%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET047^1 : 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 : n004.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 02:25:11 PM UTC 2025 % Result : Theorem 1.08s 1.35s % Output : Proof 1.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET047^1 : TPTP v9.2.0. Released v8.1.0. % 0.03/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n004.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 14:52:38 EDT 2025 % 0.12/0.33 % CPUTime : % 1.08/1.35 % SZS status Theorem % 1.08/1.35 % Mode: mode506 % 1.08/1.35 % Inferences: 10194 % 1.08/1.35 % SZS output start Proof % 1.08/1.35 thf(ty_mworld, type, mworld : $tType). % 1.08/1.35 thf(ty_element, type, element : ($i>$i>mworld>$o)). % 1.08/1.35 thf(ty_eigen__2, type, eigen__2 : $i). % 1.08/1.35 thf(ty_eigen__1, type, eigen__1 : $i). % 1.08/1.35 thf(ty_set_equal, type, set_equal : ($i>$i>mworld>$o)). % 1.08/1.35 thf(ty_eigen__0, type, eigen__0 : $i). % 1.08/1.35 thf(ty_eigen__3, type, eigen__3 : $i). % 1.08/1.35 thf(ty_mactual, type, mactual : mworld). % 1.08/1.35 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.08/1.35 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~(((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 1.08/1.35 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((((set_equal @ eigen__0) @ X1) @ mactual) = (((set_equal @ X1) @ eigen__0) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.08/1.35 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (((set_equal @ X2) @ X1) @ mactual))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.08/1.35 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~(((((element @ X1) @ eigen__0) @ mactual) = (((element @ X1) @ eigen__1) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 1.08/1.35 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (![X3:$i]:((((element @ X3) @ X1) @ mactual) = (((element @ X3) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.08/1.35 thf(sP2,plain,sP2 <=> (![X1:$i]:((((element @ X1) @ eigen__0) @ mactual) = (((element @ X1) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.08/1.35 thf(sP3,plain,sP3 <=> (![X1:$i]:((((set_equal @ eigen__0) @ X1) @ mactual) = (![X2:$i]:((((element @ X2) @ eigen__0) @ mactual) = (((element @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.08/1.35 thf(sP4,plain,sP4 <=> ((~(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))) => (![X1:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X1) => (~((X1 = (((set_equal @ eigen__1) @ eigen__0) @ mactual))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.08/1.35 thf(sP5,plain,sP5 <=> (((((set_equal @ eigen__0) @ eigen__1) @ mactual) = sP2) => (~((sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.08/1.35 thf(sP6,plain,sP6 <=> (![X1:$i]:((((set_equal @ eigen__1) @ X1) @ mactual) = (![X2:$i]:((((element @ X2) @ eigen__1) @ mactual) = (((element @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.08/1.35 thf(sP7,plain,sP7 <=> ((((set_equal @ eigen__1) @ eigen__0) @ mactual) = (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.08/1.35 thf(sP8,plain,sP8 <=> (sP2 = (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.08/1.35 thf(sP9,plain,sP9 <=> (sP7 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP9])])). % 1.08/1.35 thf(sP10,plain,sP10 <=> (![X1:$o]:(((((element @ eigen__3) @ eigen__0) @ mactual) = X1) => (X1 = (((element @ eigen__3) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.08/1.35 thf(sP11,plain,sP11 <=> (![X1:$o>$o]:((X1 @ (((set_equal @ eigen__0) @ eigen__1) @ mactual)) => (![X2:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.08/1.35 thf(sP12,plain,sP12 <=> (![X1:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X1) => (~((X1 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.08/1.35 thf(sP13,plain,sP13 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X1 = X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.08/1.35 thf(sP14,plain,sP14 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP14])])). % 1.08/1.35 thf(sP15,plain,sP15 <=> (((((element @ eigen__3) @ eigen__0) @ mactual) = (((element @ eigen__3) @ eigen__1) @ mactual)) => ((((element @ eigen__3) @ eigen__1) @ mactual) = (((element @ eigen__3) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP15])])). % 1.08/1.35 thf(sP16,plain,sP16 <=> ((~((sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))) => (![X1:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X1) => (~((sP2 = X1)))))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.08/1.35 thf(sP17,plain,sP17 <=> (((((element @ eigen__2) @ eigen__1) @ mactual) = (((element @ eigen__2) @ eigen__0) @ mactual)) => ((((element @ eigen__2) @ eigen__0) @ mactual) = (((element @ eigen__2) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP17])])). % 1.08/1.35 thf(sP18,plain,sP18 <=> ((((element @ eigen__3) @ eigen__0) @ mactual) = (((element @ eigen__3) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP18])])). % 1.08/1.35 thf(sP19,plain,sP19 <=> (![X1:$o>$o]:((X1 @ (((set_equal @ eigen__1) @ eigen__0) @ mactual)) => (![X2:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP19])])). % 1.08/1.35 thf(sP20,plain,sP20 <=> (sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP20])])). % 1.08/1.35 thf(sP21,plain,sP21 <=> (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP21])])). % 1.08/1.35 thf(sP22,plain,sP22 <=> (![X1:$i]:((((set_equal @ eigen__0) @ X1) @ mactual) = (((set_equal @ X1) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.08/1.35 thf(sP23,plain,sP23 <=> ((((element @ eigen__3) @ eigen__1) @ mactual) = (((element @ eigen__3) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP23])])). % 1.08/1.35 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (((set_equal @ X2) @ X1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP24])])). % 1.08/1.35 thf(sP25,plain,sP25 <=> (![X1:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X1) => (~((sP2 = X1))))),introduced(definition,[new_symbols(definition,[sP25])])). % 1.08/1.35 thf(sP26,plain,sP26 <=> ((((element @ eigen__2) @ eigen__0) @ mactual) = (((element @ eigen__2) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP26])])). % 1.08/1.35 thf(sP27,plain,sP27 <=> ((((element @ eigen__2) @ eigen__1) @ mactual) = (((element @ eigen__2) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP27])])). % 1.08/1.35 thf(sP28,plain,sP28 <=> (![X1:$o]:(((((element @ eigen__2) @ eigen__1) @ mactual) = X1) => (X1 = (((element @ eigen__2) @ eigen__1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP28])])). % 1.08/1.35 thf(sP29,plain,sP29 <=> ((((set_equal @ eigen__0) @ eigen__1) @ mactual) = sP2),introduced(definition,[new_symbols(definition,[sP29])])). % 1.08/1.35 thf(sP30,plain,sP30 <=> ((((set_equal @ eigen__0) @ eigen__1) @ mactual) = (((set_equal @ eigen__1) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP30])])). % 1.08/1.35 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 1.08/1.35 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 1.08/1.35 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.08/1.35 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.08/1.35 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 1.08/1.35 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 1.08/1.35 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 1.08/1.35 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 1.08/1.35 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))). % 1.08/1.35 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))). % 1.08/1.35 thf(pel43,conjecture,sP24). % 1.08/1.35 thf(h1,negated_conjecture,(~(sP24)),inference(assume_negation,[status(cth)],[pel43])). % 1.08/1.35 thf(1,plain,((~(sP15) | ~(sP18)) | sP23),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(2,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(3,plain,(~(sP14) | sP10),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(4,plain,(~(sP2) | sP18),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(5,plain,(sP21 | ~(sP23)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 1.08/1.35 thf(6,plain,((~(sP17) | ~(sP27)) | sP26),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(7,plain,(~(sP28) | sP17),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(8,plain,(~(sP14) | sP28),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(9,plain,(~(sP21) | sP27),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(10,plain,((~(sP9) | ~(sP7)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(11,plain,(~(sP25) | sP9),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(12,plain,((~(sP16) | sP20) | sP25),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(13,plain,(~(sP19) | sP16),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(14,plain,((sP8 | ~(sP2)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(15,plain,((sP8 | sP2) | sP21),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(16,plain,(sP2 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 1.08/1.35 thf(17,plain,((~(sP5) | ~(sP29)) | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(18,plain,(~(sP12) | sP5),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(19,plain,((~(sP4) | sP30) | sP12),inference(prop_rule,[status(thm)],[])). % 1.08/1.35 thf(20,plain,(~(sP11) | sP4),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(21,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(22,plain,(~(sP3) | sP29),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(23,plain,(~(sP13) | sP11),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(24,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(25,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(26,plain,(~(sP13) | sP19),inference(all_rule,[status(thm)],[])). % 1.08/1.35 thf(27,plain,sP13,inference(eq_ind,[status(thm)],[])). % 1.08/1.35 thf(28,plain,sP14,inference(eq_sym,[status(thm)],[])). % 1.08/1.35 thf(29,plain,(sP22 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.08/1.35 thf(30,plain,(sP24 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.08/1.35 thf(pel43_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((set_equal @ X1) @ X2)) @ (mforall_di @ (^[X3:$i]:((mequiv @ ((element @ X3) @ X1)) @ ((element @ X3) @ X2))))))))))). % 1.08/1.35 thf(31,plain,sP1,inference(preprocess,[status(thm)],[pel43_1]). % 1.08/1.35 thf(32,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h1])). % 1.08/1.35 thf(33,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[32,h0])). % 1.08/1.35 thf(0,theorem,sP24,inference(contra,[status(thm),contra(discharge,[h1])],[32,h1])). % 1.08/1.35 % SZS output end Proof %------------------------------------------------------------------------------