%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG013^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n017.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 01:27:38 PM UTC 2025 % Result : Theorem 13.06s 13.25s % Output : Proof 13.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEG013^1 : TPTP v9.2.0. Released v4.1.0. % 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.36 % Computer : n017.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Oct 8 12:30:08 EDT 2025 % 0.15/0.36 % CPUTime : % 13.06/13.25 % SZS status Theorem % 13.06/13.25 % Mode: mode461 % 13.06/13.25 % Inferences: 428 % 13.06/13.25 % SZS output start Proof % 13.06/13.25 thf(ty_reg, type, reg : $tType). % 13.06/13.25 thf(ty_a, type, a : ($i>$i>$o)). % 13.06/13.25 thf(ty_spain, type, spain : reg). % 13.06/13.25 thf(ty_catalunya, type, catalunya : reg). % 13.06/13.25 thf(ty_eigen__1, type, eigen__1 : $i). % 13.06/13.25 thf(ty_eigen__0, type, eigen__0 : $i). % 13.06/13.25 thf(ty_c, type, c : (reg>reg>$o)). % 13.06/13.25 thf(sP1,plain,sP1 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 13.06/13.25 thf(sP2,plain,sP2 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.06/13.25 thf(sP3,plain,sP3 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => sP2),introduced(definition,[new_symbols(definition,[sP3])])). % 13.06/13.25 thf(sP4,plain,sP4 <=> ((~(sP3)) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.06/13.25 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP4))))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.06/13.25 thf(sP6,plain,sP6 <=> (![X1:reg]:(![X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.06/13.25 thf(sP7,plain,sP7 <=> (![X1:reg]:(~(((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 13.06/13.25 thf(sP8,plain,sP8 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP4)))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.06/13.25 thf(sP9,plain,sP9 <=> (sP1 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.06/13.25 thf(sP10,plain,sP10 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP10])])). % 13.06/13.25 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 13.06/13.25 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 13.06/13.25 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.06/13.25 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.06/13.25 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 13.06/13.25 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.06/13.25 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 13.06/13.25 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 13.06/13.25 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 13.06/13.25 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 13.06/13.25 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 13.06/13.25 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 13.06/13.25 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 13.06/13.25 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.06/13.25 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 13.06/13.25 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.06/13.25 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 13.06/13.25 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 13.06/13.25 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 13.06/13.25 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 13.06/13.25 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 13.06/13.25 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 13.06/13.25 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 13.06/13.25 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 13.06/13.25 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 13.06/13.25 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 13.06/13.25 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 13.06/13.25 thf(def_mvalid,definition,(mvalid = (!!))). % 13.06/13.25 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.06/13.25 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.06/13.25 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.06/13.25 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 13.06/13.25 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 13.06/13.25 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 13.06/13.25 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 13.06/13.25 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 13.06/13.25 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 13.06/13.25 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 13.06/13.25 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 13.06/13.25 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 13.06/13.25 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP6)))))). % 13.06/13.25 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP6))))))),inference(assume_negation,[status(cth)],[con])). % 13.06/13.25 thf(h1,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP6)))))),introduced(assumption,[])). % 13.06/13.25 thf(h2,assumption,(~((sP1 => (~(sP6))))),introduced(assumption,[])). % 13.06/13.25 thf(h3,assumption,sP1,introduced(assumption,[])). % 13.06/13.25 thf(h4,assumption,sP6,introduced(assumption,[])). % 13.06/13.25 thf(1,plain,(sP10 | sP2),inference(prop_rule,[status(thm)],[])). % 13.06/13.25 thf(2,plain,(~(sP7) | ~(sP10)),inference(all_rule,[status(thm)],[])). % 13.06/13.25 thf(3,plain,(sP3 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 13.06/13.25 thf(4,plain,(sP4 | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 13.06/13.25 thf(5,plain,(~(sP5) | sP8),inference(all_rule,[status(thm)],[])). % 13.06/13.25 thf(6,plain,(~(sP8) | sP9),inference(all_rule,[status(thm)],[])). % 13.06/13.25 thf(7,plain,((~(sP9) | ~(sP1)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 13.06/13.25 thf(8,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])). % 13.06/13.25 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))). % 13.06/13.25 thf(9,plain,sP5,inference(preprocess,[status(thm)],[ax1]). % 13.06/13.25 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,h3,h4,9])). % 13.06/13.25 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,10,h3,h4])). % 13.06/13.25 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2])). % 13.06/13.25 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1])). % 13.06/13.25 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP6))))),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])). % 13.06/13.25 % SZS output end Proof %------------------------------------------------------------------------------