TSTP Solution File: SYN397^7 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN397^7 : 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 : n028.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 : Thu Jul 21 11:43:26 EDT 2022
% Result : Theorem 1.14s 1.45s
% Output : Proof 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN397^7 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jul 12 00:03:44 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.14/1.45 % SZS status Theorem
% 1.14/1.45 % Mode: mode213
% 1.14/1.45 % Inferences: 4662
% 1.14/1.45 % SZS output start Proof
% 1.14/1.45 thf(ty_mu, type, mu : $tType).
% 1.14/1.45 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 1.14/1.45 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.14/1.45 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.14/1.45 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.14/1.45 thf(ty_eigen__4, type, eigen__4 : $i).
% 1.14/1.45 thf(ty_eigen__19, type, eigen__19 : $i).
% 1.14/1.45 thf(ty_eigen__3, type, eigen__3 : mu).
% 1.14/1.45 thf(ty_eigen__20, type, eigen__20 : mu).
% 1.14/1.45 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 1.14/1.45 thf(ty_eigen__18, type, eigen__18 : $i).
% 1.14/1.45 thf(ty_f, type, f : (mu>$i>$o)).
% 1.14/1.45 thf(sP1,plain,sP1 <=> ((rel_s4 @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.14/1.45 thf(sP2,plain,sP2 <=> ((exists_in_world @ eigen__20) @ eigen__19),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.14/1.45 thf(sP3,plain,sP3 <=> (![X1:mu]:(![X2:$i]:(![X3:$i]:((~((((exists_in_world @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((exists_in_world @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.14/1.45 thf(sP4,plain,sP4 <=> (((exists_in_world @ eigen__3) @ eigen__2) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.14/1.45 thf(sP5,plain,sP5 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__19) => (![X2:$i]:(((rel_s4 @ eigen__19) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.14/1.45 thf(sP6,plain,sP6 <=> (![X1:$i]:(((rel_s4 @ eigen__19) @ X1) => ((f @ eigen__20) @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.14/1.45 thf(sP7,plain,sP7 <=> (![X1:$i]:((~((((rel_s4 @ eigen__1) @ eigen__2) => (~(((rel_s4 @ eigen__2) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.14/1.45 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.14/1.45 thf(sP9,plain,sP9 <=> (![X1:$i]:((~((((exists_in_world @ eigen__3) @ eigen__2) => (~(((rel_s4 @ eigen__2) @ X1)))))) => ((exists_in_world @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.14/1.45 thf(sP10,plain,sP10 <=> ((~(sP4)) => ((exists_in_world @ eigen__3) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.14/1.45 thf(sP11,plain,sP11 <=> ((~((((rel_s4 @ eigen__1) @ eigen__2) => (~(sP1))))) => ((rel_s4 @ eigen__1) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.14/1.45 thf(sP12,plain,sP12 <=> ((rel_s4 @ eigen__19) @ eigen__19),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.14/1.45 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_s4 @ eigen__18) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((f @ X2) @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.14/1.45 thf(sP14,plain,sP14 <=> (((exists_in_world @ eigen__3) @ eigen__4) => (~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((f @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.14/1.45 thf(sP15,plain,sP15 <=> (((rel_s4 @ eigen__1) @ eigen__4) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__4) => (~((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((f @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.14/1.45 thf(sP16,plain,sP16 <=> (sP12 => (~(sP6))),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.14/1.45 thf(sP17,plain,sP17 <=> (![X1:$i]:(((rel_s4 @ eigen__19) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ eigen__20) @ X2))))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.14/1.45 thf(sP18,plain,sP18 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.14/1.45 thf(sP19,plain,sP19 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__1) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.14/1.45 thf(sP20,plain,sP20 <=> ((rel_s4 @ eigen__1) @ eigen__4),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.14/1.45 thf(sP21,plain,sP21 <=> ((exists_in_world @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.14/1.45 thf(sP22,plain,sP22 <=> (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((f @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.14/1.45 thf(sP23,plain,sP23 <=> (![X1:$i]:(![X2:$i]:((~((((exists_in_world @ eigen__3) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((exists_in_world @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.14/1.45 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.14/1.45 thf(sP25,plain,sP25 <=> ((rel_s4 @ eigen__18) @ eigen__19),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.14/1.45 thf(sP26,plain,sP26 <=> ((exists_in_world @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP26])])).
% 1.14/1.45 thf(sP27,plain,sP27 <=> (sP25 => sP5),introduced(definition,[new_symbols(definition,[sP27])])).
% 1.14/1.45 thf(sP28,plain,sP28 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP28])])).
% 1.14/1.45 thf(sP29,plain,sP29 <=> (sP28 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP29])])).
% 1.14/1.45 thf(sP30,plain,sP30 <=> (sP2 => sP17),introduced(definition,[new_symbols(definition,[sP30])])).
% 1.14/1.45 thf(sP31,plain,sP31 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__4) => (~((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((f @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP31])])).
% 1.14/1.45 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 1.14/1.45 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.14/1.45 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.14/1.45 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 1.14/1.45 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 1.14/1.45 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 1.14/1.45 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 1.14/1.45 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 1.14/1.45 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.14/1.45 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 1.14/1.45 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 1.14/1.45 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 1.14/1.45 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 1.14/1.45 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 1.14/1.45 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 1.14/1.45 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 1.14/1.45 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 1.14/1.45 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 1.14/1.45 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 1.14/1.45 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 1.14/1.45 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 1.14/1.45 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)))))))).
% 1.14/1.45 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 1.14/1.45 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 1.14/1.45 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 1.14/1.45 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 1.14/1.45 thf(def_mvalid,definition,(mvalid = (!!))).
% 1.14/1.45 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.14/1.45 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.14/1.45 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.14/1.45 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 1.14/1.45 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 1.14/1.45 thf(kalish204,conjecture,(![X1:$i]:(~(((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6)))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5))))))))))))))))))))))).
% 1.14/1.45 thf(h0,negated_conjecture,(~((![X1:$i]:(~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6)))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5)))))))))))))))))))),inference(assume_negation,[status(cth)],[kalish204])).
% 1.14/1.45 thf(h1,assumption,((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((f @ X3) @ X4))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((f @ X3) @ X5)))))))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((f @ X3) @ X5))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((f @ X3) @ X4))))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h2,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((f @ X3) @ X4))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((f @ X3) @ X5)))))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h3,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((f @ X3) @ X5))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((f @ X3) @ X4)))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h4,assumption,(~((((rel_s4 @ eigen__0) @ eigen__1) => (sP8 => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((f @ X2) @ X4))))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h5,assumption,((rel_s4 @ eigen__0) @ eigen__1),introduced(assumption,[])).
% 1.14/1.45 thf(h6,assumption,(~((sP8 => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((f @ X2) @ X4)))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h7,assumption,sP8,introduced(assumption,[])).
% 1.14/1.45 thf(h8,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((f @ X2) @ X4))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h9,assumption,(~((sP28 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ X1) @ X3)))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h10,assumption,sP28,introduced(assumption,[])).
% 1.14/1.45 thf(h11,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ X1) @ X3))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h12,assumption,(~((sP21 => (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ eigen__3) @ X2)))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h13,assumption,sP21,introduced(assumption,[])).
% 1.14/1.45 thf(h14,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ eigen__3) @ X2))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h15,assumption,(~((sP1 => (~(sP22))))),introduced(assumption,[])).
% 1.14/1.45 thf(h16,assumption,sP1,introduced(assumption,[])).
% 1.14/1.45 thf(h17,assumption,sP22,introduced(assumption,[])).
% 1.14/1.45 thf(1,plain,(~(sP7) | sP11),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(2,plain,((~(sP11) | sP29) | sP20),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(3,plain,((~(sP29) | ~(sP28)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(4,plain,(~(sP19) | sP7),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(5,plain,(~(sP24) | sP19),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(6,plain,(~(sP9) | sP10),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(7,plain,((~(sP10) | sP4) | sP26),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(8,plain,((~(sP4) | ~(sP21)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(9,plain,(~(sP3) | sP23),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(10,plain,(~(sP23) | sP9),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(11,plain,(~(sP8) | sP15),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(12,plain,((~(sP15) | ~(sP20)) | sP31),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(13,plain,(~(sP31) | sP14),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(14,plain,((~(sP14) | ~(sP26)) | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(a2,axiom,(mtransitive @ rel_s4)).
% 1.14/1.45 thf(15,plain,sP24,inference(preprocess,[status(thm)],[a2]).
% 1.14/1.45 thf(cumulative_ax,axiom,sP3).
% 1.14/1.45 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,cumulative_ax,h7,h10,h13,h16,h17])).
% 1.14/1.45 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,16,h16,h17])).
% 1.14/1.45 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,17,h15])).
% 1.14/1.45 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,18,h13,h14])).
% 1.14/1.45 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,19,h12])).
% 1.14/1.45 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,20,h10,h11])).
% 1.14/1.45 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,21,h9])).
% 1.14/1.45 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,22,h7,h8])).
% 1.14/1.45 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,23,h5,h6])).
% 1.14/1.45 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,24,h4])).
% 1.14/1.45 thf(h18,assumption,(~((((rel_s4 @ eigen__0) @ eigen__18) => (sP13 => (![X1:$i]:(((rel_s4 @ eigen__18) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h19,assumption,((rel_s4 @ eigen__0) @ eigen__18),introduced(assumption,[])).
% 1.14/1.45 thf(h20,assumption,(~((sP13 => (![X1:$i]:(((rel_s4 @ eigen__18) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h21,assumption,sP13,introduced(assumption,[])).
% 1.14/1.45 thf(h22,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__18) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h23,assumption,(~((sP25 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__19) => (~((![X2:$i]:(((rel_s4 @ eigen__19) @ X2) => ((f @ X1) @ X2)))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h24,assumption,sP25,introduced(assumption,[])).
% 1.14/1.45 thf(h25,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__19) => (~((![X2:$i]:(((rel_s4 @ eigen__19) @ X2) => ((f @ X1) @ X2))))))))),introduced(assumption,[])).
% 1.14/1.45 thf(h26,assumption,(~((sP2 => (~(sP6))))),introduced(assumption,[])).
% 1.14/1.45 thf(h27,assumption,sP2,introduced(assumption,[])).
% 1.14/1.45 thf(h28,assumption,sP6,introduced(assumption,[])).
% 1.14/1.45 thf(26,plain,(~(sP18) | sP12),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(27,plain,(~(sP17) | sP16),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(28,plain,((~(sP16) | ~(sP12)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(29,plain,(~(sP5) | sP30),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(30,plain,((~(sP30) | ~(sP2)) | sP17),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(31,plain,(~(sP13) | sP27),inference(all_rule,[status(thm)],[])).
% 1.14/1.45 thf(32,plain,((~(sP27) | ~(sP25)) | sP5),inference(prop_rule,[status(thm)],[])).
% 1.14/1.45 thf(a1,axiom,(mreflexive @ rel_s4)).
% 1.14/1.45 thf(33,plain,sP18,inference(preprocess,[status(thm)],[a1]).
% 1.14/1.45 thf(34,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h19,h20,h18,h3,h1,h0])],[26,27,28,29,30,31,32,33,h21,h24,h27,h28])).
% 1.14/1.45 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h19,h20,h18,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,34,h27,h28])).
% 1.14/1.45 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h19,h20,h18,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__20)],[h25,35,h26])).
% 1.14/1.45 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h19,h20,h18,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,36,h24,h25])).
% 1.14/1.45 thf(38,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h18,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__19)],[h22,37,h23])).
% 1.14/1.45 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,38,h21,h22])).
% 1.14/1.45 thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,39,h19,h20])).
% 1.14/1.45 thf(41,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__18)],[h3,40,h18])).
% 1.14/1.45 thf(42,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,25,41,h2,h3])).
% 1.14/1.45 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,42,h1])).
% 1.14/1.45 thf(0,theorem,(![X1:$i]:(~(((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6)))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((f @ X4) @ X6))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((f @ X4) @ X5)))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[43,h0])).
% 1.14/1.45 % SZS output end Proof
%------------------------------------------------------------------------------