%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO067^4.001 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n028.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 03:24:49 PM UTC 2025 % Result : Theorem 18.50s 18.64s % Output : Proof 18.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SYO067^4.001 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n028.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 : Thu Oct 9 01:04:25 EDT 2025 % 0.14/0.36 % CPUTime : % 18.50/18.64 % SZS status Theorem % 18.50/18.64 % Mode: mode466 % 18.50/18.64 % Inferences: 67257 % 18.50/18.64 % SZS output start Proof % 18.50/18.64 thf(ty_eigen__2, type, eigen__2 : $i). % 18.50/18.64 thf(ty_eigen__0, type, eigen__0 : $i). % 18.50/18.64 thf(ty_eigen__3, type, eigen__3 : $i). % 18.50/18.64 thf(ty_irel, type, irel : ($i>$i>$o)). % 18.50/18.64 thf(ty_eigen__10, type, eigen__10 : $i). % 18.50/18.64 thf(ty_eigen__8, type, eigen__8 : $i). % 18.50/18.64 thf(ty_f, type, f : ($i>$o)). % 18.50/18.64 thf(ty_p1, type, p1 : ($i>$o)). % 18.50/18.64 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 18.50/18.64 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__2) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (f @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 18.50/18.64 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((f @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 18.50/18.64 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__8) @ X1) => (p1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 18.50/18.64 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (f @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 18.50/18.64 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (f @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 18.50/18.64 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 18.50/18.64 thf(sP2,plain,sP2 <=> (((irel @ eigen__0) @ eigen__0) => (f @ eigen__0)),introduced(definition,[new_symbols(definition,[sP2])])). % 18.50/18.64 thf(sP3,plain,sP3 <=> (f @ eigen__0),introduced(definition,[new_symbols(definition,[sP3])])). % 18.50/18.64 thf(sP4,plain,sP4 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (f @ X3))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 18.50/18.64 thf(sP5,plain,sP5 <=> (((irel @ eigen__2) @ eigen__3) => ((![X1:$i]:(((irel @ eigen__3) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => (f @ X1))))),introduced(definition,[new_symbols(definition,[sP5])])). % 18.50/18.64 thf(sP6,plain,sP6 <=> ((~((![X1:$i]:(((irel @ eigen__8) @ X1) => (p1 @ X1))))) => (![X1:$i]:(((irel @ eigen__8) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (f @ X2))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 18.50/18.64 thf(sP7,plain,sP7 <=> (((irel @ eigen__3) @ eigen__8) => sP6),introduced(definition,[new_symbols(definition,[sP7])])). % 18.50/18.64 thf(sP8,plain,sP8 <=> (((irel @ eigen__0) @ eigen__2) => ((~((![X1:$i]:(((irel @ eigen__2) @ X1) => (p1 @ X1))))) => (![X1:$i]:(((irel @ eigen__2) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (f @ X2)))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 18.50/18.64 thf(sP9,plain,sP9 <=> ((![X1:$i]:(((irel @ eigen__3) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => (f @ X1)))),introduced(definition,[new_symbols(definition,[sP9])])). % 18.50/18.64 thf(sP10,plain,sP10 <=> ((irel @ eigen__8) @ eigen__10),introduced(definition,[new_symbols(definition,[sP10])])). % 18.50/18.64 thf(sP11,plain,sP11 <=> (p1 @ eigen__10),introduced(definition,[new_symbols(definition,[sP11])])). % 18.50/18.64 thf(sP12,plain,sP12 <=> (sP10 => sP11),introduced(definition,[new_symbols(definition,[sP12])])). % 18.50/18.64 thf(sP13,plain,sP13 <=> (![X1:$i]:((~((((irel @ eigen__3) @ eigen__8) => (~(((irel @ eigen__8) @ X1)))))) => ((irel @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])). % 18.50/18.64 thf(sP14,plain,sP14 <=> ((irel @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP14])])). % 18.50/18.64 thf(sP15,plain,sP15 <=> ((~((sP14 => (~(sP10))))) => ((irel @ eigen__3) @ eigen__10)),introduced(definition,[new_symbols(definition,[sP15])])). % 18.50/18.64 thf(sP16,plain,sP16 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (f @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 18.50/18.64 thf(sP17,plain,sP17 <=> (sP14 => (~(sP10))),introduced(definition,[new_symbols(definition,[sP17])])). % 18.50/18.64 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__3) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP18])])). % 18.50/18.64 thf(sP19,plain,sP19 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])). % 18.50/18.64 thf(sP20,plain,sP20 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((irel @ X1) @ X2) => (~(((irel @ X2) @ X3)))))) => ((irel @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP20])])). % 18.50/18.64 thf(sP21,plain,sP21 <=> ((irel @ eigen__3) @ eigen__10),introduced(definition,[new_symbols(definition,[sP21])])). % 18.50/18.64 thf(sP22,plain,sP22 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (f @ X3))))))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (f @ X1)))),introduced(definition,[new_symbols(definition,[sP22])])). % 18.50/18.64 thf(sP23,plain,sP23 <=> ((!!) @ f),introduced(definition,[new_symbols(definition,[sP23])])). % 18.50/18.64 thf(sP24,plain,sP24 <=> (sP21 => sP11),introduced(definition,[new_symbols(definition,[sP24])])). % 18.50/18.64 thf(sP25,plain,sP25 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (f @ X1))),introduced(definition,[new_symbols(definition,[sP25])])). % 18.50/18.64 thf(sP26,plain,sP26 <=> (sP4 => sP16),introduced(definition,[new_symbols(definition,[sP26])])). % 18.50/18.64 thf(sP27,plain,sP27 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (f @ X3))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 18.50/18.64 thf(sP28,plain,sP28 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP28])])). % 18.50/18.64 thf(sP29,plain,sP29 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((![X4:$i]:(((irel @ X3) @ X4) => (p1 @ X4))) => (![X4:$i]:(((irel @ X3) @ X4) => (f @ X4))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (f @ X2))))),introduced(definition,[new_symbols(definition,[sP29])])). % 18.50/18.64 thf(sP30,plain,sP30 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (f @ X2)))))),introduced(definition,[new_symbols(definition,[sP30])])). % 18.50/18.64 thf(sP31,plain,sP31 <=> ((~((![X1:$i]:(((irel @ eigen__2) @ X1) => (p1 @ X1))))) => sP30),introduced(definition,[new_symbols(definition,[sP31])])). % 18.50/18.64 thf(sP32,plain,sP32 <=> (![X1:$i]:(((irel @ eigen__8) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP32])])). % 18.50/18.64 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 18.50/18.64 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 18.50/18.64 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 18.50/18.64 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 18.50/18.64 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 18.50/18.64 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 18.50/18.64 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 18.50/18.64 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 18.50/18.64 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 18.50/18.64 thf(def_iand,definition,(iand = mand)). % 18.50/18.64 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 18.50/18.64 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 18.50/18.64 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 18.50/18.64 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 18.50/18.64 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 18.50/18.64 thf(def_ivalid,definition,(ivalid = (!!))). % 18.50/18.64 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 18.50/18.64 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 18.50/18.64 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 18.50/18.64 thf(con,conjecture,sP23). % 18.50/18.64 thf(h1,negated_conjecture,(~(sP23)),inference(assume_negation,[status(cth)],[con])). % 18.50/18.64 thf(1,plain,((~(sP17) | ~(sP14)) | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(2,plain,((~(sP15) | sP17) | sP21),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(3,plain,((~(sP24) | ~(sP21)) | sP11),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(4,plain,(~(sP13) | sP15),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(5,plain,(~(sP28) | sP24),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(6,plain,(sP12 | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(7,plain,(sP12 | sP10),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(8,plain,(~(sP18) | sP13),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(9,plain,(sP32 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])). % 18.50/18.64 thf(10,plain,(sP6 | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(11,plain,(sP7 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(12,plain,(sP7 | sP14),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(13,plain,(sP4 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 18.50/18.64 thf(14,plain,((~(sP26) | ~(sP4)) | sP16),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(15,plain,(~(sP29) | sP26),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(16,plain,(~(sP20) | sP18),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(17,plain,(sP9 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(18,plain,(sP9 | sP28),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(19,plain,(sP5 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(20,plain,(sP30 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 18.50/18.64 thf(21,plain,(sP31 | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(22,plain,(sP8 | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(23,plain,(sP27 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 18.50/18.64 thf(24,plain,((~(sP2) | ~(sP19)) | sP3),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(25,plain,(~(sP25) | sP2),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(26,plain,((~(sP22) | ~(sP27)) | sP25),inference(prop_rule,[status(thm)],[])). % 18.50/18.64 thf(27,plain,(~(sP29) | sP22),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(28,plain,(~(sP1) | sP19),inference(all_rule,[status(thm)],[])). % 18.50/18.64 thf(29,plain,(sP23 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 18.50/18.64 thf(axiom1,axiom,(ivalid @ ((iimplies @ ((ior @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ f)))) @ (iatom @ f)))). % 18.50/18.64 thf(30,plain,sP29,inference(preprocess,[status(thm)],[axiom1]). % 18.50/18.64 thf(trans_axiom,axiom,sP20). % 18.50/18.64 thf(refl_axiom,axiom,sP1). % 18.50/18.64 thf(31,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,trans_axiom,refl_axiom,h1])). % 18.50/18.64 thf(32,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[31,h0])). % 18.50/18.64 thf(0,theorem,sP23,inference(contra,[status(thm),contra(discharge,[h1])],[31,h1])). % 18.50/18.64 % SZS output end Proof %------------------------------------------------------------------------------