%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM655^4 : 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 : n024.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 02:11:39 PM UTC 2025 % Result : Theorem 49.37s 49.57s % Output : Proof 49.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : NUM655^4 : TPTP v9.2.0. Released v7.1.0. % 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.35 % Computer : n024.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Oct 8 22:51:08 EDT 2025 % 0.13/0.35 % CPUTime : % 49.37/49.57 % SZS status Theorem % 49.37/49.57 % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 % 49.37/49.57 % Inferences: 51 % 49.37/49.57 % SZS output start Proof % 49.37/49.57 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 49.37/49.57 thf(ty_d_29_ii, type, d_29_ii : ($i>$i>$o)). % 49.37/49.57 thf(ty_eigen__1, type, eigen__1 : $i). % 49.37/49.57 thf(ty_eigen__0, type, eigen__0 : $i). % 49.37/49.57 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)). % 49.37/49.57 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 49.37/49.57 thf(ty_emptyset, type, emptyset : $i). % 49.37/49.57 thf(ty_lessis, type, lessis : ($i>$i>$o)). % 49.37/49.57 thf(ty_n_some, type, n_some : (($i>$o)>$o)). % 49.37/49.57 thf(ty_diffprop, type, diffprop : ($i>$i>$i>$o)). % 49.37/49.57 thf(ty_omega, type, omega : $i). % 49.37/49.57 thf(ty_imp, type, imp : ($o>$o>$o)). % 49.37/49.57 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 49.37/49.57 thf(ty_in, type, in : ($i>$i>$o)). % 49.37/49.57 thf(sP1,plain,sP1 <=> ((l_or @ ((d_29_ii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP1])])). % 49.37/49.57 thf(sP2,plain,sP2 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((lessis @ eigen__1) @ eigen__0) => sP1)),introduced(definition,[new_symbols(definition,[sP2])])). % 49.37/49.57 thf(sP3,plain,sP3 <=> (((is_of @ eigen__1) @ (^[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)))))))) => (((imp @ ((d_29_ii @ eigen__1) @ X1)) @ $false) => ((lessis @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP3])])). % 49.37/49.57 thf(sP4,plain,sP4 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__1) @ eigen__0)) => ((d_29_ii @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP4])])). % 49.37/49.57 thf(sP5,plain,sP5 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((d_29_ii @ eigen__1) @ X1) => (n_some @ ((diffprop @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP5])])). % 49.37/49.57 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((imp @ ((d_29_ii @ eigen__1) @ X1)) @ $false) => ((lessis @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 49.37/49.57 thf(sP7,plain,sP7 <=> ((n_some @ ((diffprop @ eigen__1) @ eigen__0)) => ((d_29_ii @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP7])])). % 49.37/49.57 thf(sP8,plain,sP8 <=> (((imp @ ((d_29_ii @ eigen__1) @ eigen__0)) @ $false) => ((lessis @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP8])])). % 49.37/49.57 thf(sP9,plain,sP9 <=> (((lessis @ eigen__1) @ eigen__0) => sP1),introduced(definition,[new_symbols(definition,[sP9])])). % 49.37/49.57 thf(sP10,plain,sP10 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 49.37/49.57 thf(sP11,plain,sP11 <=> (n_some @ ((diffprop @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP11])])). % 49.37/49.57 thf(sP12,plain,sP12 <=> ((d_29_ii @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP12])])). % 49.37/49.57 thf(sP13,plain,sP13 <=> (sP10 => sP5),introduced(definition,[new_symbols(definition,[sP13])])). % 49.37/49.57 thf(sP14,plain,sP14 <=> ((lessis @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP14])])). % 49.37/49.57 thf(sP15,plain,sP15 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ eigen__0)) => ((d_29_ii @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP15])])). % 49.37/49.57 thf(sP16,plain,sP16 <=> (sP12 => sP11),introduced(definition,[new_symbols(definition,[sP16])])). % 49.37/49.57 thf(sP17,plain,sP17 <=> (![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)))))))) => (((imp @ ((d_29_ii @ X1) @ X2)) @ $false) => ((lessis @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP17])])). % 49.37/49.57 thf(sP18,plain,sP18 <=> (![X1:$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:$i]:(~((X4 = emptyset)))))))) => (((d_29_ii @ X1) @ X2) => (n_some @ ((diffprop @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 49.37/49.57 thf(sP19,plain,sP19 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => sP8),introduced(definition,[new_symbols(definition,[sP19])])). % 49.37/49.57 thf(sP20,plain,sP20 <=> $false,introduced(definition,[new_symbols(definition,[sP20])])). % 49.37/49.57 thf(sP21,plain,sP21 <=> ((imp @ sP11) @ sP20),introduced(definition,[new_symbols(definition,[sP21])])). % 49.37/49.57 thf(sP22,plain,sP22 <=> (![X1:$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:$i]:(~((X4 = emptyset)))))))) => (((lessis @ X1) @ X2) => ((l_or @ ((d_29_ii @ X2) @ X1)) @ ((n_is @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 49.37/49.57 thf(sP23,plain,sP23 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => sP15),introduced(definition,[new_symbols(definition,[sP23])])). % 49.37/49.57 thf(sP24,plain,sP24 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 49.37/49.57 thf(sP25,plain,sP25 <=> (sP24 => sP16),introduced(definition,[new_symbols(definition,[sP25])])). % 49.37/49.57 thf(sP26,plain,sP26 <=> ((imp @ sP12) @ sP20),introduced(definition,[new_symbols(definition,[sP26])])). % 49.37/49.57 thf(sP27,plain,sP27 <=> (sP10 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((lessis @ eigen__1) @ X1) => ((l_or @ ((d_29_ii @ X1) @ eigen__1)) @ ((n_is @ X1) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP27])])). % 49.37/49.57 thf(sP28,plain,sP28 <=> (![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 @ X2) @ X1)) => ((d_29_ii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP28])])). % 49.37/49.57 thf(sP29,plain,sP29 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((lessis @ eigen__1) @ X1) => ((l_or @ ((d_29_ii @ X1) @ eigen__1)) @ ((n_is @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP29])])). % 49.37/49.57 thf(sP30,plain,sP30 <=> (sP11 = sP12),introduced(definition,[new_symbols(definition,[sP30])])). % 49.37/49.57 thf(sP31,plain,sP31 <=> (sP20 = sP20),introduced(definition,[new_symbols(definition,[sP31])])). % 49.37/49.57 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 49.37/49.57 thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ sP20)))). % 49.37/49.57 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))). % 49.37/49.57 thf(def_iii,definition,(iii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X2) @ X1)))))). % 49.37/49.57 thf(def_moreis,definition,(moreis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((d_29_ii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))). % 49.37/49.57 thf(satz10f,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)))))))) => (((imp @ (n_some @ ((diffprop @ X2) @ X1))) @ sP20) => ((l_or @ ((d_29_ii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))))). % 49.37/49.57 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)))))))) => (((imp @ (n_some @ ((diffprop @ X2) @ X1))) @ sP20) => ((l_or @ ((d_29_ii @ X1) @ X2)) @ ((n_is @ X1) @ X2))))))))),inference(assume_negation,[status(cth)],[satz10f])). % 49.37/49.57 thf(h1,assumption,(~((sP24 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((imp @ (n_some @ ((diffprop @ X1) @ eigen__0))) @ sP20) => ((l_or @ ((d_29_ii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)))))))),introduced(assumption,[])). % 49.37/49.57 thf(h2,assumption,sP24,introduced(assumption,[])). % 49.37/49.57 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((imp @ (n_some @ ((diffprop @ X1) @ eigen__0))) @ sP20) => ((l_or @ ((d_29_ii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1))))))),introduced(assumption,[])). % 49.37/49.57 thf(h4,assumption,(~((sP10 => (sP21 => sP1)))),introduced(assumption,[])). % 49.37/49.57 thf(h5,assumption,sP10,introduced(assumption,[])). % 49.37/49.57 thf(h6,assumption,(~((sP21 => sP1))),introduced(assumption,[])). % 49.37/49.57 thf(h7,assumption,sP21,introduced(assumption,[])). % 49.37/49.57 thf(h8,assumption,(~(sP1)),introduced(assumption,[])). % 49.37/49.57 thf(1,plain,((~(sP13) | ~(sP10)) | sP5),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(2,plain,(~(sP5) | sP25),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(3,plain,((~(sP25) | ~(sP24)) | sP16),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(4,plain,((~(sP16) | ~(sP12)) | sP11),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(5,plain,((~(sP23) | ~(sP24)) | sP15),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(6,plain,(~(sP15) | sP4),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(7,plain,((~(sP4) | ~(sP10)) | sP7),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(8,plain,((~(sP7) | ~(sP11)) | sP12),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(9,plain,((sP30 | ~(sP11)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(10,plain,((sP30 | sP11) | sP12),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(11,plain,~(sP20),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(12,plain,((sP31 | sP20) | sP20),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(13,plain,(((~(sP21) | sP26) | ~(sP30)) | ~(sP31)),inference(mating_rule,[status(thm)],[])). % 49.37/49.57 thf(14,plain,((~(sP3) | ~(sP10)) | sP6),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(15,plain,(~(sP6) | sP19),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(16,plain,((~(sP19) | ~(sP24)) | sP8),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(17,plain,((~(sP8) | ~(sP26)) | sP14),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(18,plain,(~(sP17) | sP3),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(19,plain,(~(sP18) | sP13),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(20,plain,(~(sP28) | sP23),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(21,plain,(~(sP22) | sP27),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(22,plain,((~(sP27) | ~(sP10)) | sP29),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(23,plain,(~(sP29) | sP2),inference(all_rule,[status(thm)],[])). % 49.37/49.57 thf(24,plain,((~(sP2) | ~(sP24)) | sP9),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(25,plain,((~(sP9) | ~(sP14)) | sP1),inference(prop_rule,[status(thm)],[])). % 49.37/49.57 thf(satz10e,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:((d_not @ ((d_29_ii @ X1) @ X2)) => ((lessis @ X1) @ X2))))))). % 49.37/49.57 thf(26,plain,sP17,inference(preprocess,[status(thm)],[satz10e]). % 49.37/49.57 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))))))). % 49.37/49.57 thf(27,plain,sP22,inference(preprocess,[status(thm)],[satz14]). % 49.37/49.57 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))))))). % 49.37/49.57 thf(28,plain,sP28,inference(preprocess,[status(thm)],[satz12]). % 49.37/49.57 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))))))). % 49.37/49.57 thf(29,plain,sP18,inference(preprocess,[status(thm)],[satz11]). % 49.37/49.57 thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h2,h5,h7,h8,26,27,28,29])). % 49.37/49.57 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,30,h7,h8])). % 49.37/49.57 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,31,h5,h6])). % 49.37/49.57 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,32,h4])). % 49.37/49.57 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,33,h2,h3])). % 49.37/49.57 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,34,h1])). % 49.37/49.57 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)))))))) => (((imp @ (n_some @ ((diffprop @ X2) @ X1))) @ sP20) => ((l_or @ ((d_29_ii @ X1) @ X2)) @ ((n_is @ X1) @ X2))))))),inference(contra,[status(thm),contra(discharge,[h0])],[35,h0])). % 49.37/49.57 % SZS output end Proof %------------------------------------------------------------------------------