77/139.57 thf(sP16,plain,sP16 <=> $false,introduced(definition,[new_symbols(definition,[sP16])])). % 139.77/139.57 thf(sP17,plain,sP17 <=> (sP15 => sP6),introduced(definition,[new_symbols(definition,[sP17])])). % 139.77/139.57 thf(sP18,plain,sP18 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))) => sP10),introduced(definition,[new_symbols(definition,[sP18])])). % 139.77/139.57 thf(sP19,plain,sP19 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((ect @ frac) @ n_eq)))),introduced(definition,[new_symbols(definition,[sP19])])). % 139.77/139.57 thf(sP20,plain,sP20 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3)))))) => ((rt_more @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP20])])). % 139.77/139.57 thf(sP21,plain,sP21 <=> ((imp @ ((rt_lessis @ eigen__1) @ eigen__0)) @ sP16),introduced(definition,[new_symbols(definition,[sP21])])). % 139.77/139.57 thf(sP22,plain,sP22 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1)) => ((imp @ ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3))))))) @ sP16)))),introduced(definition,[new_symbols(definition,[sP22])])). % 139.77/139.57 thf(sP23,plain,sP23 <=> (![X1:$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:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4)))))) => ((rt_more @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 139.77/139.57 thf(sP24,plain,sP24 <=> (sP19 => (((imp @ ((rt_more @ eigen__1) @ eigen__0)) @ sP16) => ((rt_lessis @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP24])])). % 139.77/139.57 thf(sP25,plain,sP25 <=> (sP15 => sP3),introduced(definition,[new_symbols(definition,[sP25])])). % 139.77/139.57 thf(sP26,plain,sP26 <=> (((imp @ ((rt_more @ eigen__1) @ eigen__0)) @ sP16) => ((rt_lessis @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP26])])). % 139.77/139.57 thf(sP27,plain,sP27 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2)) => ((imp @ ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4))))))) @ sP16)))))),introduced(definition,[new_symbols(definition,[sP27])])). % 139.77/139.57 thf(sP28,plain,sP28 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((imp @ ((rt_more @ X1) @ X2)) @ sP16) => ((rt_lessis @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP28])])). % 139.77/139.57 thf(sP29,plain,sP29 <=> ((l_some @ frac) @ (^[X1:$i]:((l_some @ frac) @ (^[X2:$i]:(((and3 @ ((inf @ X1) @ (class @ eigen__0))) @ ((inf @ X2) @ (class @ eigen__1))) @ ((lessf @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP29])])). % 139.77/139.57 thf(sP30,plain,sP30 <=> (sP29 = ((rt_more @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP30])])). % 139.77/139.57 thf(sP31,plain,sP31 <=> (sP1 => ((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP31])])). % 139.77/139.57 thf(sP32,plain,sP32 <=> ((rt_more @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP32])])). % 139.77/139.57 thf(sP33,plain,sP33 <=> (sP19 => sP20),introduced(definition,[new_symbols(definition,[sP33])])). % 139.77/139.57 thf(sP34,plain,sP34 <=> ((l_or @ ((rt_more @ eigen__0) @ eigen__1)) @ ((rt_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP34])])). % 139.77/139.57 thf(sP35,plain,sP35 <=> ((imp @ sP32) @ sP16),introduced(definition,[new_symbols(definition,[sP35])])). % 139.77/139.57 thf(sP36,plain,sP36 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((imp @ ((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4))))))) @ sP16) => ((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 139.77/139.57 thf(sP37,plain,sP37 <=> (sP15 => sP11),introduced(definition,[new_symbols(definition,[sP37])])). % 139.77/139.57 thf(sP38,plain,sP38 <=> ((rt_lessis @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP38])])). % 139.77/139.57 thf(sP39,plain,sP39 <=> (sP38 = sP29),introduced(definition,[new_symbols(definition,[sP39])])). % 139.77/139.57 thf(sP40,plain,sP40 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((imp @ ((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3))))))) @ sP16) => ((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP40])])). % 139.77/139.57 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 139.77/139.57 thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ sP16)))). % 139.77/139.57 thf(def_rat,definition,(rat = ((ect @ frac) @ n_eq))). % 139.77/139.57 thf(def_rt_less,definition,(rt_less = (^[X1:$i]:(^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4)))))))))). % 139.77/139.57 thf(def_rt_moreis,definition,(rt_moreis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2)))))). % 139.77/139.57 thf(satz81h,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4)))))) => ((imp @ ((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2))) @ sP16))))))). % 139.77/139.57 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4)))))) => ((imp @ ((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2))) @ sP16)))))))),inference(assume_negation,[status(cth)],[satz81h])). % 139.77/139.57 thf(h1,assumption,(~((sP19 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X2:$i]:((l_some @ frac) @ (^[X3:$i]:(((and3 @ ((inf @ X2) @ (class @ eigen__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3)))))) => ((imp @ ((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1))) @ sP16))))))),introduced(assumption,[])). % 139.77/139.57 thf(h2,assumption,sP19,introduced(assumption,[])). % 139.77/139.57 thf(h3,assumption,(~((![X1:$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__0))) @ ((inf @ X3) @ (class @ X1))) @ ((lessf @ X2) @ X3)))))) => ((imp @ ((l_or @ ((rt_more @ eigen__0) @ X1)) @ ((rt_is @ eigen__0) @ X1))) @ sP16)))))),introduced(assumption,[])). % 139.77/139.57 thf(h4,assumption,(~((sP15 => (sP29 => sP14)))),introduced(assumption,[])). % 139.77/139.57 thf(h5,assumption,sP15,introduced(assumption,[])). % 139.77/139.57 thf(h6,assumption,(~((sP29 => sP14))),introduced(assumption,[])). % 139.77/139.57 thf(h7,assumption,sP29,introduced(assumption,[])). % 139.77/139.57 thf(h8,assumption,(~(sP14)),introduced(assumption,[])). % 139.77/139.57 thf(1,plain,((sP39 | ~(sP38)) | ~(sP29)),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(2,plain,(((~(sP21) | sP1) | ~(sP39)) | ~(sP13)),inference(mating_rule,[status(thm)],[])). % 139.77/139.57 thf(3,plain,((sP30 | ~(sP29)) | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(4,plain,(((~(sP1) | sP35) | ~(sP30)) | ~(sP13)),inference(mating_rule,[status(thm)],[])). % 139.77/139.57 thf(5,plain,((~(sP9) | ~(sP19)) | sP22),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(6,plain,(~(sP22) | sP4),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(7,plain,((~(sP4) | ~(sP15)) | sP7),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(8,plain,((~(sP7) | ~(sP34)) | sP1),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(9,plain,((~(sP17) | ~(sP15)) | sP6),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(10,plain,(~(sP6) | sP24),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(11,plain,((~(sP24) | ~(sP19)) | sP26),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(12,plain,((~(sP26) | ~(sP35)) | sP38),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(13,plain,((~(sP8) | ~(sP19)) | sP40),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(14,plain,(~(sP40) | sP12),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(15,plain,((~(sP12) | ~(sP15)) | sP31),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(16,plain,((~(sP31) | ~(sP1)) | sP34),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(17,plain,((sP5 | ~(sP38)) | ~(sP34)),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(18,plain,((sP5 | sP38) | sP34),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(19,plain,~(sP16),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(20,plain,((sP13 | sP16) | sP16),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(21,plain,(((~(sP21) | sP14) | ~(sP5)) | ~(sP13)),inference(mating_rule,[status(thm)],[])). % 139.77/139.57 thf(22,plain,((~(sP25) | ~(sP15)) | sP3),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(23,plain,(~(sP3) | sP18),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(24,plain,((~(sP18) | ~(sP19)) | sP10),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(25,plain,((~(sP10) | ~(sP32)) | sP21),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(26,plain,(~(sP36) | sP8),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(27,plain,(~(sP27) | sP9),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(28,plain,(~(sP2) | sP25),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(29,plain,(~(sP28) | sP17),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(30,plain,(~(sP23) | sP33),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(31,plain,((~(sP33) | ~(sP19)) | sP20),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(32,plain,(~(sP20) | sP37),inference(all_rule,[status(thm)],[])). % 139.77/139.57 thf(33,plain,((~(sP37) | ~(sP15)) | sP11),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(34,plain,((~(sP11) | ~(sP29)) | sP32),inference(prop_rule,[status(thm)],[])). % 139.77/139.57 thf(satz81g,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_more @ X1) @ X2) => (d_not @ ((rt_lessis @ X1) @ X2)))))))). % 139.77/139.57 thf(35,plain,sP2,inference(preprocess,[status(thm)],[satz81g]). % 139.77/139.57 thf(satz81f,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:((d_not @ ((rt_less @ X1) @ X2)) => ((rt_moreis @ X1) @ X2))))))). % 139.77/139.57 thf(36,plain,sP36,inference(preprocess,[status(thm)],[satz81f]). % 139.77/139.57 thf(satz81e,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:((d_not @ ((rt_more @ X1) @ X2)) => ((rt_lessis @ X1) @ X2))))))). % 139.77/139.57 thf(37,plain,sP28,inference(preprocess,[status(thm)],[satz81e]). % 139.77/139.57 thf(satz81c,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_moreis @ X1) @ X2) => (d_not @ ((rt_less @ X1) @ X2)))))))). % 139.77/139.57 thf(38,plain,sP27,inference(preprocess,[status(thm)],[satz81c]). % 139.77/139.57 thf(satz83,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ rat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ rat))) @ (^[X2:$i]:(((rt_less @ X1) @ X2) => ((rt_more @ X2) @ X1))))))). % 139.77/139.57 thf(39,plain,sP23,inference(preprocess,[status(thm)],[satz83]). % 139.77/139.57 thf(40,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h2,h5,h7,h8,35,36,37,38,39])). % 139.77/139.57 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,40,h7,h8])). % 139.77/139.57 thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,41,h5,h6])). % 139.77/139.57 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,42,h4])). % 139.77/139.57 thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,43,h2,h3])). % 139.77/139.57 thf(45,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,44,h1])). % 139.77/139.57 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((ect @ frac) @ n_eq)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((ect @ frac) @ n_eq)))) => (((l_some @ frac) @ (^[X3:$i]:((l_some @ frac) @ (^[X4:$i]:(((and3 @ ((inf @ X3) @ (class @ X1))) @ ((inf @ X4) @ (class @ X2))) @ ((lessf @ X3) @ X4)))))) => ((imp @ ((l_or @ ((rt_more @ X1) @ X2)) @ ((rt_is @ X1) @ X2))) @ sP16)))))),inference(contra,[status(thm),contra(discharge,[h0])],[45,h0])). % 139.77/139.57 % SZS output end Proof %------------------------------------------------------------------------------