%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET907^7 : 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 : n012.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 02:26:33 PM UTC 2025 % Result : Theorem 94.02s 92.36s % Output : Proof 94.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET907^7 : TPTP v9.2.0. Released v5.5.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n012.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Oct 8 14:33:08 EDT 2025 % 0.12/0.34 % CPUTime : % 62.18/60.18 slave returned with unknown status % 94.02/92.36 % SZS status Theorem % 94.02/92.36 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 94.02/92.36 % Inferences: 7717 % 94.02/92.36 % SZS output start Proof % 94.02/92.36 thf(ty_mu, type, mu : $tType). % 94.02/92.36 thf(ty_subset, type, subset : (mu>mu>$i>$o)). % 94.02/92.36 thf(ty_eigen__2, type, eigen__2 : mu). % 94.02/92.36 thf(ty_eigen__1, type, eigen__1 : mu). % 94.02/92.36 thf(ty_eigen__0, type, eigen__0 : $i). % 94.02/92.36 thf(ty_unordered_pair, type, unordered_pair : (mu>mu>mu)). % 94.02/92.36 thf(ty_eigen__3, type, eigen__3 : mu). % 94.02/92.36 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)). % 94.02/92.36 thf(ty_set_union2, type, set_union2 : (mu>mu>mu)). % 94.02/92.36 thf(ty_qmltpeq, type, qmltpeq : (mu>mu>$i>$o)). % 94.02/92.36 thf(ty_in, type, in : (mu>mu>$i>$o)). % 94.02/92.36 thf(h0, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 94.02/92.36 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__0) => ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ X1) @ eigen__2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ X1)) @ eigen__2)) @ eigen__2) @ eigen__0))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 94.02/92.36 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => ((~(((((in @ X1) @ X2) @ eigen__0) => (~((((in @ X3) @ X2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X1) @ X3)) @ X2)) @ X2) @ eigen__0))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 94.02/92.36 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 94.02/92.36 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (![X4:mu]:(((exists_in_world @ X4) @ X1) => ((~(((((in @ X2) @ X3) @ X1) => (~((((in @ X4) @ X3) @ X1)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X2) @ X4)) @ X3)) @ X3) @ X1)))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 94.02/92.36 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((~(((((in @ eigen__1) @ X1) @ eigen__0) => (~((((in @ X2) @ X1) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ X2)) @ X1)) @ X1) @ eigen__0))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 94.02/92.36 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (![X4:mu]:(((exists_in_world @ X4) @ X1) => (~((((((subset @ ((unordered_pair @ X2) @ X3)) @ X4) @ X1) => (~(((((in @ X2) @ X4) @ X1) => (~((((in @ X3) @ X4) @ X1))))))) => (~(((~(((((in @ X2) @ X4) @ X1) => (~((((in @ X3) @ X4) @ X1)))))) => (((subset @ ((unordered_pair @ X2) @ X3)) @ X4) @ X1)))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 94.02/92.36 thf(sP2,plain,sP2 <=> ((((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2) @ eigen__0) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2)) @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP2])])). % 94.02/92.36 thf(sP3,plain,sP3 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (~((((((subset @ ((unordered_pair @ eigen__1) @ X1)) @ X2) @ eigen__0) => (~(((((in @ eigen__1) @ X2) @ eigen__0) => (~((((in @ X1) @ X2) @ eigen__0))))))) => (~(((~(((((in @ eigen__1) @ X2) @ eigen__0) => (~((((in @ X1) @ X2) @ eigen__0)))))) => (((subset @ ((unordered_pair @ eigen__1) @ X1)) @ X2) @ eigen__0))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 94.02/92.36 thf(sP4,plain,sP4 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((((((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1) @ eigen__0) => (~(((((in @ eigen__1) @ X1) @ eigen__0) => (~((((in @ eigen__3) @ X1) @ eigen__0))))))) => (~(((~(((((in @ eigen__1) @ X1) @ eigen__0) => (~((((in @ eigen__3) @ X1) @ eigen__0)))))) => (((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1) @ eigen__0))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 94.02/92.36 thf(sP5,plain,sP5 <=> ((exists_in_world @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 94.02/92.36 thf(sP6,plain,sP6 <=> ((exists_in_world @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 94.02/92.36 thf(sP7,plain,sP7 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => (~((((((subset @ ((unordered_pair @ X1) @ X2)) @ X3) @ eigen__0) => (~(((((in @ X1) @ X3) @ eigen__0) => (~((((in @ X2) @ X3) @ eigen__0))))))) => (~(((~(((((in @ X1) @ X3) @ eigen__0) => (~((((in @ X2) @ X3) @ eigen__0)))))) => (((subset @ ((unordered_pair @ X1) @ X2)) @ X3) @ eigen__0))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 94.02/92.36 thf(sP8,plain,sP8 <=> (![X1:mu]:((exists_in_world @ ((unordered_pair @ eigen__1) @ X1)) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP8])])). % 94.02/92.36 thf(sP9,plain,sP9 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((~(((((in @ eigen__1) @ X1) @ eigen__0) => (~((((in @ X2) @ X1) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ X2)) @ X1)) @ X1) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 94.02/92.36 thf(sP10,plain,sP10 <=> ((exists_in_world @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP10])])). % 94.02/92.36 thf(sP11,plain,sP11 <=> (((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP11])])). % 94.02/92.36 thf(sP12,plain,sP12 <=> (sP10 => sP4),introduced(definition,[new_symbols(definition,[sP12])])). % 94.02/92.36 thf(sP13,plain,sP13 <=> (sP6 => sP2),introduced(definition,[new_symbols(definition,[sP13])])). % 94.02/92.36 thf(sP14,plain,sP14 <=> (sP5 => sP9),introduced(definition,[new_symbols(definition,[sP14])])). % 94.02/92.36 thf(sP15,plain,sP15 <=> (sP10 => ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2)) @ eigen__2) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP15])])). % 94.02/92.36 thf(sP16,plain,sP16 <=> (![X1:mu]:(![X2:mu]:((exists_in_world @ ((unordered_pair @ X1) @ X2)) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP16])])). % 94.02/92.36 thf(sP17,plain,sP17 <=> (sP6 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ X1) @ eigen__2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ X1)) @ eigen__2)) @ eigen__2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP17])])). % 94.02/92.36 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:mu]:(![X3:mu]:((exists_in_world @ ((unordered_pair @ X2) @ X3)) @ X1)))),introduced(definition,[new_symbols(definition,[sP18])])). % 94.02/92.36 thf(sP19,plain,sP19 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ X1) @ eigen__2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ X1)) @ eigen__2)) @ eigen__2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP19])])). % 94.02/92.36 thf(sP20,plain,sP20 <=> ((exists_in_world @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__0),introduced(definition,[new_symbols(definition,[sP20])])). % 94.02/92.36 thf(sP21,plain,sP21 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((subset @ X1) @ X2) @ eigen__0) => (((qmltpeq @ ((set_union2 @ X1) @ X2)) @ X2) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP21])])). % 94.02/92.36 thf(sP22,plain,sP22 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((((subset @ X2) @ X3) @ X1) => (((qmltpeq @ ((set_union2 @ X2) @ X3)) @ X3) @ X1))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 94.02/92.36 thf(sP23,plain,sP23 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (![X4:mu]:(((exists_in_world @ X4) @ X1) => ((~(((((in @ X2) @ X3) @ X1) => (~((((in @ X4) @ X3) @ X1)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X2) @ X4)) @ X3)) @ X3) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 94.02/92.36 thf(sP24,plain,sP24 <=> (sP6 => (~(((sP11 => (~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0))))))) => (~(((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0)))))) => sP11))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 94.02/92.36 thf(sP25,plain,sP25 <=> (sP5 => sP3),introduced(definition,[new_symbols(definition,[sP25])])). % 94.02/92.36 thf(sP26,plain,sP26 <=> ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0)))))) => sP11),introduced(definition,[new_symbols(definition,[sP26])])). % 94.02/92.36 thf(sP27,plain,sP27 <=> (sP20 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1) @ eigen__0) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1)) @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP27])])). % 94.02/92.36 thf(sP28,plain,sP28 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => ((~(((((in @ X1) @ X2) @ eigen__0) => (~((((in @ X3) @ X2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X1) @ X3)) @ X2)) @ X2) @ eigen__0)))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 94.02/92.36 thf(sP29,plain,sP29 <=> ((~(((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0)))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2)) @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP29])])). % 94.02/92.36 thf(sP30,plain,sP30 <=> (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ eigen__2)) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP30])])). % 94.02/92.36 thf(sP31,plain,sP31 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((subset @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1) @ eigen__0) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ eigen__1) @ eigen__3)) @ X1)) @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP31])])). % 94.02/92.36 thf(sP32,plain,sP32 <=> ((((in @ eigen__1) @ eigen__2) @ eigen__0) => (~((((in @ eigen__3) @ eigen__2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP32])])). % 94.02/92.36 thf(sP33,plain,sP33 <=> ((sP11 => (~(sP32))) => (~(sP26))),introduced(definition,[new_symbols(definition,[sP33])])). % 94.02/92.36 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 94.02/92.36 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 94.02/92.36 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 94.02/92.36 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 94.02/92.36 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 94.02/92.36 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 94.02/92.36 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 94.02/92.36 thf(def_mvalid,definition,(mvalid = (!!))). % 94.02/92.36 thf(t48_zfmisc_1,conjecture,(![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (![X4:mu]:(((exists_in_world @ X4) @ X1) => ((~((~((~(((~((~((((in @ X2) @ X3) @ X1))))) => (~((((in @ X4) @ X3) @ X1)))))))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X2) @ X4)) @ X3)) @ X3) @ X1)))))))))). % 94.02/92.36 thf(h2,negated_conjecture,(~(sP23)),inference(assume_negation,[status(cth)],[t48_zfmisc_1])). % 94.02/92.36 thf(1,plain,((~(sP26) | sP32) | sP11),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(2,plain,(sP33 | sP26),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(3,plain,(~(sP4) | sP24),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(4,plain,((~(sP24) | ~(sP6)) | ~(sP33)),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(5,plain,(~(sP18) | sP16),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(6,plain,(~(sP16) | sP8),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(7,plain,(~(sP8) | sP20),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(8,plain,(~(sP3) | sP12),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(9,plain,((~(sP12) | ~(sP10)) | sP4),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(10,plain,(~(sP21) | sP27),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(11,plain,((~(sP27) | ~(sP20)) | sP31),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(12,plain,(~(sP31) | sP13),inference(all_rule,[status(thm)],[])). % 94.02/92.36 thf(13,plain,((~(sP13) | ~(sP6)) | sP2),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(14,plain,((~(sP2) | ~(sP11)) | sP30),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(15,plain,(sP29 | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 94.02/92.36 thf(16,plain,(sP29 | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(17,plain,(sP15 | ~(sP29)),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(18,plain,(sP15 | sP10),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(19,plain,(sP19 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 94.02/92.37 thf(20,plain,(sP17 | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(21,plain,(sP17 | sP6),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(22,plain,(sP9 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 94.02/92.37 thf(23,plain,(~(sP1) | sP7),inference(all_rule,[status(thm)],[])). % 94.02/92.37 thf(24,plain,(~(sP7) | sP25),inference(all_rule,[status(thm)],[])). % 94.02/92.37 thf(25,plain,((~(sP25) | ~(sP5)) | sP3),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(26,plain,(~(sP22) | sP21),inference(all_rule,[status(thm)],[])). % 94.02/92.37 thf(27,plain,(sP14 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(28,plain,(sP14 | sP5),inference(prop_rule,[status(thm)],[])). % 94.02/92.37 thf(29,plain,(sP28 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 94.02/92.37 thf(30,plain,(sP23 | ~(sP28)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 94.02/92.37 thf(existence_of_unordered_pair_ax,axiom,sP18). % 94.02/92.37 thf(t12_xboole_1,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mimplies @ ((subset @ X1) @ X2)) @ ((qmltpeq @ ((set_union2 @ X1) @ X2)) @ X2)))))))). % 94.02/92.37 thf(31,plain,sP22,inference(preprocess,[status(thm)],[t12_xboole_1]). % 94.02/92.37 thf(t38_zfmisc_1,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:(mforall_ind @ (^[X3:mu]:((mequiv @ ((subset @ ((unordered_pair @ X1) @ X2)) @ X3)) @ ((mand @ ((in @ X1) @ X3)) @ ((in @ X2) @ X3))))))))))). % 94.02/92.37 thf(32,plain,sP1,inference(preprocess,[status(thm)],[t38_zfmisc_1]). % 94.02/92.37 thf(33,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,existence_of_unordered_pair_ax,31,32,h2])). % 94.02/92.37 thf(34,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[33,h1])). % 94.02/92.37 thf(35,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[34,h0])). % 94.02/92.37 thf(0,theorem,(![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (![X4:mu]:(((exists_in_world @ X4) @ X1) => ((~((~((~(((~((~((((in @ X2) @ X3) @ X1))))) => (~((((in @ X4) @ X3) @ X1)))))))))) => (((qmltpeq @ ((set_union2 @ ((unordered_pair @ X2) @ X4)) @ X3)) @ X3) @ X1))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[33,h2])). % 94.02/92.37 % SZS output end Proof %------------------------------------------------------------------------------