%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM653^4 : 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 : 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 02:11:38 PM UTC 2025 % Result : Theorem 49.36s 49.59s % Output : Proof 49.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.14 % Problem : NUM653^4 : TPTP v9.2.0. Released v7.1.0. % 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n002.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Wed Oct 8 22:55:23 EDT 2025 % 0.14/0.36 % CPUTime : % 49.36/49.59 % SZS status Theorem % 49.36/49.59 % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 % 49.36/49.59 % Inferences: 49 % 49.36/49.59 % SZS output start Proof % 49.36/49.59 thf(ty_moreis, type, moreis : ($i>$i>$o)). % 49.36/49.59 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 49.36/49.59 thf(ty_eigen__1, type, eigen__1 : $i). % 49.36/49.59 thf(ty_eigen__0, type, eigen__0 : $i). % 49.36/49.59 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)). % 49.36/49.59 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 49.36/49.59 thf(ty_emptyset, type, emptyset : $i). % 49.36/49.59 thf(ty_n_some, type, n_some : (($i>$o)>$o)). % 49.36/49.59 thf(ty_diffprop, type, diffprop : ($i>$i>$i>$o)). % 49.36/49.59 thf(ty_omega, type, omega : $i). % 49.36/49.59 thf(ty_imp, type, imp : ($o>$o>$o)). % 49.36/49.59 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 49.36/49.59 thf(ty_in, type, in : ($i>$i>$o)). % 49.36/49.59 thf(ty_iii, type, iii : ($i>$i>$o)). % 49.36/49.59 thf(sP1,plain,sP1 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 49.36/49.59 thf(sP2,plain,sP2 <=> ((imp @ ((iii @ eigen__1) @ eigen__0)) @ $false),introduced(definition,[new_symbols(definition,[sP2])])). % 49.36/49.59 thf(sP3,plain,sP3 <=> (sP1 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__1) @ X1) => (n_some @ ((diffprop @ X1) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP3])])). % 49.36/49.59 thf(sP4,plain,sP4 <=> (((iii @ eigen__1) @ eigen__0) = (n_some @ ((diffprop @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])). % 49.36/49.59 thf(sP5,plain,sP5 <=> ($false = $false),introduced(definition,[new_symbols(definition,[sP5])])). % 49.36/49.59 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((moreis @ eigen__1) @ X1) => ((imp @ ((iii @ eigen__1) @ X1)) @ $false)))),introduced(definition,[new_symbols(definition,[sP6])])). % 49.36/49.59 thf(sP7,plain,sP7 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((moreis @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP7])])). % 49.36/49.59 thf(sP8,plain,sP8 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((moreis @ X1) @ X2) => ((imp @ ((iii @ X1) @ X2)) @ $false)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 49.36/49.59 thf(sP9,plain,sP9 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((moreis @ eigen__1) @ eigen__0) => sP2)),introduced(definition,[new_symbols(definition,[sP9])])). % 49.36/49.59 thf(sP10,plain,sP10 <=> ((l_or @ ((iii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP10])])). % 49.36/49.59 thf(sP11,plain,sP11 <=> (sP1 => ((n_some @ ((diffprop @ eigen__0) @ eigen__1)) => ((iii @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP11])])). % 49.36/49.59 thf(sP12,plain,sP12 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ X2)) => ((iii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 49.36/49.59 thf(sP13,plain,sP13 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((moreis @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP13])])). % 49.36/49.59 thf(sP14,plain,sP14 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__1) @ X1) => (n_some @ ((diffprop @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP14])])). % 49.36/49.59 thf(sP15,plain,sP15 <=> $false,introduced(definition,[new_symbols(definition,[sP15])])). % 49.36/49.59 thf(sP16,plain,sP16 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 49.36/49.59 thf(sP17,plain,sP17 <=> (sP10 => ((moreis @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP17])])). % 49.36/49.59 thf(sP18,plain,sP18 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((moreis @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP18])])). % 49.36/49.59 thf(sP19,plain,sP19 <=> ((moreis @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])). % 49.36/49.59 thf(sP20,plain,sP20 <=> (sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((iii @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP20])])). % 49.36/49.59 thf(sP21,plain,sP21 <=> (sP1 => sP6),introduced(definition,[new_symbols(definition,[sP21])])). % 49.36/49.59 thf(sP22,plain,sP22 <=> ((iii @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP22])])). % 49.36/49.59 thf(sP23,plain,sP23 <=> (sP19 => sP2),introduced(definition,[new_symbols(definition,[sP23])])). % 49.36/49.59 thf(sP24,plain,sP24 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ X1) @ X2) => (n_some @ ((diffprop @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 49.36/49.59 thf(sP25,plain,sP25 <=> (n_some @ ((diffprop @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP25])])). % 49.36/49.59 thf(sP26,plain,sP26 <=> (sP25 => sP22),introduced(definition,[new_symbols(definition,[sP26])])). % 49.36/49.59 thf(sP27,plain,sP27 <=> (sP22 => sP25),introduced(definition,[new_symbols(definition,[sP27])])). % 49.36/49.59 thf(sP28,plain,sP28 <=> (sP1 => sP17),introduced(definition,[new_symbols(definition,[sP28])])). % 49.36/49.59 thf(sP29,plain,sP29 <=> (sP16 => sP27),introduced(definition,[new_symbols(definition,[sP29])])). % 49.36/49.59 thf(sP30,plain,sP30 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((iii @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP30])])). % 49.36/49.59 thf(sP31,plain,sP31 <=> ((imp @ sP25) @ sP15),introduced(definition,[new_symbols(definition,[sP31])])). % 49.36/49.59 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 49.36/49.59 thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ sP15)))). % 49.36/49.59 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))). % 49.36/49.59 thf(def_d_29_ii,definition,(d_29_ii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X1) @ X2)))))). % 49.36/49.59 thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))). % 49.36/49.59 thf(satz10d,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15))))))). % 49.36/49.59 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15)))))))),inference(assume_negation,[status(cth)],[satz10d])). % 49.36/49.59 thf(h1,assumption,(~((sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((imp @ (n_some @ ((diffprop @ eigen__0) @ X1))) @ sP15))))))),introduced(assumption,[])). % 49.36/49.59 thf(h2,assumption,sP16,introduced(assumption,[])). % 49.36/49.59 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((imp @ (n_some @ ((diffprop @ eigen__0) @ X1))) @ sP15)))))),introduced(assumption,[])). % 49.36/49.59 thf(h4,assumption,(~((sP1 => (sP10 => sP31)))),introduced(assumption,[])). % 49.36/49.59 thf(h5,assumption,sP1,introduced(assumption,[])). % 49.36/49.59 thf(h6,assumption,(~((sP10 => sP31))),introduced(assumption,[])). % 49.36/49.59 thf(h7,assumption,sP10,introduced(assumption,[])). % 49.36/49.59 thf(h8,assumption,(~(sP31)),introduced(assumption,[])). % 49.36/49.59 thf(1,plain,((~(sP20) | ~(sP16)) | sP30),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(2,plain,(~(sP30) | sP11),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(3,plain,((~(sP11) | ~(sP1)) | sP26),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(4,plain,((~(sP26) | ~(sP25)) | sP22),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(5,plain,((~(sP3) | ~(sP1)) | sP14),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(6,plain,(~(sP14) | sP29),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(7,plain,((~(sP29) | ~(sP16)) | sP27),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(8,plain,((~(sP27) | ~(sP22)) | sP25),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(9,plain,((sP4 | ~(sP22)) | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(10,plain,((sP4 | sP22) | sP25),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(11,plain,~(sP15),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(12,plain,((sP5 | sP15) | sP15),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(13,plain,(((~(sP2) | sP31) | ~(sP4)) | ~(sP5)),inference(mating_rule,[status(thm)],[])). % 49.36/49.59 thf(14,plain,((~(sP21) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(15,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(16,plain,((~(sP9) | ~(sP16)) | sP23),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(17,plain,((~(sP23) | ~(sP19)) | sP2),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(18,plain,(~(sP12) | sP20),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(19,plain,(~(sP8) | sP21),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(20,plain,(~(sP24) | sP3),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(21,plain,(~(sP18) | sP7),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(22,plain,((~(sP7) | ~(sP16)) | sP13),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(23,plain,(~(sP13) | sP28),inference(all_rule,[status(thm)],[])). % 49.36/49.59 thf(24,plain,((~(sP28) | ~(sP1)) | sP17),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(25,plain,((~(sP17) | ~(sP10)) | sP19),inference(prop_rule,[status(thm)],[])). % 49.36/49.59 thf(satz10c,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((moreis @ X1) @ X2) => (d_not @ ((iii @ X1) @ X2)))))))). % 49.36/49.59 thf(26,plain,sP8,inference(preprocess,[status(thm)],[satz10c]). % 49.36/49.59 thf(satz14,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((lessis @ X1) @ X2) => ((moreis @ X2) @ X1))))))). % 49.36/49.59 thf(27,plain,sP18,inference(preprocess,[status(thm)],[satz14]). % 49.36/49.59 thf(satz12,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((iii @ X1) @ X2) => ((d_29_ii @ X2) @ X1))))))). % 49.36/49.59 thf(28,plain,sP24,inference(preprocess,[status(thm)],[satz12]). % 49.36/49.59 thf(satz11,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ X1) @ X2) => ((iii @ X2) @ X1))))))). % 49.36/49.59 thf(29,plain,sP12,inference(preprocess,[status(thm)],[satz11]). % 49.36/49.59 thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h2,h5,h7,h8,26,27,28,29])). % 49.36/49.59 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,30,h7,h8])). % 49.36/49.59 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,31,h5,h6])). % 49.36/49.59 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,32,h4])). % 49.36/49.59 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,33,h2,h3])). % 49.36/49.59 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,34,h1])). % 49.36/49.59 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15)))))),inference(contra,[status(thm),contra(discharge,[h0])],[35,h0])). % 49.36/49.59 % SZS output end Proof %------------------------------------------------------------------------------