%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYN044^4 : 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 : n015.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 03:17:39 PM UTC 2025 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYN044^4 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n015.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 : Wed Oct 8 15:12:23 EDT 2025 % 0.12/0.35 % CPUTime : % 0.20/0.52 % SZS status Theorem % 0.20/0.52 % Mode: mode213 % 0.20/0.52 % Inferences: 1820 % 0.20/0.52 % SZS output start Proof % 0.20/0.52 thf(ty_p, type, p : ($i>$o)). % 0.20/0.52 thf(ty_q, type, q : ($i>$o)). % 0.20/0.52 thf(ty_eigen__1, type, eigen__1 : $i). % 0.20/0.52 thf(ty_eigen__0, type, eigen__0 : $i). % 0.20/0.52 thf(ty_eigen__5, type, eigen__5 : $i). % 0.20/0.52 thf(ty_r, type, r : ($i>$o)). % 0.20/0.52 thf(ty_eigen__3, type, eigen__3 : $i). % 0.20/0.52 thf(ty_irel, type, irel : ($i>$i>$o)). % 0.20/0.52 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.20/0.52 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (r @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 0.20/0.52 thf(sP1,plain,sP1 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.52 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((irel @ eigen__3) @ X1) => (q @ X1))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => (r @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.20/0.52 thf(sP3,plain,sP3 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (r @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.20/0.52 thf(sP4,plain,sP4 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (r @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((p @ X2) => (~((q @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.52 thf(sP5,plain,sP5 <=> ((irel @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP5])])). % 0.20/0.52 thf(sP6,plain,sP6 <=> (sP5 => (r @ eigen__3)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.52 thf(sP7,plain,sP7 <=> (((irel @ eigen__0) @ eigen__3) => (r @ eigen__3)),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.52 thf(sP8,plain,sP8 <=> (p @ eigen__5),introduced(definition,[new_symbols(definition,[sP8])])). % 0.20/0.52 thf(sP9,plain,sP9 <=> (((irel @ eigen__0) @ eigen__5) => (~((sP8 => (~((q @ eigen__5))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.20/0.52 thf(sP10,plain,sP10 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (q @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2))))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.20/0.52 thf(sP11,plain,sP11 <=> ((irel @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP11])])). % 0.20/0.52 thf(sP12,plain,sP12 <=> (r @ eigen__3),introduced(definition,[new_symbols(definition,[sP12])])). % 0.20/0.52 thf(sP13,plain,sP13 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (r @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((p @ X1) => (~((q @ X1))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.20/0.52 thf(sP14,plain,sP14 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (q @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2)))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.20/0.52 thf(sP15,plain,sP15 <=> ((irel @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP15])])). % 0.20/0.52 thf(sP16,plain,sP16 <=> (sP1 => (~(((p @ eigen__1) => (~((q @ eigen__1))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.20/0.52 thf(sP17,plain,sP17 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.20/0.52 thf(sP18,plain,sP18 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (r @ X1))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.20/0.52 thf(sP19,plain,sP19 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.20/0.52 thf(sP20,plain,sP20 <=> (sP11 => ((~(sP17)) => sP3)),introduced(definition,[new_symbols(definition,[sP20])])). % 0.20/0.52 thf(sP21,plain,sP21 <=> (sP8 => (~((q @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.20/0.52 thf(sP22,plain,sP22 <=> (q @ eigen__1),introduced(definition,[new_symbols(definition,[sP22])])). % 0.20/0.52 thf(sP23,plain,sP23 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP23])])). % 0.20/0.52 thf(sP24,plain,sP24 <=> ((~(sP17)) => sP3),introduced(definition,[new_symbols(definition,[sP24])])). % 0.20/0.52 thf(sP25,plain,sP25 <=> (sP19 => sP14),introduced(definition,[new_symbols(definition,[sP25])])). % 0.20/0.52 thf(sP26,plain,sP26 <=> ((p @ eigen__1) => (~(sP22))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.20/0.52 thf(sP27,plain,sP27 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (q @ X1))) => sP18),introduced(definition,[new_symbols(definition,[sP27])])). % 0.20/0.52 thf(sP28,plain,sP28 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (q @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (r @ X3)))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.20/0.52 thf(sP29,plain,sP29 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((p @ X1) => (~((q @ X1)))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 0.20/0.52 thf(sP30,plain,sP30 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.20/0.52 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.20/0.52 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.20/0.52 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.20/0.52 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.20/0.52 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 0.20/0.52 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 0.20/0.52 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 0.20/0.52 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 0.20/0.52 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 0.20/0.52 thf(def_iand,definition,(iand = mand)). % 0.20/0.52 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.20/0.52 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.20/0.52 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 0.20/0.52 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 0.20/0.52 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 0.20/0.52 thf(def_ivalid,definition,(ivalid = (!!))). % 0.20/0.52 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.20/0.52 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.20/0.52 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.20/0.52 thf(pel10,conjecture,(![X1:$i]:(~((((~((~((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((~((~((![X2:$i]:(((irel @ X1) @ X2) => (q @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))))))))))). % 0.20/0.52 thf(h1,negated_conjecture,(~((![X1:$i]:(~((((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((irel @ X1) @ X2) => (q @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p @ X2)))))))))))),inference(assume_negation,[status(cth)],[pel10])). % 0.20/0.52 thf(h2,assumption,((sP19 => sP30) => (~((sP30 => sP19)))),introduced(assumption,[])). % 0.20/0.52 thf(h3,assumption,(~((sP19 => sP30))),introduced(assumption,[])). % 0.20/0.52 thf(h4,assumption,(~((sP30 => sP19))),introduced(assumption,[])). % 0.20/0.52 thf(h5,assumption,sP19,introduced(assumption,[])). % 0.20/0.52 thf(h6,assumption,(~(sP30)),introduced(assumption,[])). % 0.20/0.52 thf(h7,assumption,(~((sP1 => sP22))),introduced(assumption,[])). % 0.20/0.52 thf(h8,assumption,sP1,introduced(assumption,[])). % 0.20/0.52 thf(h9,assumption,(~(sP22)),introduced(assumption,[])). % 0.20/0.52 thf(1,plain,(~(sP23) | sP5),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(2,plain,(~(sP10) | sP2),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(3,plain,((~(sP2) | ~(sP17)) | sP3),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(4,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(5,plain,((~(sP6) | ~(sP5)) | sP12),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(6,plain,(~(sP14) | sP20),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(7,plain,((~(sP20) | ~(sP11)) | sP24),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(8,plain,((~(sP24) | sP17) | sP3),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(9,plain,(sP7 | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(10,plain,(sP7 | sP11),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(11,plain,(sP26 | sP22),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(12,plain,(sP18 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 0.20/0.52 thf(13,plain,(~(sP29) | sP16),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(14,plain,((~(sP16) | ~(sP1)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(15,plain,(~(sP4) | sP13),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(16,plain,((~(sP13) | ~(sP18)) | sP29),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(17,plain,(~(sP28) | sP25),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(18,plain,((~(sP25) | ~(sP19)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(refl_axiom,axiom,sP23). % 0.20/0.52 thf(pel10_1,axiom,(ivalid @ ((iimplies @ (iatom @ q)) @ (iatom @ r)))). % 0.20/0.52 thf(19,plain,sP10,inference(preprocess,[status(thm)],[pel10_1]). % 0.20/0.52 thf(pel10_2,axiom,(ivalid @ ((iimplies @ (iatom @ r)) @ ((iand @ (iatom @ p)) @ (iatom @ q))))). % 0.20/0.52 thf(20,plain,sP4,inference(preprocess,[status(thm)],[pel10_2]). % 0.20/0.52 thf(pel10_3,axiom,(ivalid @ ((iimplies @ (iatom @ p)) @ ((ior @ (iatom @ q)) @ (iatom @ r))))). % 0.20/0.52 thf(21,plain,sP28,inference(preprocess,[status(thm)],[pel10_3]). % 0.20/0.52 thf(22,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,refl_axiom,19,20,21,h5,h8,h9])). % 0.20/0.52 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,22,h8,h9])). % 0.20/0.52 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,23,h7])). % 0.20/0.52 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,24,h5,h6])). % 0.20/0.52 thf(h10,assumption,sP30,introduced(assumption,[])). % 0.20/0.52 thf(h11,assumption,(~(sP19)),introduced(assumption,[])). % 0.20/0.52 thf(h12,assumption,(~((sP15 => sP8))),introduced(assumption,[])). % 0.20/0.52 thf(h13,assumption,sP15,introduced(assumption,[])). % 0.20/0.52 thf(h14,assumption,(~(sP8)),introduced(assumption,[])). % 0.20/0.52 thf(26,plain,(sP21 | sP8),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(27,plain,(~(sP4) | sP13),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(28,plain,((~(sP13) | ~(sP18)) | sP29),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(29,plain,(~(sP29) | sP9),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(30,plain,((~(sP9) | ~(sP15)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(31,plain,(~(sP10) | sP27),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(32,plain,((~(sP27) | ~(sP30)) | sP18),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(33,plain,$false,inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h4,h2,h1,h0])],[26,27,28,29,30,31,32,19,20,h10,h13,h14])). % 0.20/0.52 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,33,h13,h14])). % 0.20/0.52 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h11,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__5)],[h11,34,h12])). % 0.20/0.52 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h4,35,h10,h11])). % 0.20/0.52 thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,25,36,h3,h4])). % 0.20/0.52 thf(38,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,37,h2])). % 0.20/0.52 thf(39,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[38,h0])). % 0.20/0.52 thf(0,theorem,(![X1:$i]:(~((((~((~((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((~((~((![X2:$i]:(((irel @ X1) @ X2) => (q @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (p @ X2)))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[38,h1])). % 0.20/0.52 % SZS output end Proof %------------------------------------------------------------------------------