%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM694^4 : 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 02:11:50 PM UTC 2025 % Result : Theorem 0.68s 0.87s % Output : Proof 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : NUM694^4 : TPTP v9.2.0. Released v7.1.0. % 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.35 % Computer : n008.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Wed Oct 8 23:10:08 EDT 2025 % 0.15/0.36 % CPUTime : % 0.68/0.87 % SZS status Theorem % 0.68/0.87 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 % 0.68/0.87 % Inferences: 51 % 0.68/0.87 % SZS output start Proof % 0.68/0.87 thf(ty_moreis, type, moreis : ($i>$i>$o)). % 0.68/0.87 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 0.68/0.87 thf(ty_eigen__0, type, eigen__0 : $i). % 0.68/0.87 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)). % 0.68/0.87 thf(ty_ordsucc, type, ordsucc : ($i>$i)). % 0.68/0.87 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 0.68/0.87 thf(ty_emptyset, type, emptyset : $i). % 0.68/0.87 thf(ty_omega, type, omega : $i). % 0.68/0.87 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 0.68/0.87 thf(ty_in, type, in : ($i>$i>$o)). % 0.68/0.87 thf(ty_iii, type, iii : ($i>$i>$o)). % 0.68/0.87 thf(sP1,plain,sP1 <=> (((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:$i]:(~((X3 = emptyset)))))))) => (((moreis @ eigen__0) @ X1) => ((l_or @ ((iii @ X1) @ eigen__0)) @ ((n_is @ X1) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.68/0.87 thf(sP2,plain,sP2 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((moreis @ eigen__0) @ X1) => ((l_or @ ((iii @ X1) @ eigen__0)) @ ((n_is @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.68/0.87 thf(sP3,plain,sP3 <=> ((is_of @ (ordsucc @ emptyset)) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.68/0.87 thf(sP4,plain,sP4 <=> (![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) => ((l_or @ ((iii @ X2) @ X1)) @ ((n_is @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.68/0.87 thf(sP5,plain,sP5 <=> ((moreis @ eigen__0) @ (ordsucc @ emptyset)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.68/0.87 thf(sP6,plain,sP6 <=> (sP3 => (sP5 => ((l_or @ ((iii @ (ordsucc @ emptyset)) @ eigen__0)) @ ((n_is @ (ordsucc @ emptyset)) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.68/0.87 thf(sP7,plain,sP7 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((moreis @ X1) @ (ordsucc @ emptyset)))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.68/0.87 thf(sP8,plain,sP8 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.68/0.87 thf(sP9,plain,sP9 <=> (sP8 => sP5),introduced(definition,[new_symbols(definition,[sP9])])). % 0.68/0.87 thf(sP10,plain,sP10 <=> (sP5 => ((l_or @ ((iii @ (ordsucc @ emptyset)) @ eigen__0)) @ ((n_is @ (ordsucc @ emptyset)) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.68/0.87 thf(sP11,plain,sP11 <=> ((l_or @ ((iii @ (ordsucc @ emptyset)) @ eigen__0)) @ ((n_is @ (ordsucc @ emptyset)) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP11])])). % 0.68/0.87 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 0.68/0.87 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))). % 0.68/0.87 thf(def_n_1,definition,(n_1 = (ordsucc @ emptyset))). % 0.68/0.87 thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))). % 0.68/0.87 thf(satz24a,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((l_or @ ((iii @ (ordsucc @ emptyset)) @ X1)) @ ((n_is @ (ordsucc @ emptyset)) @ X1))))). % 0.68/0.87 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((l_or @ ((iii @ (ordsucc @ emptyset)) @ X1)) @ ((n_is @ (ordsucc @ emptyset)) @ X1)))))),inference(assume_negation,[status(cth)],[satz24a])). % 0.68/0.87 thf(h1,assumption,(~((sP8 => sP11))),introduced(assumption,[])). % 0.68/0.87 thf(h2,assumption,sP8,introduced(assumption,[])). % 0.68/0.87 thf(h3,assumption,(~(sP11)),introduced(assumption,[])). % 0.68/0.87 thf(1,plain,(~(sP4) | sP1),inference(all_rule,[status(thm)],[])). % 0.68/0.87 thf(2,plain,((~(sP1) | ~(sP8)) | sP2),inference(prop_rule,[status(thm)],[])). % 0.68/0.87 thf(3,plain,(~(sP2) | sP6),inference(all_rule,[status(thm)],[])). % 0.68/0.87 thf(4,plain,((~(sP6) | ~(sP3)) | sP10),inference(prop_rule,[status(thm)],[])). % 0.68/0.87 thf(5,plain,((~(sP10) | ~(sP5)) | sP11),inference(prop_rule,[status(thm)],[])). % 0.68/0.87 thf(6,plain,(~(sP7) | sP9),inference(all_rule,[status(thm)],[])). % 0.68/0.87 thf(7,plain,((~(sP9) | ~(sP8)) | sP5),inference(prop_rule,[status(thm)],[])). % 0.68/0.87 thf(satz24,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((moreis @ X1) @ n_1)))). % 0.68/0.87 thf(8,plain,sP7,inference(preprocess,[status(thm)],[satz24]). % 0.68/0.87 thf(satz13,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((moreis @ X1) @ X2) => ((lessis @ X2) @ X1))))))). % 0.68/0.87 thf(9,plain,sP4,inference(preprocess,[status(thm)],[satz13]). % 0.68/0.87 thf(n_1_p,axiom,((is_of @ n_1) @ (^[X1:$i]:((in @ X1) @ nat)))). % 0.68/0.87 thf(10,plain,sP3,inference(preprocess,[status(thm)],[n_1_p]). % 0.68/0.87 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h3,8,9,10])). % 0.68/0.87 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3])). % 0.68/0.87 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1])). % 0.68/0.87 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((l_or @ ((iii @ (ordsucc @ emptyset)) @ X1)) @ ((n_is @ (ordsucc @ emptyset)) @ X1)))),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])). % 0.68/0.87 % SZS output end Proof 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