TSTP Solution File: SET576^7 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET576^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : 600s
% DateTime : Tue Jul 19 04:54:01 EDT 2022
% Result : Theorem 1.99s 2.24s
% Output : Proof 1.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET576^7 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.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 : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:40:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.99/2.24 % SZS status Theorem
% 1.99/2.24 % Mode: mode506
% 1.99/2.24 % Inferences: 38784
% 1.99/2.24 % SZS output start Proof
% 1.99/2.24 thf(ty_mu, type, mu : $tType).
% 1.99/2.24 thf(ty_eigen__2, type, eigen__2 : mu).
% 1.99/2.24 thf(ty_eigen__1, type, eigen__1 : mu).
% 1.99/2.24 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.99/2.24 thf(ty_member, type, member : (mu>mu>$i>$o)).
% 1.99/2.24 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 1.99/2.24 thf(ty_disjoint, type, disjoint : (mu>mu>$i>$o)).
% 1.99/2.24 thf(ty_intersect, type, intersect : (mu>mu>$i>$o)).
% 1.99/2.24 thf(h0, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.99/2.24 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) => ((((member @ X3) @ X1) @ eigen__0) => (~((((member @ X3) @ X2) @ eigen__0)))))) => (((disjoint @ X1) @ X2) @ eigen__0))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 1.99/2.24 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 1.99/2.24 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((![X4:mu]:(((exists_in_world @ X4) @ X1) => ((((member @ X4) @ X2) @ X1) => (~((((member @ X4) @ X3) @ X1)))))) => (((disjoint @ X2) @ X3) @ X1)))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.99/2.24 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) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0)))))) => (((disjoint @ eigen__1) @ X1) @ eigen__0))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 1.99/2.24 thf(sP1,plain,sP1 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (~((((((intersect @ X1) @ X2) @ eigen__0) => (~((![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => ((((member @ X3) @ X1) @ eigen__0) => (~((((member @ X3) @ X2) @ eigen__0))))))))) => (~(((~((![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => ((((member @ X3) @ X1) @ eigen__0) => (~((((member @ X3) @ X2) @ eigen__0)))))))) => (((intersect @ X1) @ X2) @ eigen__0))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.99/2.24 thf(sP2,plain,sP2 <=> (((((intersect @ eigen__1) @ eigen__2) @ eigen__0) => (~((![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((member @ X1) @ eigen__1) @ eigen__0) => (~((((member @ X1) @ eigen__2) @ eigen__0))))))))) => (~(((~((![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((member @ X1) @ eigen__1) @ eigen__0) => (~((((member @ X1) @ eigen__2) @ eigen__0)))))))) => (((intersect @ eigen__1) @ eigen__2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.99/2.24 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (~((((((disjoint @ X2) @ X3) @ X1) => (~((((intersect @ X2) @ X3) @ X1)))) => (~(((~((((intersect @ X2) @ X3) @ X1))) => (((disjoint @ X2) @ X3) @ X1)))))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.99/2.24 thf(sP4,plain,sP4 <=> (((((disjoint @ eigen__1) @ eigen__2) @ eigen__0) => (~((((intersect @ eigen__1) @ eigen__2) @ eigen__0)))) => (~(((~((((intersect @ eigen__1) @ eigen__2) @ eigen__0))) => (((disjoint @ eigen__1) @ eigen__2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.99/2.24 thf(sP5,plain,sP5 <=> (((exists_in_world @ eigen__1) @ eigen__0) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0)))))) => (((disjoint @ eigen__1) @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.99/2.24 thf(sP6,plain,sP6 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((((((disjoint @ eigen__1) @ X1) @ eigen__0) => (~((((intersect @ eigen__1) @ X1) @ eigen__0)))) => (~(((~((((intersect @ eigen__1) @ X1) @ eigen__0))) => (((disjoint @ eigen__1) @ X1) @ eigen__0))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.99/2.24 thf(sP7,plain,sP7 <=> (((exists_in_world @ eigen__1) @ eigen__0) => sP6),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.99/2.24 thf(sP8,plain,sP8 <=> (((exists_in_world @ eigen__2) @ eigen__0) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.99/2.24 thf(sP9,plain,sP9 <=> ((~((((intersect @ eigen__1) @ eigen__2) @ eigen__0))) => (((disjoint @ eigen__1) @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.99/2.24 thf(sP10,plain,sP10 <=> (((intersect @ eigen__1) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.99/2.24 thf(sP11,plain,sP11 <=> (((exists_in_world @ eigen__2) @ eigen__0) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.99/2.24 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => (~((((((intersect @ X2) @ X3) @ X1) => (~((![X4:mu]:(((exists_in_world @ X4) @ X1) => ((((member @ X4) @ X2) @ X1) => (~((((member @ X4) @ X3) @ X1))))))))) => (~(((~((![X4:mu]:(((exists_in_world @ X4) @ X1) => ((((member @ X4) @ X2) @ X1) => (~((((member @ X4) @ X3) @ X1)))))))) => (((intersect @ X2) @ X3) @ X1)))))))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.99/2.24 thf(sP13,plain,sP13 <=> (((disjoint @ eigen__1) @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.99/2.24 thf(sP14,plain,sP14 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => (~((((((disjoint @ X1) @ X2) @ eigen__0) => (~((((intersect @ X1) @ X2) @ eigen__0)))) => (~(((~((((intersect @ X1) @ X2) @ eigen__0))) => (((disjoint @ X1) @ X2) @ eigen__0))))))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.99/2.24 thf(sP15,plain,sP15 <=> (((exists_in_world @ eigen__2) @ eigen__0) => ((![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((member @ X1) @ eigen__1) @ eigen__0) => (~((((member @ X1) @ eigen__2) @ eigen__0)))))) => sP13)),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.99/2.24 thf(sP16,plain,sP16 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((![X3:mu]:(((exists_in_world @ X3) @ eigen__0) => ((((member @ X3) @ X1) @ eigen__0) => (~((((member @ X3) @ X2) @ eigen__0)))))) => (((disjoint @ X1) @ X2) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.99/2.24 thf(sP17,plain,sP17 <=> ((exists_in_world @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.99/2.24 thf(sP18,plain,sP18 <=> (sP17 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((((((intersect @ eigen__1) @ X1) @ eigen__0) => (~((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0))))))))) => (~(((~((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0)))))))) => (((intersect @ eigen__1) @ X1) @ eigen__0)))))))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.99/2.24 thf(sP19,plain,sP19 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((((member @ X1) @ eigen__1) @ eigen__0) => (~((((member @ X1) @ eigen__2) @ eigen__0)))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.99/2.24 thf(sP20,plain,sP20 <=> (![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((![X4:mu]:(((exists_in_world @ X4) @ X1) => ((((member @ X4) @ X2) @ X1) => (~((((member @ X4) @ X3) @ X1)))))) => (((disjoint @ X2) @ X3) @ X1))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.99/2.24 thf(sP21,plain,sP21 <=> (sP10 => (~(sP19))),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.99/2.24 thf(sP22,plain,sP22 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0)))))) => (((disjoint @ eigen__1) @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.99/2.24 thf(sP23,plain,sP23 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((((((intersect @ eigen__1) @ X1) @ eigen__0) => (~((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0))))))))) => (~(((~((![X2:mu]:(((exists_in_world @ X2) @ eigen__0) => ((((member @ X2) @ eigen__1) @ eigen__0) => (~((((member @ X2) @ X1) @ eigen__0)))))))) => (((intersect @ eigen__1) @ X1) @ eigen__0))))))))),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.99/2.24 thf(sP24,plain,sP24 <=> (sP19 => sP13),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.99/2.24 thf(sP25,plain,sP25 <=> ((exists_in_world @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.99/2.24 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 1.99/2.24 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.99/2.24 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.99/2.24 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 1.99/2.24 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 1.99/2.24 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 1.99/2.24 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 1.99/2.24 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 1.99/2.24 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.99/2.24 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 1.99/2.24 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 1.99/2.24 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 1.99/2.24 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 1.99/2.24 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 1.99/2.24 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 1.99/2.24 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 1.99/2.24 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 1.99/2.24 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 1.99/2.24 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 1.99/2.24 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 1.99/2.24 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 1.99/2.24 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)))))))).
% 1.99/2.24 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 1.99/2.24 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 1.99/2.24 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 1.99/2.24 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 1.99/2.24 thf(def_mvalid,definition,(mvalid = (!!))).
% 1.99/2.24 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.99/2.24 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.99/2.24 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.99/2.24 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 1.99/2.24 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 1.99/2.24 thf(prove_th17,conjecture,(![X1:$i]:(![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:mu]:(((exists_in_world @ X3) @ X1) => ((~((~((![X4:mu]:(((exists_in_world @ X4) @ X1) => ((~((~((((member @ X4) @ X2) @ X1))))) => (~((((member @ X4) @ X3) @ X1)))))))))) => (((disjoint @ X2) @ X3) @ X1)))))))).
% 1.99/2.24 thf(h2,negated_conjecture,(~(sP20)),inference(assume_negation,[status(cth)],[prove_th17])).
% 1.99/2.24 thf(1,plain,((~(sP21) | ~(sP10)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(2,plain,((~(sP9) | sP10) | sP13),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(3,plain,(sP4 | sP9),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(4,plain,(~(sP6) | sP11),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(5,plain,((~(sP11) | ~(sP25)) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(6,plain,(sP2 | sP21),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(7,plain,(~(sP23) | sP8),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(8,plain,((~(sP8) | ~(sP25)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(9,plain,(~(sP1) | sP18),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(10,plain,((~(sP18) | ~(sP17)) | sP23),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(11,plain,(~(sP14) | sP7),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(12,plain,((~(sP7) | ~(sP17)) | sP6),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(13,plain,(~(sP12) | sP1),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(14,plain,(~(sP3) | sP14),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(15,plain,(sP24 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(16,plain,(sP24 | sP19),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(17,plain,(sP15 | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(18,plain,(sP15 | sP25),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(19,plain,(sP22 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 1.99/2.24 thf(20,plain,(sP5 | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(21,plain,(sP5 | sP17),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(22,plain,(sP16 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 1.99/2.24 thf(23,plain,(sP20 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])).
% 1.99/2.24 thf(disjoint_defn,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mequiv @ ((disjoint @ X1) @ X2)) @ (mnot @ ((intersect @ X1) @ X2))))))))).
% 1.99/2.24 thf(24,plain,sP3,inference(preprocess,[status(thm)],[disjoint_defn]).
% 1.99/2.24 thf(intersect_defn,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mequiv @ ((intersect @ X1) @ X2)) @ (mexists_ind @ (^[X3:mu]:((mand @ ((member @ X3) @ X1)) @ ((member @ X3) @ X2))))))))))).
% 1.99/2.24 thf(25,plain,sP12,inference(preprocess,[status(thm)],[intersect_defn]).
% 1.99/2.24 thf(26,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,h2])).
% 1.99/2.24 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1])).
% 1.99/2.24 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0])).
% 1.99/2.24 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) => ((~((~((((member @ X4) @ X2) @ X1))))) => (~((((member @ X4) @ X3) @ X1)))))))))) => (((disjoint @ X2) @ X3) @ X1))))))),inference(contra,[status(thm),contra(discharge,[h2])],[26,h2])).
% 1.99/2.24 % SZS output end Proof
%------------------------------------------------------------------------------