%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET925^7 : 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 : n002.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 02:26:34 PM UTC 2025 % Result : Theorem 1.07s 1.27s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET925^7 : TPTP v9.2.0. Released v5.5.0. % 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n002.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 14:41:38 EDT 2025 % 0.13/0.34 % CPUTime : % 1.07/1.27 % SZS status Theorem % 1.07/1.27 % Mode: mode506 % 1.07/1.27 % Inferences: 0 % 1.07/1.27 % SZS output start Proof % 1.07/1.27 thf(ty_mu, type, mu : $tType). % 1.07/1.27 thf(ty_singleton, type, singleton : (mu>mu)). % 1.07/1.27 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 1.07/1.27 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 1.07/1.27 thf(ty_qmltpeq, type, qmltpeq : (mu>mu>$i>$o)). % 1.07/1.27 thf(ty_empty_set, type, empty_set : mu). % 1.07/1.27 thf(ty_set_difference, type, set_difference : (mu>mu>mu)). % 1.07/1.27 thf(ty_in, type, in : (mu>mu>$i>$o)). % 1.07/1.27 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.07/1.27 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 1.07/1.27 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.07/1.27 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.07/1.27 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.07/1.27 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 1.07/1.27 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.07/1.27 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 1.07/1.27 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 1.07/1.27 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.07/1.27 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 1.07/1.27 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 1.07/1.27 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 1.07/1.27 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 1.07/1.27 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 1.07/1.27 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 1.07/1.27 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 1.07/1.27 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 1.07/1.27 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 1.07/1.27 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 1.07/1.27 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 1.07/1.27 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 1.07/1.27 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)))))))). % 1.07/1.27 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 1.07/1.27 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 1.07/1.27 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 1.07/1.27 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 1.07/1.27 thf(def_mvalid,definition,(mvalid = (!!))). % 1.07/1.27 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.07/1.27 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.07/1.27 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.07/1.27 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 1.07/1.27 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 1.07/1.27 thf(t68_zfmisc_1,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((~((~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))))))))))))))))). % 1.07/1.27 thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[t68_zfmisc_1])). % 1.07/1.27 thf(l36_zfmisc_1,axiom,(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X1:mu]:(mbox_s4 @ (mforall_ind @ (^[X2:mu]:((mand @ (mbox_s4 @ ((mimplies @ (mbox_s4 @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set))) @ (mbox_s4 @ ((in @ X1) @ X2))))) @ (mbox_s4 @ ((mimplies @ (mbox_s4 @ ((in @ X1) @ X2))) @ (mbox_s4 @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set))))))))))))). % 1.07/1.27 thf(1,plain,sP1,inference(preprocess,[status(thm)],[l36_zfmisc_1]). % 1.07/1.27 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h0])],[1,h0])). % 1.07/1.27 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((~((~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7)))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])). % 1.07/1.27 % SZS output end Proof %------------------------------------------------------------------------------