%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PLA053^18 : 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 : n014.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 02:14:10 PM UTC 2025 % Result : Theorem 1.09s 1.42s % Output : Proof 1.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PLA053^18 : TPTP v9.2.0. Released v8.1.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n014.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 12:20:08 EDT 2025 % 0.13/0.34 % CPUTime : % 1.09/1.42 % SZS status Theorem % 1.09/1.42 % Mode: mode506 % 1.09/1.42 % Inferences: 40114 % 1.09/1.42 % SZS output start Proof % 1.09/1.42 thf(ty_mworld, type, mworld : $tType). % 1.09/1.42 thf(ty_h, type, h : ($i>mworld>$o)). % 1.09/1.42 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)). % 1.09/1.42 thf(ty_eigen__1, type, eigen__1 : $i). % 1.09/1.42 thf(ty_eigen__0, type, eigen__0 : mworld). % 1.09/1.42 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 1.09/1.42 thf(ty_eigen__8, type, eigen__8 : $i). % 1.09/1.42 thf(ty_mactual, type, mactual : mworld). % 1.09/1.42 thf(ty_bomb, type, bomb : ($i>mworld>$o)). % 1.09/1.42 thf(ty_defused, type, defused : ($i>mworld>$o)). % 1.09/1.42 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.09/1.42 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ eigen__0) => (~((![X2:$i]:(((eiw_di @ X2) @ eigen__0) => (~(((~((((bomb @ X1) @ eigen__0) => (~(((h @ X2) @ eigen__0)))))) => ((defused @ X1) @ eigen__0))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.09/1.42 thf(h1, assumption, (![X1:mworld>$o]:(![X2:mworld]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 1.09/1.42 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:mworld]:(~((((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (~((![X3:$i]:(((eiw_di @ X3) @ X1) => (~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.09/1.42 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ eigen__0) => (~((![X2:mworld]:(((mrel @ eigen__0) @ X2) => ((~((((bomb @ eigen__1) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__1) @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 1.09/1.42 thf(sP1,plain,sP1 <=> (![X1:mworld]:((!!) @ (mrel @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.09/1.42 thf(sP2,plain,sP2 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (~((![X3:$i]:(((eiw_di @ X3) @ X1) => (~((![X4:mworld]:(((mrel @ X1) @ X4) => ((~((((bomb @ X2) @ X4) => (~(((h @ X3) @ X4)))))) => ((defused @ X2) @ X4)))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.09/1.42 thf(sP3,plain,sP3 <=> ((~((((bomb @ eigen__1) @ eigen__0) => (~(((h @ eigen__8) @ eigen__0)))))) => ((defused @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP3])])). % 1.09/1.42 thf(sP4,plain,sP4 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~((![X2:$i]:(((eiw_di @ X2) @ eigen__0) => (~(((~((((bomb @ X1) @ eigen__0) => (~(((h @ X2) @ eigen__0)))))) => ((defused @ X1) @ eigen__0)))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.09/1.42 thf(sP5,plain,sP5 <=> ((!!) @ (mrel @ mactual)),introduced(definition,[new_symbols(definition,[sP5])])). % 1.09/1.42 thf(sP6,plain,sP6 <=> ((eiw_di @ eigen__8) @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 1.09/1.42 thf(sP7,plain,sP7 <=> (sP6 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.09/1.42 thf(sP8,plain,sP8 <=> (((mrel @ eigen__0) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP8])])). % 1.09/1.42 thf(sP9,plain,sP9 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((~((((bomb @ eigen__1) @ X1) => (~(((h @ eigen__8) @ X1)))))) => ((defused @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP9])])). % 1.09/1.42 thf(sP10,plain,sP10 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~(((~((((bomb @ eigen__1) @ eigen__0) => (~(((h @ X1) @ eigen__0)))))) => ((defused @ eigen__1) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.09/1.42 thf(sP11,plain,sP11 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP11])])). % 1.09/1.42 thf(sP12,plain,sP12 <=> (((eiw_di @ eigen__1) @ eigen__0) => (~(sP10))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.09/1.42 thf(sP13,plain,sP13 <=> ((mrel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP13])])). % 1.09/1.42 thf(sP14,plain,sP14 <=> (sP11 => (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~((![X2:$i]:(((eiw_di @ X2) @ eigen__0) => (~((![X3:mworld]:(((mrel @ eigen__0) @ X3) => ((~((((bomb @ X1) @ X3) => (~(((h @ X2) @ X3)))))) => ((defused @ X1) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 1.09/1.42 thf(sP15,plain,sP15 <=> (((eiw_di @ eigen__1) @ eigen__0) => (~((![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~((![X2:mworld]:(((mrel @ eigen__0) @ X2) => ((~((((bomb @ eigen__1) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 1.09/1.42 thf(sP16,plain,sP16 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (~((![X3:$i]:(((eiw_di @ X3) @ X1) => (~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1)))))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.09/1.42 thf(sP17,plain,sP17 <=> (sP6 => (~(sP9))),introduced(definition,[new_symbols(definition,[sP17])])). % 1.09/1.42 thf(sP18,plain,sP18 <=> (sP11 => sP4),introduced(definition,[new_symbols(definition,[sP18])])). % 1.09/1.42 thf(sP19,plain,sP19 <=> ((eiw_di @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])). % 1.09/1.42 thf(sP20,plain,sP20 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~((![X2:$i]:(((eiw_di @ X2) @ eigen__0) => (~((![X3:mworld]:(((mrel @ eigen__0) @ X3) => ((~((((bomb @ X1) @ X3) => (~(((h @ X2) @ X3)))))) => ((defused @ X1) @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 1.09/1.42 thf(sP21,plain,sP21 <=> ((!!) @ (mrel @ eigen__0)),introduced(definition,[new_symbols(definition,[sP21])])). % 1.09/1.42 thf(sP22,plain,sP22 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (~((![X2:mworld]:(((mrel @ eigen__0) @ X2) => ((~((((bomb @ eigen__1) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.09/1.42 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 1.09/1.42 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 1.09/1.42 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.09/1.42 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.09/1.42 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 1.09/1.42 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 1.09/1.42 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 1.09/1.42 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 1.09/1.42 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 1.09/1.42 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))). % 1.09/1.42 thf(con,conjecture,sP16). % 1.09/1.42 thf(h2,negated_conjecture,(~(sP16)),inference(assume_negation,[status(cth)],[con])). % 1.09/1.42 thf(1,plain,((~(sP7) | ~(sP6)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(2,plain,(~(sP5) | sP11),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(3,plain,(~(sP10) | sP7),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(4,plain,(~(sP9) | sP8),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(5,plain,((~(sP8) | ~(sP13)) | sP3),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(6,plain,(sP17 | sP9),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(7,plain,(sP17 | sP6),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(8,plain,(sP22 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 1.09/1.42 thf(9,plain,(~(sP20) | sP15),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(10,plain,((~(sP15) | ~(sP19)) | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(11,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(12,plain,((~(sP14) | ~(sP11)) | sP20),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(13,plain,(~(sP21) | sP13),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(14,plain,(~(sP1) | sP21),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(15,plain,(~(sP2) | sP14),inference(all_rule,[status(thm)],[])). % 1.09/1.42 thf(16,plain,(sP12 | sP10),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(17,plain,(sP12 | sP19),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(18,plain,(sP4 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.09/1.42 thf(19,plain,(sP18 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 1.09/1.42 thf(20,plain,(sP16 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 1.09/1.42 thf(ax3,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mexists_di @ (^[X2:$i]:(mbox @ ((mimplies @ ((mand @ (bomb @ X1)) @ (h @ X2))) @ (defused @ X1)))))))))). % 1.09/1.42 thf(21,plain,sP2,inference(preprocess,[status(thm)],[ax3]). % 1.09/1.42 thf(mrel_universal,axiom,sP1). % 1.09/1.42 thf(22,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,mrel_universal,h2])). % 1.09/1.42 thf(23,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[22,h1])). % 1.09/1.42 thf(24,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[23,h0])). % 1.09/1.42 thf(0,theorem,sP16,inference(contra,[status(thm),contra(discharge,[h2])],[22,h2])). % 1.09/1.42 % SZS output end Proof %------------------------------------------------------------------------------