%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV428^2 : TPTP v9.2.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n027.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 03:07:20 PM UTC 2025 % Result : Theorem 13.14s 13.31s % Output : Proof 13.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV428^2 : TPTP v9.2.0. Released v3.6.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n027.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Oct 8 14:26:38 EDT 2025 % 0.14/0.34 % CPUTime : % 13.14/13.31 % SZS status Theorem % 13.14/13.31 % Mode: mode454 % 13.14/13.31 % Inferences: 57 % 13.14/13.31 % SZS output start Proof % 13.14/13.31 thf(ty_eigen__2, type, eigen__2 : $i). % 13.14/13.31 thf(ty_eigen__1, type, eigen__1 : $i). % 13.14/13.31 thf(ty_eigen__0, type, eigen__0 : $i). % 13.14/13.31 thf(ty_admin, type, admin : ($i>$o)). % 13.14/13.31 thf(ty_deletefile1, type, deletefile1 : ($i>$o)). % 13.14/13.31 thf(ty_bob, type, bob : ($i>$o)). % 13.14/13.31 thf(ty_rel, type, rel : ($i>$i>$o)). % 13.14/13.31 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.14/13.31 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__0) @ X1) => (deletefile1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.14/13.31 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.14/13.31 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__1) @ X1) => ((~((admin @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 13.14/13.31 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((bob @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 13.14/13.31 thf(sP2,plain,sP2 <=> (admin @ eigen__2),introduced(definition,[new_symbols(definition,[sP2])])). % 13.14/13.31 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (deletefile1 @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.14/13.31 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((admin @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((bob @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (deletefile1 @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.14/13.31 thf(sP5,plain,sP5 <=> (deletefile1 @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])). % 13.14/13.31 thf(sP6,plain,sP6 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((bob @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.14/13.31 thf(sP7,plain,sP7 <=> ((rel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP7])])). % 13.14/13.31 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => (deletefile1 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.14/13.31 thf(sP9,plain,sP9 <=> (![X1:$i]:((![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((bob @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (deletefile1 @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3)))))) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((bob @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.14/13.31 thf(sP10,plain,sP10 <=> ((~(sP2)) => sP6),introduced(definition,[new_symbols(definition,[sP10])])). % 13.14/13.31 thf(sP11,plain,sP11 <=> (sP6 => ((![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((bob @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))) => sP8)),introduced(definition,[new_symbols(definition,[sP11])])). % 13.14/13.31 thf(sP12,plain,sP12 <=> ((~(sP2)) => sP8),introduced(definition,[new_symbols(definition,[sP12])])). % 13.14/13.31 thf(sP13,plain,sP13 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((rel @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP13])])). % 13.14/13.31 thf(sP14,plain,sP14 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((bob @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP14])])). % 13.14/13.31 thf(sP15,plain,sP15 <=> (sP7 => sP12),introduced(definition,[new_symbols(definition,[sP15])])). % 13.14/13.31 thf(sP16,plain,sP16 <=> ((![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((admin @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))) => (![X1:$i]:(((rel @ eigen__1) @ X1) => (deletefile1 @ X1)))),introduced(definition,[new_symbols(definition,[sP16])])). % 13.14/13.31 thf(sP17,plain,sP17 <=> ((rel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP17])])). % 13.14/13.31 thf(sP18,plain,sP18 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => (deletefile1 @ X1))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.14/13.31 thf(sP19,plain,sP19 <=> (![X1:$i]:((![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2))) => (deletefile1 @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 13.14/13.31 thf(sP20,plain,sP20 <=> (sP14 => sP8),introduced(definition,[new_symbols(definition,[sP20])])). % 13.14/13.31 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((admin @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => ((~((bob @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (deletefile1 @ X5)))))) => (![X4:$i]:(((rel @ X3) @ X4) => (deletefile1 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 13.14/13.31 thf(sP22,plain,sP22 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))),introduced(definition,[new_symbols(definition,[sP22])])). % 13.14/13.31 thf(sP23,plain,sP23 <=> (sP7 => sP10),introduced(definition,[new_symbols(definition,[sP23])])). % 13.14/13.31 thf(sP24,plain,sP24 <=> (sP17 => sP5),introduced(definition,[new_symbols(definition,[sP24])])). % 13.14/13.31 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((admin @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 13.14/13.31 thf(sP26,plain,sP26 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((admin @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => (deletefile1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP26])])). % 13.14/13.31 thf(sP27,plain,sP27 <=> (sP17 => sP16),introduced(definition,[new_symbols(definition,[sP27])])). % 13.14/13.31 thf(sP28,plain,sP28 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((admin @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (deletefile1 @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => (deletefile1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 13.14/13.31 thf(sP29,plain,sP29 <=> (sP18 => sP5),introduced(definition,[new_symbols(definition,[sP29])])). % 13.14/13.31 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 13.14/13.31 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.14/13.31 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.14/13.31 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.14/13.31 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 13.14/13.31 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.14/13.31 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 13.14/13.31 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.14/13.31 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 13.14/13.31 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 13.14/13.31 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 13.14/13.31 thf(def_mvalid,definition,(mvalid = (!!))). % 13.14/13.31 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.14/13.31 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.14/13.31 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.14/13.31 thf(def_icl_atom,definition,(icl_atom = (mbox @ rel))). % 13.14/13.31 thf(def_icl_princ,definition,(icl_princ = (^[X1:$i>$o]:X1))). % 13.14/13.31 thf(def_icl_and,definition,(icl_and = mand)). % 13.14/13.31 thf(def_icl_or,definition,(icl_or = mor)). % 13.14/13.31 thf(def_icl_impl,definition,(icl_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mimpl @ X1) @ X2)))))). % 13.14/13.31 thf(def_icl_true,definition,(icl_true = mtrue)). % 13.14/13.31 thf(def_icl_false,definition,(icl_false = mfalse)). % 13.14/13.31 thf(def_icl_says,definition,(icl_says = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mor @ X1) @ X2)))))). % 13.14/13.31 thf(def_iclval,definition,(iclval = mvalid)). % 13.14/13.31 thf(ex1,conjecture,sP22). % 13.14/13.31 thf(h1,negated_conjecture,(~(sP22)),inference(assume_negation,[status(cth)],[ex1])). % 13.14/13.31 thf(1,plain,(~(sP9) | sP11),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(2,plain,((~(sP11) | ~(sP6)) | sP20),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(3,plain,((~(sP20) | ~(sP14)) | sP8),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(4,plain,(~(sP13) | sP9),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(5,plain,(~(sP1) | sP14),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(6,plain,(sP12 | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(7,plain,(sP12 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(8,plain,(~(sP21) | sP4),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(9,plain,(~(sP4) | sP23),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(10,plain,((~(sP23) | ~(sP7)) | sP10),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(11,plain,((~(sP10) | sP2) | sP6),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(12,plain,(sP15 | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(13,plain,(sP15 | sP7),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(14,plain,(sP25 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 13.14/13.31 thf(15,plain,(~(sP13) | sP19),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(16,plain,(~(sP19) | sP29),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(17,plain,((~(sP29) | ~(sP18)) | sP5),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(18,plain,(~(sP28) | sP26),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(19,plain,(~(sP26) | sP27),inference(all_rule,[status(thm)],[])). % 13.14/13.31 thf(20,plain,((~(sP27) | ~(sP17)) | sP16),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(21,plain,((~(sP16) | ~(sP25)) | sP18),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(22,plain,(sP24 | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(23,plain,(sP24 | sP17),inference(prop_rule,[status(thm)],[])). % 13.14/13.31 thf(24,plain,(sP3 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.14/13.31 thf(25,plain,(sP22 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.14/13.31 thf(refl_axiom,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ rel) @ X1)) @ X1)))). % 13.14/13.31 thf(26,plain,sP13,inference(preprocess,[status(thm)],[refl_axiom]). % 13.14/13.31 thf(ax1,axiom,(iclval @ ((icl_impl @ ((icl_says @ (icl_princ @ admin)) @ (icl_atom @ deletefile1))) @ (icl_atom @ deletefile1)))). % 13.14/13.31 thf(27,plain,sP28,inference(preprocess,[status(thm)],[ax1]). % 13.14/13.31 thf(ax2,axiom,(iclval @ ((icl_says @ (icl_princ @ admin)) @ ((icl_impl @ ((icl_says @ (icl_princ @ bob)) @ (icl_atom @ deletefile1))) @ (icl_atom @ deletefile1))))). % 13.14/13.31 thf(28,plain,sP21,inference(preprocess,[status(thm)],[ax2]). % 13.14/13.31 thf(ax3,axiom,(iclval @ ((icl_says @ (icl_princ @ bob)) @ (icl_atom @ deletefile1)))). % 13.14/13.31 thf(29,plain,sP1,inference(preprocess,[status(thm)],[ax3]). % 13.14/13.31 thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,h1])). % 13.14/13.31 thf(31,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[30,h0])). % 13.14/13.31 thf(0,theorem,sP22,inference(contra,[status(thm),contra(discharge,[h1])],[30,h1])). % 13.14/13.31 % SZS output end Proof %------------------------------------------------------------------------------