%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : KRS276^7 : 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 : n003.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 01:50:29 PM UTC 2025 % Result : Theorem 0.14s 0.37s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KRS276^7 : TPTP v9.2.0. Released v5.5.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Oct 8 13:10:38 EDT 2025 % 0.14/0.35 % CPUTime : % 0.14/0.37 % SZS status Theorem % 0.14/0.37 % Mode: mode213 % 0.14/0.37 % Inferences: 14 % 0.14/0.37 % SZS output start Proof % 0.14/0.37 thf(ty_mu, type, mu : $tType). % 0.14/0.37 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 0.14/0.37 thf(ty_eigen__1, type, eigen__1 : $i). % 0.14/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.37 thf(ty_john, type, john : mu). % 0.14/0.37 thf(ty_math, type, math : mu). % 0.14/0.37 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 0.14/0.37 thf(ty_psych, type, psych : mu). % 0.14/0.37 thf(ty_teach, type, teach : (mu>mu>$i>$o)). % 0.14/0.37 thf(ty_cs, type, cs : mu). % 0.14/0.37 thf(ty_mary, type, mary : mu). % 0.14/0.37 thf(ty_sue, type, sue : mu). % 0.14/0.37 thf(sP1,plain,sP1 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.37 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~(((((teach @ john) @ math) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((((teach @ X2) @ cs) @ X1))))))) => ((((teach @ mary) @ psych) @ X1) => (~((((teach @ sue) @ psych) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.37 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((((teach @ john) @ math) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((((teach @ X3) @ cs) @ X2))))))) => ((((teach @ mary) @ psych) @ X2) => (~((((teach @ sue) @ psych) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.14/0.37 thf(sP4,plain,sP4 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~((((teach @ X1) @ cs) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.14/0.37 thf(sP5,plain,sP5 <=> (sP1 => (~(((((teach @ john) @ math) @ eigen__1) => ((~(sP4)) => ((((teach @ mary) @ psych) @ eigen__1) => (~((((teach @ sue) @ psych) @ eigen__1))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.14/0.37 thf(sP6,plain,sP6 <=> ((((teach @ john) @ math) @ eigen__1) => ((~(sP4)) => ((((teach @ mary) @ psych) @ eigen__1) => (~((((teach @ sue) @ psych) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.14/0.37 thf(sP7,plain,sP7 <=> ((~(sP4)) => ((((teach @ mary) @ psych) @ eigen__1) => (~((((teach @ sue) @ psych) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.14/0.37 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.14/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.14/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.14/0.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.14/0.37 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.14/0.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.14/0.37 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.14/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.14/0.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.14/0.37 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.14/0.37 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.14/0.37 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.14/0.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.14/0.37 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 0.14/0.37 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.14/0.37 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.14/0.37 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.14/0.37 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.14/0.37 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.14/0.37 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.14/0.37 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.14/0.37 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.14/0.37 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.14/0.37 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.14/0.37 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))))))))). % 0.14/0.37 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.14/0.37 thf(def_mvalid,definition,(mvalid = (!!))). % 0.14/0.37 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.14/0.37 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.14/0.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.14/0.37 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 0.14/0.37 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 0.14/0.37 thf(query,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((((teach @ X3) @ cs) @ X2))))))))))). % 0.14/0.37 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((((teach @ X3) @ cs) @ X2)))))))))))),inference(assume_negation,[status(cth)],[query])). % 0.14/0.37 thf(h1,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((((teach @ X2) @ cs) @ X1))))))))))),introduced(assumption,[])). % 0.14/0.37 thf(h2,assumption,(~((sP1 => (~(sP4))))),introduced(assumption,[])). % 0.14/0.37 thf(h3,assumption,sP1,introduced(assumption,[])). % 0.14/0.37 thf(h4,assumption,sP4,introduced(assumption,[])). % 0.14/0.37 thf(1,plain,(sP7 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.14/0.37 thf(2,plain,(sP6 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 0.14/0.37 thf(3,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])). % 0.14/0.37 thf(4,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])). % 0.14/0.37 thf(5,plain,((~(sP5) | ~(sP1)) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 0.14/0.37 thf(db,axiom,(mvalid @ (mbox_s4 @ ((mand @ ((teach @ john) @ math)) @ ((mand @ (mexists_ind @ (^[X1:mu]:((teach @ X1) @ cs)))) @ ((mand @ ((teach @ mary) @ psych)) @ ((teach @ sue) @ psych))))))). % 0.14/0.37 thf(6,plain,sP3,inference(preprocess,[status(thm)],[db]). % 0.14/0.37 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h3,h4])). % 0.14/0.37 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,7,h3,h4])). % 0.14/0.37 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2])). % 0.14/0.37 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1])). % 0.14/0.37 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((((teach @ X3) @ cs) @ X2)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). % 0.14/0.37 % SZS output end Proof %------------------------------------------------------------------------------