%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO068^4.001 : 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 : n002.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 1.29s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO068^4.001 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n002.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 : Thu Oct 9 01:14:08 EDT 2025 % 0.13/0.34 % CPUTime : % 1.07/1.29 % SZS status Theorem % 1.07/1.29 % Mode: mode506 % 1.07/1.29 % Inferences: 19456 % 1.07/1.29 % SZS output start Proof % 1.07/1.29 thf(ty_eigen__1, type, eigen__1 : $i). % 1.07/1.29 thf(ty_eigen__0, type, eigen__0 : $i). % 1.07/1.29 thf(ty_irel, type, irel : ($i>$i>$o)). % 1.07/1.29 thf(ty_p0, type, p0 : ($i>$o)). % 1.07/1.29 thf(ty_p1, type, p1 : ($i>$o)). % 1.07/1.29 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.07/1.29 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.07/1.29 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.07/1.29 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 1.07/1.29 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.07/1.29 thf(sP3,plain,sP3 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP3])])). % 1.07/1.29 thf(sP4,plain,sP4 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.07/1.29 thf(sP5,plain,sP5 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 1.07/1.29 thf(sP6,plain,sP6 <=> (((irel @ eigen__0) @ eigen__1) => (p1 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP6])])). % 1.07/1.29 thf(sP7,plain,sP7 <=> (p1 @ eigen__1),introduced(definition,[new_symbols(definition,[sP7])])). % 1.07/1.29 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1)))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.07/1.29 thf(sP9,plain,sP9 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP9])])). % 1.07/1.29 thf(sP10,plain,sP10 <=> (sP3 => sP5),introduced(definition,[new_symbols(definition,[sP10])])). % 1.07/1.29 thf(sP11,plain,sP11 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP11])])). % 1.07/1.29 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.07/1.29 thf(sP13,plain,sP13 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.07/1.29 thf(sP14,plain,sP14 <=> (sP3 => sP8),introduced(definition,[new_symbols(definition,[sP14])])). % 1.07/1.29 thf(sP15,plain,sP15 <=> ((!!) @ p1),introduced(definition,[new_symbols(definition,[sP15])])). % 1.07/1.29 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.07/1.29 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.07/1.29 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.07/1.29 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.07/1.29 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 1.07/1.29 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 1.07/1.29 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 1.07/1.29 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 1.07/1.29 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 1.07/1.29 thf(def_iand,definition,(iand = mand)). % 1.07/1.29 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.07/1.29 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.07/1.29 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 1.07/1.29 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 1.07/1.29 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 1.07/1.29 thf(def_ivalid,definition,(ivalid = (!!))). % 1.07/1.29 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.07/1.29 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.07/1.29 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.07/1.29 thf(con,conjecture,sP11). % 1.07/1.29 thf(h1,negated_conjecture,(~(sP11)),inference(assume_negation,[status(cth)],[con])). % 1.07/1.29 thf(1,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])). % 1.07/1.29 thf(2,plain,(sP6 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 1.07/1.29 thf(3,plain,(sP12 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.07/1.29 thf(4,plain,(~(sP9) | sP10),inference(all_rule,[status(thm)],[])). % 1.07/1.29 thf(5,plain,((~(sP10) | ~(sP3)) | sP5),inference(prop_rule,[status(thm)],[])). % 1.07/1.29 thf(6,plain,((~(sP2) | ~(sP12)) | sP13),inference(prop_rule,[status(thm)],[])). % 1.07/1.29 thf(7,plain,(~(sP13) | sP14),inference(all_rule,[status(thm)],[])). % 1.07/1.29 thf(8,plain,((~(sP14) | ~(sP3)) | sP8),inference(prop_rule,[status(thm)],[])). % 1.07/1.29 thf(9,plain,((~(sP8) | ~(sP12)) | sP9),inference(prop_rule,[status(thm)],[])). % 1.07/1.29 thf(10,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])). % 1.07/1.29 thf(11,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])). % 1.07/1.29 thf(12,plain,(sP11 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.07/1.29 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))). % 1.07/1.29 thf(13,plain,sP4,inference(preprocess,[status(thm)],[axiom2]). % 1.07/1.29 thf(axiom1,axiom,(ivalid @ (iatom @ p1))). % 1.07/1.29 thf(14,plain,sP15,inference(preprocess,[status(thm)],[axiom1]). % 1.07/1.29 thf(refl_axiom,axiom,sP1). % 1.07/1.29 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,refl_axiom,h1])). % 1.07/1.29 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0])). % 1.07/1.29 thf(0,theorem,sP11,inference(contra,[status(thm),contra(discharge,[h1])],[15,h1])). % 1.07/1.29 % SZS output end Proof %------------------------------------------------------------------------------