%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET926^20 : TPTP v9.2.0. Released v8.1.0. % 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 02:26:35 PM UTC 2025 % Result : Theorem 1.10s 1.30s % Output : Proof 1.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET926^20 : TPTP v9.2.0. Released v8.1.0. % 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n002.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 14:41:23 EDT 2025 % 0.13/0.34 % CPUTime : % 1.10/1.30 % SZS status Theorem % 1.10/1.30 % Mode: mode506 % 1.10/1.30 % Inferences: 8226 % 1.10/1.30 % SZS output start Proof % 1.10/1.30 thf(ty_mworld, type, mworld : $tType). % 1.10/1.30 thf(ty_singleton, type, singleton : ($i>$i)). % 1.10/1.30 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)). % 1.10/1.30 thf(ty_eigen__1, type, eigen__1 : $i). % 1.10/1.30 thf(ty_eigen__0, type, eigen__0 : $i). % 1.10/1.30 thf(ty_mactual, type, mactual : mworld). % 1.10/1.30 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)). % 1.10/1.30 thf(ty_empty_set, type, empty_set : $i). % 1.10/1.30 thf(ty_set_difference, type, set_difference : ($i>$i>$i)). % 1.10/1.30 thf(ty_in, type, in : ($i>$i>mworld>$o)). % 1.10/1.30 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.10/1.30 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.10/1.30 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.10/1.30 thf(sP1,plain,sP1 <=> (((eiw_di @ eigen__0) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.10/1.30 thf(sP2,plain,sP2 <=> ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ empty_set) @ mactual) = (((in @ eigen__0) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP2])])). % 1.10/1.30 thf(sP3,plain,sP3 <=> (((eiw_di @ eigen__1) @ mactual) => sP2),introduced(definition,[new_symbols(definition,[sP3])])). % 1.10/1.30 thf(sP4,plain,sP4 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual) = (((in @ eigen__0) @ X1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.10/1.30 thf(sP5,plain,sP5 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual) = (~((((in @ eigen__0) @ X1) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.10/1.30 thf(sP6,plain,sP6 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual)))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.10/1.30 thf(sP7,plain,sP7 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X3 = X1) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.10/1.30 thf(sP8,plain,sP8 <=> ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ (singleton @ eigen__0)) @ mactual) = (~((((in @ eigen__0) @ eigen__1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.10/1.30 thf(sP9,plain,sP9 <=> (((eiw_di @ eigen__1) @ mactual) => sP8),introduced(definition,[new_symbols(definition,[sP9])])). % 1.10/1.30 thf(sP10,plain,sP10 <=> (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ (singleton @ eigen__0)) @ mactual),introduced(definition,[new_symbols(definition,[sP10])])). % 1.10/1.30 thf(sP11,plain,sP11 <=> (sP8 => sP10),introduced(definition,[new_symbols(definition,[sP11])])). % 1.10/1.30 thf(sP12,plain,sP12 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual) = (((in @ X1) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.10/1.30 thf(sP13,plain,sP13 <=> (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP13])])). % 1.10/1.30 thf(sP14,plain,sP14 <=> (((eiw_di @ eigen__0) @ mactual) => sP4),introduced(definition,[new_symbols(definition,[sP14])])). % 1.10/1.30 thf(sP15,plain,sP15 <=> ((eiw_di @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP15])])). % 1.10/1.30 thf(sP16,plain,sP16 <=> (![X1:$o>$o]:((X1 @ (~((((in @ eigen__0) @ eigen__1) @ mactual)))) => (![X2:$o]:((X2 = (~((((in @ eigen__0) @ eigen__1) @ mactual)))) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.10/1.30 thf(sP17,plain,sP17 <=> ((eiw_di @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP17])])). % 1.10/1.30 thf(sP18,plain,sP18 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual) = (~((((in @ X1) @ X2) @ mactual)))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 1.10/1.30 thf(sP19,plain,sP19 <=> (sP17 => ((~(sP13)) => sP10)),introduced(definition,[new_symbols(definition,[sP19])])). % 1.10/1.30 thf(sP20,plain,sP20 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP20])])). % 1.10/1.30 thf(sP21,plain,sP21 <=> (((in @ eigen__0) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP21])])). % 1.10/1.30 thf(sP22,plain,sP22 <=> ((~(sP21)) => (![X1:$o]:((X1 = (~(sP21))) => X1))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.10/1.30 thf(sP23,plain,sP23 <=> (sP15 => sP5),introduced(definition,[new_symbols(definition,[sP23])])). % 1.10/1.30 thf(sP24,plain,sP24 <=> (![X1:$o]:((X1 = (~(sP21))) => X1)),introduced(definition,[new_symbols(definition,[sP24])])). % 1.10/1.30 thf(sP25,plain,sP25 <=> ((~(sP13)) => sP10),introduced(definition,[new_symbols(definition,[sP25])])). % 1.10/1.30 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 1.10/1.30 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 1.10/1.30 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.10/1.30 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.10/1.30 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 1.10/1.30 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 1.10/1.30 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 1.10/1.30 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 1.10/1.30 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 1.10/1.30 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))). % 1.10/1.30 thf(t69_zfmisc_1,conjecture,sP20). % 1.10/1.30 thf(h1,negated_conjecture,(~(sP20)),inference(assume_negation,[status(cth)],[t69_zfmisc_1])). % 1.10/1.30 thf(1,plain,((~(sP11) | ~(sP8)) | sP10),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(2,plain,(~(sP24) | sP11),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(3,plain,((~(sP22) | sP21) | sP24),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(4,plain,(~(sP16) | sP22),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(5,plain,(~(sP7) | sP16),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(6,plain,(~(sP18) | sP23),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(7,plain,((~(sP23) | ~(sP15)) | sP5),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(8,plain,(~(sP5) | sP9),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(9,plain,((~(sP9) | ~(sP17)) | sP8),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(10,plain,((~(sP2) | sP13) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(11,plain,sP7,inference(eq_ind_sym,[status(thm)],[])). % 1.10/1.30 thf(12,plain,(~(sP12) | sP14),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(13,plain,((~(sP14) | ~(sP15)) | sP4),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(14,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])). % 1.10/1.30 thf(15,plain,((~(sP3) | ~(sP17)) | sP2),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(16,plain,(sP25 | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(17,plain,(sP25 | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(18,plain,(sP19 | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(19,plain,(sP19 | sP17),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(20,plain,(sP6 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.10/1.30 thf(21,plain,(sP1 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(22,plain,(sP1 | sP15),inference(prop_rule,[status(thm)],[])). % 1.10/1.30 thf(23,plain,(sP20 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.10/1.30 thf(l36_zfmisc_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set)) @ ((in @ X1) @ X2)))))))). % 1.10/1.30 thf(24,plain,sP12,inference(preprocess,[status(thm)],[l36_zfmisc_1]). % 1.10/1.30 thf(l34_zfmisc_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1))) @ (mnot @ ((in @ X1) @ X2))))))))). % 1.10/1.30 thf(25,plain,sP18,inference(preprocess,[status(thm)],[l34_zfmisc_1]). % 1.10/1.30 thf(26,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h1])). % 1.10/1.30 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0])). % 1.10/1.30 thf(0,theorem,sP20,inference(contra,[status(thm),contra(discharge,[h1])],[26,h1])). % 1.10/1.30 % SZS output end Proof %------------------------------------------------------------------------------