%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NLP264^7 : TPTP v9.2.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n010.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 02:04:43 PM UTC 2025 % Result : Theorem 0.20s 0.37s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NLP264^7 : TPTP v9.2.0. Released v5.5.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n010.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 : Wed Oct 8 13:04:23 EDT 2025 % 0.13/0.34 % CPUTime : % 0.20/0.37 % SZS status Theorem % 0.20/0.37 % Mode: mode213 % 0.20/0.37 % Inferences: 23 % 0.20/0.37 % SZS output start Proof % 0.20/0.37 thf(ty_mu, type, mu : $tType). % 0.20/0.37 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 0.20/0.37 thf(ty_seventy, type, seventy : mu). % 0.20/0.37 thf(ty_paris, type, paris : mu). % 0.20/0.37 thf(ty_eigen__1, type, eigen__1 : $i). % 0.20/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.20/0.37 thf(ty_class, type, class : (mu>$i>$o)). % 0.20/0.37 thf(ty_price, type, price : (mu>$i>$o)). % 0.20/0.37 thf(ty_dest, type, dest : (mu>$i>$o)). % 0.20/0.37 thf(ty_second, type, second : mu). % 0.20/0.37 thf(sP1,plain,sP1 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.37 thf(sP2,plain,sP2 <=> ((~((((dest @ paris) @ eigen__1) => (~(((class @ second) @ eigen__1)))))) => ((price @ seventy) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.20/0.37 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((((dest @ paris) @ X2) => (~(((class @ second) @ X2)))))) => ((price @ seventy) @ X2))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.20/0.37 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((~((((dest @ paris) @ X1) => (~(((class @ second) @ X1)))))) => ((price @ seventy) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.37 thf(sP5,plain,sP5 <=> ((class @ second) @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])). % 0.20/0.37 thf(sP6,plain,sP6 <=> (((dest @ paris) @ eigen__1) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.37 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((dest @ paris) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.37 thf(sP8,plain,sP8 <=> (sP1 => ((dest @ paris) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP8])])). % 0.20/0.37 thf(sP9,plain,sP9 <=> (sP1 => sP2),introduced(definition,[new_symbols(definition,[sP9])])). % 0.20/0.37 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((class @ second) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.20/0.37 thf(sP11,plain,sP11 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((class @ second) @ X2)))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.20/0.37 thf(sP12,plain,sP12 <=> (sP1 => sP5),introduced(definition,[new_symbols(definition,[sP12])])). % 0.20/0.37 thf(sP13,plain,sP13 <=> ((price @ seventy) @ eigen__1),introduced(definition,[new_symbols(definition,[sP13])])). % 0.20/0.37 thf(sP14,plain,sP14 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((dest @ paris) @ X2)))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.20/0.37 thf(sP15,plain,sP15 <=> ((dest @ paris) @ eigen__1),introduced(definition,[new_symbols(definition,[sP15])])). % 0.20/0.37 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.20/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.20/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.20/0.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.20/0.37 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.20/0.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.20/0.37 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.20/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.20/0.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.20/0.37 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.20/0.37 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.20/0.37 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.20/0.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.20/0.37 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 0.20/0.37 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.20/0.37 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.20/0.37 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.20/0.37 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.20/0.37 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.20/0.37 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.20/0.37 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.20/0.37 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.20/0.37 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.20/0.37 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.20/0.37 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))))))))). % 0.20/0.37 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.20/0.37 thf(def_mvalid,definition,(mvalid = (!!))). % 0.20/0.37 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.20/0.37 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.20/0.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.20/0.37 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 0.20/0.37 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 0.20/0.37 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((price @ seventy) @ X2))))). % 0.20/0.37 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((price @ seventy) @ X2)))))),inference(assume_negation,[status(cth)],[con])). % 0.20/0.37 thf(h1,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((price @ seventy) @ X1))))),introduced(assumption,[])). % 0.20/0.37 thf(h2,assumption,(~((sP1 => sP13))),introduced(assumption,[])). % 0.20/0.37 thf(h3,assumption,sP1,introduced(assumption,[])). % 0.20/0.37 thf(h4,assumption,(~(sP13)),introduced(assumption,[])). % 0.20/0.37 thf(1,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(2,plain,(~(sP4) | sP9),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(3,plain,((~(sP9) | ~(sP1)) | sP2),inference(prop_rule,[status(thm)],[])). % 0.20/0.37 thf(4,plain,((~(sP2) | sP6) | sP13),inference(prop_rule,[status(thm)],[])). % 0.20/0.37 thf(5,plain,((~(sP6) | ~(sP15)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.20/0.37 thf(6,plain,(~(sP14) | sP7),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(7,plain,(~(sP7) | sP8),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(8,plain,((~(sP8) | ~(sP1)) | sP15),inference(prop_rule,[status(thm)],[])). % 0.20/0.37 thf(9,plain,(~(sP11) | sP10),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(10,plain,(~(sP10) | sP12),inference(all_rule,[status(thm)],[])). % 0.20/0.37 thf(11,plain,((~(sP12) | ~(sP1)) | sP5),inference(prop_rule,[status(thm)],[])). % 0.20/0.37 thf(law2,axiom,(mvalid @ (mbox_s4 @ ((mimplies @ ((mand @ (dest @ paris)) @ (class @ second))) @ (price @ seventy))))). % 0.20/0.37 thf(12,plain,sP3,inference(preprocess,[status(thm)],[law2]). % 0.20/0.37 thf(belief1,axiom,(mvalid @ (mbox_s4 @ (dest @ paris)))). % 0.20/0.37 thf(13,plain,sP14,inference(preprocess,[status(thm)],[belief1]). % 0.20/0.37 thf(belief2,axiom,(mvalid @ (mbox_s4 @ (class @ second)))). % 0.20/0.37 thf(14,plain,sP11,inference(preprocess,[status(thm)],[belief2]). % 0.20/0.37 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h4])). % 0.20/0.37 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4])). % 0.20/0.37 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2])). % 0.20/0.37 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1])). % 0.20/0.37 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((price @ seventy) @ X2)))),inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])). % 0.20/0.37 % SZS output end Proof %------------------------------------------------------------------------------