%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO068^4.005 : 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 : n013.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 03:24:50 PM UTC 2025 % Result : Theorem 1.07s 1.32s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYO068^4.005 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 9 00:56:23 EDT 2025 % 0.12/0.34 % CPUTime : % 1.07/1.32 % SZS status Theorem % 1.07/1.32 % Mode: mode506 % 1.07/1.32 % Inferences: 19607 % 1.07/1.32 % SZS output start Proof % 1.07/1.32 thf(ty_eigen__6, type, eigen__6 : $i). % 1.07/1.32 thf(ty_eigen__0, type, eigen__0 : $i). % 1.07/1.32 thf(ty_p3, type, p3 : ($i>$o)). % 1.07/1.32 thf(ty_p4, type, p4 : ($i>$o)). % 1.07/1.32 thf(ty_p2, type, p2 : ($i>$o)). % 1.07/1.32 thf(ty_irel, type, irel : ($i>$i>$o)). % 1.07/1.32 thf(ty_p0, type, p0 : ($i>$o)). % 1.07/1.32 thf(ty_p5, type, p5 : ($i>$o)). % 1.07/1.32 thf(ty_p1, type, p1 : ($i>$o)). % 1.07/1.32 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.07/1.32 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p5 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 1.07/1.32 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.07/1.32 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 1.07/1.32 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.07/1.32 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.07/1.32 thf(sP4,plain,sP4 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.07/1.32 thf(sP5,plain,sP5 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.07/1.32 thf(sP6,plain,sP6 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.07/1.32 thf(sP7,plain,sP7 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.07/1.32 thf(sP8,plain,sP8 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.07/1.32 thf(sP9,plain,sP9 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])). % 1.07/1.32 thf(sP10,plain,sP10 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.07/1.32 thf(sP11,plain,sP11 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.07/1.32 thf(sP12,plain,sP12 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.07/1.32 thf(sP13,plain,sP13 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.07/1.32 thf(sP14,plain,sP14 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 1.07/1.32 thf(sP15,plain,sP15 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP15])])). % 1.07/1.32 thf(sP16,plain,sP16 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.07/1.32 thf(sP17,plain,sP17 <=> (((irel @ eigen__0) @ eigen__0) => sP11),introduced(definition,[new_symbols(definition,[sP17])])). % 1.07/1.32 thf(sP18,plain,sP18 <=> (((irel @ eigen__0) @ eigen__0) => sP12),introduced(definition,[new_symbols(definition,[sP18])])). % 1.07/1.32 thf(sP19,plain,sP19 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 1.07/1.32 thf(sP20,plain,sP20 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 1.07/1.32 thf(sP21,plain,sP21 <=> (p5 @ eigen__6),introduced(definition,[new_symbols(definition,[sP21])])). % 1.07/1.32 thf(sP22,plain,sP22 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.07/1.32 thf(sP23,plain,sP23 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => sP6),introduced(definition,[new_symbols(definition,[sP23])])). % 1.07/1.32 thf(sP24,plain,sP24 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))),introduced(definition,[new_symbols(definition,[sP24])])). % 1.07/1.32 thf(sP25,plain,sP25 <=> (sP14 => sP15),introduced(definition,[new_symbols(definition,[sP25])])). % 1.07/1.32 thf(sP26,plain,sP26 <=> (((irel @ eigen__0) @ eigen__0) => sP9),introduced(definition,[new_symbols(definition,[sP26])])). % 1.07/1.32 thf(sP27,plain,sP27 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 1.07/1.32 thf(sP28,plain,sP28 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP28])])). % 1.07/1.32 thf(sP29,plain,sP29 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))),introduced(definition,[new_symbols(definition,[sP29])])). % 1.07/1.32 thf(sP30,plain,sP30 <=> (sP24 => sP4),introduced(definition,[new_symbols(definition,[sP30])])). % 1.07/1.32 thf(sP31,plain,sP31 <=> (((irel @ eigen__0) @ eigen__6) => sP21),introduced(definition,[new_symbols(definition,[sP31])])). % 1.07/1.32 thf(sP32,plain,sP32 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP32])])). % 1.07/1.32 thf(sP33,plain,sP33 <=> (sP14 => sP22),introduced(definition,[new_symbols(definition,[sP33])])). % 1.07/1.32 thf(sP34,plain,sP34 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP34])])). % 1.07/1.32 thf(sP35,plain,sP35 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP35])])). % 1.07/1.32 thf(sP36,plain,sP36 <=> (sP16 => sP35),introduced(definition,[new_symbols(definition,[sP36])])). % 1.07/1.32 thf(sP37,plain,sP37 <=> (sP28 => sP3),introduced(definition,[new_symbols(definition,[sP37])])). % 1.07/1.32 thf(sP38,plain,sP38 <=> ((!!) @ p5),introduced(definition,[new_symbols(definition,[sP38])])). % 1.07/1.32 thf(sP39,plain,sP39 <=> (sP22 => sP2),introduced(definition,[new_symbols(definition,[sP39])])). % 1.07/1.32 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.07/1.32 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.07/1.32 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.07/1.32 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.07/1.32 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 1.07/1.32 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 1.07/1.32 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 1.07/1.32 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 1.07/1.32 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 1.07/1.32 thf(def_iand,definition,(iand = mand)). % 1.07/1.32 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.07/1.32 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.07/1.32 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 1.07/1.32 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 1.07/1.32 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 1.07/1.32 thf(def_ivalid,definition,(ivalid = (!!))). % 1.07/1.32 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.07/1.32 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.07/1.32 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.07/1.32 thf(con,conjecture,sP32). % 1.07/1.32 thf(h1,negated_conjecture,(~(sP32)),inference(assume_negation,[status(cth)],[con])). % 1.07/1.32 thf(1,plain,(~(sP38) | sP21),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(2,plain,(sP31 | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(3,plain,(sP14 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 1.07/1.32 thf(4,plain,(~(sP19) | sP26),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(5,plain,((~(sP26) | ~(sP28)) | sP9),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(6,plain,((~(sP25) | ~(sP14)) | sP15),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(7,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(8,plain,((~(sP7) | ~(sP28)) | sP33),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(9,plain,((~(sP33) | ~(sP14)) | sP22),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(10,plain,((~(sP39) | ~(sP22)) | sP2),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(11,plain,(~(sP2) | sP8),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(12,plain,((~(sP8) | ~(sP28)) | sP10),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(13,plain,((~(sP10) | ~(sP22)) | sP29),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(14,plain,((~(sP23) | ~(sP29)) | sP6),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(15,plain,(~(sP6) | sP18),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(16,plain,((~(sP18) | ~(sP28)) | sP12),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(17,plain,((~(sP12) | ~(sP29)) | sP24),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(18,plain,((~(sP30) | ~(sP24)) | sP4),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(19,plain,(~(sP4) | sP17),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(20,plain,((~(sP17) | ~(sP28)) | sP11),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(21,plain,((~(sP11) | ~(sP24)) | sP16),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(22,plain,((~(sP36) | ~(sP16)) | sP35),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(23,plain,(~(sP35) | sP37),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(24,plain,((~(sP37) | ~(sP28)) | sP3),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(25,plain,((~(sP3) | ~(sP16)) | sP19),inference(prop_rule,[status(thm)],[])). % 1.07/1.32 thf(26,plain,(~(sP1) | sP28),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(27,plain,(~(sP27) | sP25),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(28,plain,(~(sP34) | sP39),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(29,plain,(~(sP5) | sP23),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(30,plain,(~(sP20) | sP30),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(31,plain,(~(sP13) | sP36),inference(all_rule,[status(thm)],[])). % 1.07/1.32 thf(32,plain,(sP32 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.07/1.32 thf(axiom6,axiom,(ivalid @ ((iimplies @ (iatom @ p5)) @ ((iimplies @ (iatom @ p5)) @ (iatom @ p4))))). % 1.07/1.32 thf(33,plain,sP27,inference(preprocess,[status(thm)],[axiom6]). % 1.07/1.32 thf(axiom5,axiom,(ivalid @ ((iimplies @ (iatom @ p4)) @ ((iimplies @ (iatom @ p4)) @ (iatom @ p3))))). % 1.07/1.32 thf(34,plain,sP34,inference(preprocess,[status(thm)],[axiom5]). % 1.07/1.32 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ p3)) @ ((iimplies @ (iatom @ p3)) @ (iatom @ p2))))). % 1.07/1.32 thf(35,plain,sP5,inference(preprocess,[status(thm)],[axiom4]). % 1.07/1.32 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ p2)) @ ((iimplies @ (iatom @ p2)) @ (iatom @ p1))))). % 1.07/1.32 thf(36,plain,sP20,inference(preprocess,[status(thm)],[axiom3]). % 1.07/1.32 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))). % 1.07/1.32 thf(37,plain,sP13,inference(preprocess,[status(thm)],[axiom2]). % 1.07/1.32 thf(axiom1,axiom,(ivalid @ (iatom @ p5))). % 1.07/1.32 thf(38,plain,sP38,inference(preprocess,[status(thm)],[axiom1]). % 1.07/1.32 thf(refl_axiom,axiom,sP1). % 1.07/1.32 thf(39,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,refl_axiom,h1])). % 1.07/1.32 thf(40,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[39,h0])). % 1.07/1.32 thf(0,theorem,sP32,inference(contra,[status(thm),contra(discharge,[h1])],[39,h1])). % 1.07/1.32 % SZS output end Proof %------------------------------------------------------------------------------