%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET027^3 : 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 : 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 02:25:07 PM UTC 2025 % Result : Theorem 0.22s 0.42s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET027^3 : TPTP v9.2.0. Released v8.1.0. % 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n008.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 14:33:38 EDT 2025 % 0.14/0.36 % CPUTime : % 0.22/0.42 % SZS status Theorem % 0.22/0.42 % Mode: mode213 % 0.22/0.42 % Inferences: 593 % 0.22/0.42 % SZS output start Proof % 0.22/0.42 thf(ty_mworld, type, mworld : $tType). % 0.22/0.42 thf(ty_subset, type, subset : ($i>$i>mworld>$o)). % 0.22/0.42 thf(ty_eigen__2, type, eigen__2 : $i). % 0.22/0.42 thf(ty_eigen__1, type, eigen__1 : $i). % 0.22/0.42 thf(ty_eigen__0, type, eigen__0 : $i). % 0.22/0.42 thf(ty_member, type, member : ($i>$i>mworld>$o)). % 0.22/0.42 thf(ty_eigen__8, type, eigen__8 : $i). % 0.22/0.42 thf(ty_mactual, type, mactual : mworld). % 0.22/0.42 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.22/0.42 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~(((((member @ X1) @ eigen__0) @ mactual) => (((member @ X1) @ eigen__2) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 0.22/0.42 thf(sP1,plain,sP1 <=> (![X1:$i]:((((subset @ eigen__0) @ X1) @ mactual) = (![X2:$i]:((((member @ X2) @ eigen__0) @ mactual) => (((member @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.22/0.42 thf(sP2,plain,sP2 <=> (((subset @ eigen__1) @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP2])])). % 0.22/0.42 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:((((subset @ X1) @ X2) @ mactual) = (![X3:$i]:((((member @ X3) @ X1) @ mactual) => (((member @ X3) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.22/0.42 thf(sP4,plain,sP4 <=> ((((subset @ eigen__0) @ eigen__2) @ mactual) = (![X1:$i]:((((member @ X1) @ eigen__0) @ mactual) => (((member @ X1) @ eigen__2) @ mactual)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.22/0.42 thf(sP5,plain,sP5 <=> (((member @ eigen__8) @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP5])])). % 0.22/0.42 thf(sP6,plain,sP6 <=> ((((member @ eigen__8) @ eigen__0) @ mactual) => (((member @ eigen__8) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.22/0.42 thf(sP7,plain,sP7 <=> (((member @ eigen__8) @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP7])])). % 0.22/0.42 thf(sP8,plain,sP8 <=> (sP7 => sP5),introduced(definition,[new_symbols(definition,[sP8])])). % 0.22/0.42 thf(sP9,plain,sP9 <=> ((((member @ eigen__8) @ eigen__1) @ mactual) => sP5),introduced(definition,[new_symbols(definition,[sP9])])). % 0.22/0.42 thf(sP10,plain,sP10 <=> (![X1:$i]:((((member @ X1) @ eigen__1) @ mactual) => (((member @ X1) @ eigen__2) @ mactual))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.22/0.42 thf(sP11,plain,sP11 <=> (((subset @ eigen__0) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP11])])). % 0.22/0.42 thf(sP12,plain,sP12 <=> (((subset @ eigen__0) @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP12])])). % 0.22/0.42 thf(sP13,plain,sP13 <=> (sP2 = sP10),introduced(definition,[new_symbols(definition,[sP13])])). % 0.22/0.42 thf(sP14,plain,sP14 <=> (((member @ eigen__8) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP14])])). % 0.22/0.42 thf(sP15,plain,sP15 <=> (![X1:$i]:((((member @ X1) @ eigen__0) @ mactual) => (((member @ X1) @ eigen__2) @ mactual))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.22/0.42 thf(sP16,plain,sP16 <=> (![X1:$i]:((((member @ X1) @ eigen__0) @ mactual) => (((member @ X1) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.22/0.42 thf(sP17,plain,sP17 <=> (sP11 = sP16),introduced(definition,[new_symbols(definition,[sP17])])). % 0.22/0.42 thf(sP18,plain,sP18 <=> (![X1:$i]:((((subset @ eigen__1) @ X1) @ mactual) = (![X2:$i]:((((member @ X2) @ eigen__1) @ mactual) => (((member @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.22/0.42 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 0.22/0.42 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 0.22/0.42 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.22/0.42 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.22/0.42 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 0.22/0.42 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 0.22/0.42 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 0.22/0.42 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 0.22/0.42 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))). % 0.22/0.42 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))). % 0.22/0.42 thf(prove_transitivity_of_subset,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((((subset @ X1) @ X2) @ mactual) => (~((((subset @ X2) @ X3) @ mactual)))))) => (((subset @ X1) @ X3) @ mactual)))))). % 0.22/0.42 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((((subset @ X1) @ X2) @ mactual) => (~((((subset @ X2) @ X3) @ mactual)))))) => (((subset @ X1) @ X3) @ mactual))))))),inference(assume_negation,[status(cth)],[prove_transitivity_of_subset])). % 0.22/0.42 thf(h2,assumption,(~((![X1:$i]:(![X2:$i]:((~(((((subset @ eigen__0) @ X1) @ mactual) => (~((((subset @ X1) @ X2) @ mactual)))))) => (((subset @ eigen__0) @ X2) @ mactual)))))),introduced(assumption,[])). % 0.22/0.42 thf(h3,assumption,(~((![X1:$i]:((~((sP11 => (~((((subset @ eigen__1) @ X1) @ mactual)))))) => (((subset @ eigen__0) @ X1) @ mactual))))),introduced(assumption,[])). % 0.22/0.42 thf(h4,assumption,(~(((~((sP11 => (~(sP2))))) => sP12))),introduced(assumption,[])). % 0.22/0.42 thf(h5,assumption,(~((sP11 => (~(sP2))))),introduced(assumption,[])). % 0.22/0.42 thf(h6,assumption,(~(sP12)),introduced(assumption,[])). % 0.22/0.42 thf(h7,assumption,sP11,introduced(assumption,[])). % 0.22/0.42 thf(h8,assumption,sP2,introduced(assumption,[])). % 0.22/0.42 thf(1,plain,(~(sP10) | sP9),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(2,plain,((~(sP9) | ~(sP14)) | sP5),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(3,plain,(~(sP16) | sP6),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(4,plain,((~(sP6) | ~(sP7)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(5,plain,(sP8 | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(6,plain,(sP8 | sP7),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(7,plain,(sP15 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 0.22/0.42 thf(8,plain,((~(sP13) | ~(sP2)) | sP10),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(9,plain,((~(sP4) | sP12) | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(10,plain,(~(sP18) | sP13),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(11,plain,(~(sP1) | sP4),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(12,plain,((~(sP17) | ~(sP11)) | sP16),inference(prop_rule,[status(thm)],[])). % 0.22/0.42 thf(13,plain,(~(sP1) | sP17),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(14,plain,(~(sP3) | sP1),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(15,plain,(~(sP3) | sP18),inference(all_rule,[status(thm)],[])). % 0.22/0.42 thf(subset_defn,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((subset @ X1) @ X2)) @ (mforall_di @ (^[X3:$i]:((mimplies @ ((member @ X3) @ X1)) @ ((member @ X3) @ X2))))))))))). % 0.22/0.42 thf(16,plain,sP3,inference(preprocess,[status(thm)],[subset_defn]). % 0.22/0.42 thf(17,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h7,h8,h6])). % 0.22/0.42 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,17,h7,h8])). % 0.22/0.42 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,18,h5,h6])). % 0.22/0.42 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,19,h4])). % 0.22/0.42 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,20,h3])). % 0.22/0.42 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,21,h2])). % 0.22/0.42 thf(23,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0])). % 0.22/0.42 thf(0,theorem,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((((subset @ X1) @ X2) @ mactual) => (~((((subset @ X2) @ X3) @ mactual)))))) => (((subset @ X1) @ X3) @ mactual))))),inference(contra,[status(thm),contra(discharge,[h1])],[22,h1])). % 0.22/0.42 % SZS output end Proof %------------------------------------------------------------------------------