%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO060^4 : 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 : n019.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 03:24:47 PM UTC 2025 % Result : Theorem 0.13s 0.37s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO060^4 : 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 : n019.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 00:42:08 EDT 2025 % 0.13/0.34 % CPUTime : % 0.13/0.37 % SZS status Theorem % 0.13/0.37 % Mode: mode213 % 0.13/0.37 % Inferences: 7 % 0.13/0.37 % SZS output start Proof % 0.13/0.37 thf(ty_a, type, a : ($i>$o)). % 0.13/0.37 thf(ty_eigen__2, type, eigen__2 : $i). % 0.13/0.37 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.37 thf(ty_b, type, b : ($i>$o)). % 0.13/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.37 thf(ty_irel, type, irel : ($i>$i>$o)). % 0.13/0.37 thf(sP1,plain,sP1 <=> ((irel @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.37 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.37 thf(sP3,plain,sP3 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.37 thf(sP4,plain,sP4 <=> (((irel @ eigen__0) @ eigen__1) => (~((![X1:$i]:(((irel @ eigen__1) @ X1) => (b @ X1)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.37 thf(sP5,plain,sP5 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))))))) => sP2),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.37 thf(sP6,plain,sP6 <=> (sP1 => (~((![X1:$i]:(((irel @ eigen__2) @ X1) => (a @ X1)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.37 thf(sP7,plain,sP7 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (b @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.37 thf(sP8,plain,sP8 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.13/0.37 thf(sP9,plain,sP9 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.13/0.37 thf(sP10,plain,sP10 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP10])])). % 0.13/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.13/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.13/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.13/0.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.13/0.37 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 0.13/0.37 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 0.13/0.37 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 0.13/0.37 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 0.13/0.37 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 0.13/0.37 thf(def_iand,definition,(iand = mand)). % 0.13/0.37 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.13/0.37 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.13/0.37 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 0.13/0.37 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 0.13/0.37 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 0.13/0.37 thf(def_ivalid,definition,(ivalid = (!!))). % 0.13/0.37 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.13/0.37 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.13/0.37 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.13/0.37 thf(con,conjecture,(![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3)))))))))). % 0.13/0.37 thf(h0,negated_conjecture,(~((![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3))))))))))),inference(assume_negation,[status(cth)],[con])). % 0.13/0.37 thf(h1,assumption,(~(((~(sP2)) => sP9))),introduced(assumption,[])). % 0.13/0.37 thf(h2,assumption,(~(sP2)),introduced(assumption,[])). % 0.13/0.37 thf(h3,assumption,(~(sP9)),introduced(assumption,[])). % 0.13/0.37 thf(h4,assumption,(~(sP4)),introduced(assumption,[])). % 0.13/0.37 thf(h5,assumption,sP10,introduced(assumption,[])). % 0.13/0.37 thf(h6,assumption,sP7,introduced(assumption,[])). % 0.13/0.37 thf(h7,assumption,(~(sP6)),introduced(assumption,[])). % 0.13/0.37 thf(h8,assumption,sP1,introduced(assumption,[])). % 0.13/0.37 thf(h9,assumption,sP8,introduced(assumption,[])). % 0.13/0.37 thf(1,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(2,plain,((~(sP6) | ~(sP1)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(3,plain,(~(sP3) | sP5),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(4,plain,((~(sP5) | sP9) | sP2),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(5,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(6,plain,((~(sP4) | ~(sP10)) | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(axiom1,axiom,(ivalid @ ((ior @ (inot @ (iatom @ a))) @ (inot @ (iatom @ b))))). % 0.13/0.37 thf(7,plain,sP3,inference(preprocess,[status(thm)],[axiom1]). % 0.13/0.37 thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h5,h6,h8,h9])). % 0.13/0.37 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,8,h8,h9])). % 0.13/0.37 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,9,h7])). % 0.13/0.37 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,10,h5,h6])). % 0.13/0.37 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,11,h4])). % 0.13/0.37 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3])). % 0.13/0.37 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])). % 0.13/0.37 thf(0,theorem,(![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])). % 0.13/0.37 % SZS output end Proof %------------------------------------------------------------------------------