%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PHI043^1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n001.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 02:13:41 PM UTC 2025 % Result : Theorem 18.21s 18.76s % Output : Proof 18.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : PHI043^1 : TPTP v9.2.0. Released v7.5.0. % 0.05/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.10/0.32 % Computer : n001.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Wed Oct 8 23:17:38 EDT 2025 % 0.10/0.32 % CPUTime : % 18.21/18.76 % SZS status Theorem % 18.21/18.76 % Mode: mode485 % 18.21/18.76 % Inferences: 2679 % 18.21/18.76 % SZS output start Proof % 18.21/18.76 thf(ty_mu, type, mu : $tType). % 18.21/18.76 thf(ty_p, type, p : ((mu>$i>$o)>$i>$o)). % 18.21/18.76 thf(ty_eigen__1, type, eigen__1 : (mu>$i>$o)). % 18.21/18.76 thf(ty_eigen__0, type, eigen__0 : $i). % 18.21/18.76 thf(ty_eigen__26, type, eigen__26 : mu). % 18.21/18.76 thf(ty_eigen__19, type, eigen__19 : $i). % 18.21/18.76 thf(ty_rel, type, rel : ($i>$i>$o)). % 18.21/18.76 thf(h0, assumption, (![X1:(mu>$i>$o)>$o]:(![X2:mu>$i>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 18.21/18.76 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:mu>$i>$o]:(~((((p @ X1) @ eigen__0) => (~((![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:(~(((X1 @ X3) @ X2))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 18.21/18.76 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 18.21/18.76 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:mu>$i>$o]:(((p @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (![X4:mu]:(~(((X2 @ X4) @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 18.21/18.76 thf(h2, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])). % 18.21/18.76 thf(eigendef_eigen__26, definition, eigen__26 = (eps__2 @ (^[X1:mu]:(~((((eigen__1 @ X1) @ eigen__19) = (~((X1 = X1)))))))), introduced(definition,[new_symbols(definition,[eigen__26])])). % 18.21/18.76 thf(eigendef_eigen__19, definition, eigen__19 = (eps__1 @ (^[X1:$i]:(~((((rel @ eigen__0) @ X1) => (![X2:mu]:(((eigen__1 @ X2) @ X1) = (~((X2 = X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__19])])). % 18.21/18.76 thf(sP1,plain,sP1 <=> (![X1:$i]:(~(((p @ (^[X2:mu]:(^[X3:$i]:(~((X2 = X2)))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])). % 18.21/18.76 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(~(((eigen__1 @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 18.21/18.76 thf(sP3,plain,sP3 <=> (![X1:mu]:(~(((eigen__1 @ X1) @ eigen__19)))),introduced(definition,[new_symbols(definition,[sP3])])). % 18.21/18.76 thf(sP4,plain,sP4 <=> (((rel @ eigen__0) @ eigen__19) => (![X1:mu]:(((eigen__1 @ X1) @ eigen__19) = (~((X1 = X1)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 18.21/18.76 thf(sP5,plain,sP5 <=> (![X1:$o]:((X1 = ((p @ (^[X2:mu]:(^[X3:$i]:(~((X2 = X2)))))) @ eigen__0)) => (~(X1)))),introduced(definition,[new_symbols(definition,[sP5])])). % 18.21/18.76 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(((eigen__1 @ X2) @ X1) = (~((X2 = X2))))))) => (((p @ eigen__1) @ eigen__0) = ((p @ (^[X1:mu]:(^[X2:$i]:(~((X1 = X1)))))) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP6])])). % 18.21/18.76 thf(sP7,plain,sP7 <=> ((rel @ eigen__0) @ eigen__19),introduced(definition,[new_symbols(definition,[sP7])])). % 18.21/18.76 thf(sP8,plain,sP8 <=> ((~(((p @ (^[X1:mu]:(^[X2:$i]:(~((X1 = X1)))))) @ eigen__0))) => sP5),introduced(definition,[new_symbols(definition,[sP8])])). % 18.21/18.76 thf(sP9,plain,sP9 <=> (![X1:mu]:(((eigen__1 @ X1) @ eigen__19) = (~((X1 = X1))))),introduced(definition,[new_symbols(definition,[sP9])])). % 18.21/18.76 thf(sP10,plain,sP10 <=> (((p @ eigen__1) @ eigen__0) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP10])])). % 18.21/18.76 thf(sP11,plain,sP11 <=> ((((p @ eigen__1) @ eigen__0) = ((p @ (^[X1:mu]:(^[X2:$i]:(~((X1 = X1)))))) @ eigen__0)) => (~(((p @ eigen__1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP11])])). % 18.21/18.76 thf(sP12,plain,sP12 <=> ((p @ (^[X1:mu]:(^[X2:$i]:(~((X1 = X1)))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP12])])). % 18.21/18.76 thf(sP13,plain,sP13 <=> (![X1:mu>$i>$o]:(![X2:mu>$i>$o]:((![X3:$i]:(((rel @ eigen__0) @ X3) => (![X4:mu]:(((X1 @ X4) @ X3) = ((X2 @ X4) @ X3))))) => (((p @ X1) @ eigen__0) = ((p @ X2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP13])])). % 18.21/18.76 thf(sP14,plain,sP14 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X3 = X1) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP14])])). % 18.21/18.76 thf(sP15,plain,sP15 <=> ((p @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP15])])). % 18.21/18.76 thf(sP16,plain,sP16 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(((eigen__1 @ X2) @ X1) = (~((X2 = X2))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 18.21/18.76 thf(sP17,plain,sP17 <=> (sP7 => sP3),introduced(definition,[new_symbols(definition,[sP17])])). % 18.21/18.76 thf(sP18,plain,sP18 <=> (((eigen__1 @ eigen__26) @ eigen__19) = (~((eigen__26 = eigen__26)))),introduced(definition,[new_symbols(definition,[sP18])])). % 18.21/18.76 thf(sP19,plain,sP19 <=> (eigen__26 = eigen__26),introduced(definition,[new_symbols(definition,[sP19])])). % 18.21/18.76 thf(sP20,plain,sP20 <=> (![X1:$o>$o]:((X1 @ sP12) => (![X2:$o]:((X2 = sP12) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP20])])). % 18.21/18.76 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:mu>$i>$o]:(![X3:mu>$i>$o]:((![X4:$i]:(((rel @ X1) @ X4) => (![X5:mu]:(((X2 @ X5) @ X4) = ((X3 @ X5) @ X4))))) => (((p @ X2) @ X1) = ((p @ X3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP21])])). % 18.21/18.76 thf(sP22,plain,sP22 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((p @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (![X4:mu]:(~(((X2 @ X4) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 18.21/18.76 thf(sP23,plain,sP23 <=> (![X1:mu>$i>$o]:((![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:(((eigen__1 @ X3) @ X2) = ((X1 @ X3) @ X2))))) => (sP15 = ((p @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP23])])). % 18.21/18.76 thf(sP24,plain,sP24 <=> ((eigen__1 @ eigen__26) @ eigen__19),introduced(definition,[new_symbols(definition,[sP24])])). % 18.21/18.76 thf(sP25,plain,sP25 <=> (sP15 = sP12),introduced(definition,[new_symbols(definition,[sP25])])). % 18.21/18.76 thf(sP26,plain,sP26 <=> (![X1:mu>$i>$o]:(((p @ X1) @ eigen__0) => (~((![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:(~(((X1 @ X3) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 18.21/18.76 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 18.21/18.76 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 18.21/18.76 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 18.21/18.76 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 18.21/18.76 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 18.21/18.76 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 18.21/18.76 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))). % 18.21/18.76 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))). % 18.21/18.76 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 18.21/18.76 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))). % 18.21/18.76 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 18.21/18.76 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))). % 18.21/18.76 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 18.21/18.76 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))). % 18.21/18.76 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 18.21/18.76 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 18.21/18.76 thf(def_mbox_generic,definition,(mbox_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 18.21/18.76 thf(def_mdia_generic,definition,(mdia_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 18.21/18.76 thf(def_mbox,definition,(mbox = (mbox_generic @ rel))). % 18.21/18.76 thf(def_mdia,definition,(mdia = (mdia_generic @ rel))). % 18.21/18.76 thf(def_mvalid,definition,(mvalid = (!!))). % 18.21/18.76 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 18.21/18.76 thf(possible_instantiation_of_the_positive,conjecture,(![X1:$i]:(![X2:mu>$i>$o]:(((p @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (~((~((![X4:mu]:(~(((X2 @ X4) @ X3)))))))))))))))). % 18.21/18.76 thf(h3,negated_conjecture,(~(sP22)),inference(assume_negation,[status(cth)],[possible_instantiation_of_the_positive])). % 18.21/18.76 thf(1,plain,sP19,inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(2,plain,(~(sP3) | ~(sP24)),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(3,plain,((sP18 | sP24) | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(4,plain,(sP9 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__26])). % 18.21/18.76 thf(5,plain,(~(sP2) | sP17),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(6,plain,((~(sP17) | ~(sP7)) | sP3),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(7,plain,(sP4 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(8,plain,(sP4 | sP7),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(9,plain,(sP16 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19])). % 18.21/18.76 thf(10,plain,(~(sP23) | sP6),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(11,plain,((~(sP6) | ~(sP16)) | sP25),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(12,plain,((~(sP11) | ~(sP25)) | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(13,plain,(~(sP5) | sP11),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(14,plain,((~(sP8) | sP12) | sP5),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(15,plain,(~(sP20) | sP8),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(16,plain,(~(sP14) | sP20),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(17,plain,sP14,inference(eq_ind_sym,[status(thm)],[])). % 18.21/18.76 thf(18,plain,(~(sP13) | sP23),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(19,plain,(~(sP21) | sP13),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(20,plain,(~(sP1) | ~(sP12)),inference(all_rule,[status(thm)],[])). % 18.21/18.76 thf(21,plain,(sP10 | sP2),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(22,plain,(sP10 | sP15),inference(prop_rule,[status(thm)],[])). % 18.21/18.76 thf(23,plain,(sP26 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 18.21/18.76 thf(24,plain,(sP22 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 18.21/18.76 thf(ax17,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (mbox @ (mforall_ind @ (^[X3:mu]:((mequiv @ (X1 @ X3)) @ (X2 @ X3)))))) @ ((mequiv @ (p @ X1)) @ (p @ X2))))))))). % 18.21/18.76 thf(25,plain,sP21,inference(preprocess,[status(thm)],[ax17]). % 18.21/18.76 thf(ax16,axiom,(mvalid @ (mnot @ (p @ (^[X1:mu]:(^[X2:$i]:(~((X1 = X1))))))))). % 18.21/18.76 thf(26,plain,sP1,inference(preprocess,[status(thm)],[ax16]). % 18.21/18.76 thf(27,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,h3])). % 18.21/18.76 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[27,h2])). % 18.21/18.76 thf(29,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[28,h1])). % 18.21/18.76 thf(30,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[29,h0])). % 18.21/18.76 thf(0,theorem,(![X1:$i]:(![X2:mu>$i>$o]:(((p @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (~((~((![X4:mu]:(~(((X2 @ X4) @ X3))))))))))))))),inference(contra,[status(thm),contra(discharge,[h3])],[27,h3])). % 18.21/18.76 % SZS output end Proof %------------------------------------------------------------------------------