TSTP Solution File: SWV441^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWV441^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : Wed Jul 20 21:25:09 EDT 2022
% Result : Theorem 12.80s 13.02s
% Output : Proof 12.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV441^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 03:16:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 12.80/13.02 % SZS status Theorem
% 12.80/13.02 % Mode: mode515
% 12.80/13.02 % Inferences: 5008
% 12.80/13.02 % SZS output start Proof
% 12.80/13.02 thf(ty_individuals, type, individuals : $tType).
% 12.80/13.02 thf(ty_eigen__6, type, eigen__6 : $i).
% 12.80/13.02 thf(ty_relr, type, relr : ($i>$i>$o)).
% 12.80/13.02 thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
% 12.80/13.02 thf(ty_eigen__7, type, eigen__7 : $i).
% 12.80/13.02 thf(ty_eigen__1, type, eigen__1 : ($i>$o)).
% 12.80/13.02 thf(ty_eigen__0, type, eigen__0 : individuals).
% 12.80/13.02 thf(ty_eigen__4, type, eigen__4 : $i).
% 12.80/13.02 thf(ty_eigen__5, type, eigen__5 : $i).
% 12.80/13.02 thf(ty_reli, type, reli : ($i>$i>$o)).
% 12.80/13.02 thf(ty_eigen__3, type, eigen__3 : $i).
% 12.80/13.02 thf(ty_eigen__8, type, eigen__8 : $i).
% 12.80/13.02 thf(ty_princ_inj, type, princ_inj : (individuals>$i>$o)).
% 12.80/13.02 thf(sP1,plain,sP1 <=> (![X1:$i]:(((reli @ eigen__8) @ X1) => ((princ_inj @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP1])])).
% 12.80/13.02 thf(sP2,plain,sP2 <=> (((reli @ eigen__7) @ eigen__8) => (sP1 => (eigen__1 @ eigen__8))),introduced(definition,[new_symbols(definition,[sP2])])).
% 12.80/13.02 thf(sP3,plain,sP3 <=> ((reli @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP3])])).
% 12.80/13.02 thf(sP4,plain,sP4 <=> (![X1:$i]:(((reli @ eigen__7) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => ((princ_inj @ eigen__0) @ X2))) => (![X2:$i]:(((reli @ X1) @ X2) => ((eigen__1 @ X2) => (eigen__2 @ X2))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 12.80/13.02 thf(sP5,plain,sP5 <=> (![X1:$i]:(((relr @ eigen__6) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => ((princ_inj @ eigen__0) @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => ((eigen__1 @ X3) => (eigen__2 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 12.80/13.02 thf(sP6,plain,sP6 <=> (((relr @ eigen__6) @ eigen__7) => sP4),introduced(definition,[new_symbols(definition,[sP6])])).
% 12.80/13.02 thf(sP7,plain,sP7 <=> ((reli @ eigen__5) @ eigen__6),introduced(definition,[new_symbols(definition,[sP7])])).
% 12.80/13.02 thf(sP8,plain,sP8 <=> ((eigen__1 @ eigen__8) => (eigen__2 @ eigen__8)),introduced(definition,[new_symbols(definition,[sP8])])).
% 12.80/13.02 thf(sP9,plain,sP9 <=> ((![X1:$i]:(((reli @ eigen__8) @ X1) => ((eigen__1 @ X1) => (eigen__2 @ X1)))) => sP8),introduced(definition,[new_symbols(definition,[sP9])])).
% 12.80/13.02 thf(sP10,plain,sP10 <=> (sP1 => (eigen__1 @ eigen__8)),introduced(definition,[new_symbols(definition,[sP10])])).
% 12.80/13.02 thf(sP11,plain,sP11 <=> ((![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__1 @ X4) => (eigen__2 @ X4))))))))))) => (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__1 @ X5) => (eigen__2 @ X5)))))))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 12.80/13.02 thf(sP12,plain,sP12 <=> (sP7 => sP5),introduced(definition,[new_symbols(definition,[sP12])])).
% 12.80/13.02 thf(sP13,plain,sP13 <=> (![X1:$i]:(((reli @ eigen__5) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__1 @ X4) => (eigen__2 @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 12.80/13.02 thf(sP14,plain,sP14 <=> (sP1 => (![X1:$i]:(((reli @ eigen__8) @ X1) => ((eigen__1 @ X1) => (eigen__2 @ X1))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 12.80/13.02 thf(sP15,plain,sP15 <=> (eigen__1 @ eigen__8),introduced(definition,[new_symbols(definition,[sP15])])).
% 12.80/13.02 thf(sP16,plain,sP16 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__1 @ X5) => (eigen__2 @ X5))))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => ((princ_inj @ eigen__0) @ X6))) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__1 @ X6) => (eigen__2 @ X6))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 12.80/13.02 thf(sP17,plain,sP17 <=> (![X1:$i]:(((reli @ eigen__5) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (eigen__1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 12.80/13.02 thf(sP18,plain,sP18 <=> (((reli @ eigen__7) @ eigen__8) => sP14),introduced(definition,[new_symbols(definition,[sP18])])).
% 12.80/13.02 thf(sP19,plain,sP19 <=> (sP3 => sP13),introduced(definition,[new_symbols(definition,[sP19])])).
% 12.80/13.02 thf(sP20,plain,sP20 <=> (sP7 => (![X1:$i]:(((relr @ eigen__6) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => ((princ_inj @ eigen__0) @ X3))) => (eigen__1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 12.80/13.02 thf(sP21,plain,sP21 <=> (((relr @ eigen__6) @ eigen__7) => (![X1:$i]:(((reli @ eigen__7) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => ((princ_inj @ eigen__0) @ X2))) => (eigen__1 @ X1))))),introduced(definition,[new_symbols(definition,[sP21])])).
% 12.80/13.02 thf(sP22,plain,sP22 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 12.80/13.02 thf(sP23,plain,sP23 <=> (![X1:$i]:(((reli @ eigen__8) @ X1) => ((eigen__1 @ X1) => (eigen__2 @ X1)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 12.80/13.02 thf(sP24,plain,sP24 <=> (![X1:$i]:(((relr @ eigen__6) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => ((princ_inj @ eigen__0) @ X3))) => (eigen__1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 12.80/13.02 thf(sP25,plain,sP25 <=> ((reli @ eigen__7) @ eigen__8),introduced(definition,[new_symbols(definition,[sP25])])).
% 12.80/13.02 thf(sP26,plain,sP26 <=> (eigen__2 @ eigen__8),introduced(definition,[new_symbols(definition,[sP26])])).
% 12.80/13.02 thf(sP27,plain,sP27 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => ((eigen__1 @ X2) => (eigen__2 @ X2)))) => ((eigen__1 @ X1) => (eigen__2 @ X1)))),introduced(definition,[new_symbols(definition,[sP27])])).
% 12.80/13.02 thf(sP28,plain,sP28 <=> (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => ((eigen__1 @ X4) => (eigen__2 @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP28])])).
% 12.80/13.02 thf(sP29,plain,sP29 <=> (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__1 @ X5) => (eigen__2 @ X5))))))))))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 12.80/13.02 thf(sP30,plain,sP30 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 12.80/13.02 thf(sP31,plain,sP31 <=> ((relr @ eigen__6) @ eigen__7),introduced(definition,[new_symbols(definition,[sP31])])).
% 12.80/13.02 thf(sP32,plain,sP32 <=> (![X1:$i]:(((reli @ eigen__7) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => ((princ_inj @ eigen__0) @ X2))) => (eigen__1 @ X1)))),introduced(definition,[new_symbols(definition,[sP32])])).
% 12.80/13.02 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 12.80/13.02 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 12.80/13.02 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 12.80/13.02 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 12.80/13.02 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 12.80/13.02 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 12.80/13.02 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
% 12.80/13.02 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 12.80/13.02 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 12.80/13.02 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
% 12.80/13.02 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
% 12.80/13.02 thf(def_mvalid,definition,(mvalid = (!!))).
% 12.80/13.02 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 12.80/13.02 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 12.80/13.02 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 12.80/13.02 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))).
% 12.80/13.02 thf(def_cs4_and,definition,(cs4_and = mand)).
% 12.80/13.02 thf(def_cs4_or,definition,(cs4_or = mor)).
% 12.80/13.02 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))).
% 12.80/13.02 thf(def_cs4_true,definition,(cs4_true = mtrue)).
% 12.80/13.02 thf(def_cs4_false,definition,(cs4_false = mfalse)).
% 12.80/13.02 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))).
% 12.80/13.02 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))).
% 12.80/13.02 thf(def_cs4_valid,definition,(cs4_valid = mvalid)).
% 12.80/13.02 thf(def_bl_atom,definition,(bl_atom = cs4_atom)).
% 12.80/13.02 thf(def_bl_princ,definition,(bl_princ = cs4_atom)).
% 12.80/13.02 thf(def_bl_and,definition,(bl_and = cs4_and)).
% 12.80/13.02 thf(def_bl_or,definition,(bl_or = cs4_or)).
% 12.80/13.02 thf(def_bl_impl,definition,(bl_impl = cs4_impl)).
% 12.80/13.02 thf(def_bl_all,definition,(bl_all = cs4_all)).
% 12.80/13.02 thf(def_bl_true,definition,(bl_true = cs4_true)).
% 12.80/13.02 thf(def_bl_false,definition,(bl_false = cs4_false)).
% 12.80/13.02 thf(def_bl_says,definition,(bl_says = (^[X1:individuals]:(^[X2:$i>$o]:(cs4_box @ ((cs4_impl @ (bl_princ @ (princ_inj @ X1))) @ X2)))))).
% 12.80/13.02 thf(def_bl_valid,definition,(bl_valid = mvalid)).
% 12.80/13.02 thf(bl_k,conjecture,(![X1:individuals]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:(![X5:$i]:(((reli @ X4) @ X5) => ((~((~((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((~((~((![X9:$i]:(((reli @ X8) @ X9) => ((princ_inj @ X1) @ X9))))))) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((X2 @ X9))))) => (X3 @ X9))))))))))))))) => (![X6:$i]:(((reli @ X5) @ X6) => ((~((~((![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))))))) => (X2 @ X9)))))))))))) => (![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))))))) => (X3 @ X9))))))))))))))))))).
% 12.80/13.02 thf(h0,negated_conjecture,(~((![X1:individuals]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:(![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((![X9:$i]:(((reli @ X8) @ X9) => ((princ_inj @ X1) @ X9))) => (![X9:$i]:(((reli @ X8) @ X9) => ((X2 @ X9) => (X3 @ X9))))))))))) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))) => (X2 @ X9)))))))) => (![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))) => (X3 @ X9)))))))))))))))))))),inference(assume_negation,[status(cth)],[bl_k])).
% 12.80/13.02 thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:(![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((![X8:$i]:(((reli @ X7) @ X8) => ((princ_inj @ eigen__0) @ X8))) => (![X8:$i]:(((reli @ X7) @ X8) => ((X1 @ X8) => (X2 @ X8))))))))))) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((![X9:$i]:(((reli @ X8) @ X9) => ((princ_inj @ eigen__0) @ X9))) => (X1 @ X8)))))))) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((![X9:$i]:(((reli @ X8) @ X9) => ((princ_inj @ eigen__0) @ X9))) => (X2 @ X8))))))))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h2,assumption,(~((![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => ((princ_inj @ eigen__0) @ X7))) => (![X7:$i]:(((reli @ X6) @ X7) => ((eigen__1 @ X7) => (X1 @ X7))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((![X8:$i]:(((reli @ X7) @ X8) => ((princ_inj @ eigen__0) @ X8))) => (eigen__1 @ X7)))))))) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((![X8:$i]:(((reli @ X7) @ X8) => ((princ_inj @ eigen__0) @ X8))) => (X1 @ X7)))))))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h3,assumption,(~((![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => ((princ_inj @ eigen__0) @ X6))) => (![X6:$i]:(((reli @ X5) @ X6) => ((eigen__1 @ X6) => (eigen__2 @ X6))))))))))) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => ((princ_inj @ eigen__0) @ X7))) => (eigen__1 @ X6)))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => ((princ_inj @ eigen__0) @ X7))) => (eigen__2 @ X6))))))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h4,assumption,(~((![X1:$i]:(((reli @ eigen__3) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => ((eigen__1 @ X5) => (eigen__2 @ X5))))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => ((princ_inj @ eigen__0) @ X6))) => (eigen__1 @ X5)))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => ((princ_inj @ eigen__0) @ X6))) => (eigen__2 @ X5)))))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h5,assumption,(~((((reli @ eigen__3) @ eigen__4) => (sP28 => (![X1:$i]:(((reli @ eigen__4) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__1 @ X4)))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__2 @ X4))))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h6,assumption,((reli @ eigen__3) @ eigen__4),introduced(assumption,[])).
% 12.80/13.02 thf(h7,assumption,(~((sP28 => (![X1:$i]:(((reli @ eigen__4) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__1 @ X4)))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__2 @ X4)))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h8,assumption,sP28,introduced(assumption,[])).
% 12.80/13.02 thf(h9,assumption,(~((![X1:$i]:(((reli @ eigen__4) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__1 @ X4)))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => ((princ_inj @ eigen__0) @ X5))) => (eigen__2 @ X4))))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h10,assumption,(~((sP3 => (sP17 => (![X1:$i]:(((reli @ eigen__5) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (eigen__2 @ X3)))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h11,assumption,sP3,introduced(assumption,[])).
% 12.80/13.02 thf(h12,assumption,(~((sP17 => (![X1:$i]:(((reli @ eigen__5) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (eigen__2 @ X3))))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h13,assumption,sP17,introduced(assumption,[])).
% 12.80/13.02 thf(h14,assumption,(~((![X1:$i]:(((reli @ eigen__5) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => ((princ_inj @ eigen__0) @ X4))) => (eigen__2 @ X3)))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h15,assumption,(~((sP7 => (![X1:$i]:(((relr @ eigen__6) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => ((princ_inj @ eigen__0) @ X3))) => (eigen__2 @ X2))))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h16,assumption,sP7,introduced(assumption,[])).
% 12.80/13.02 thf(h17,assumption,(~((![X1:$i]:(((relr @ eigen__6) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => ((princ_inj @ eigen__0) @ X3))) => (eigen__2 @ X2)))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h18,assumption,(~((sP31 => (![X1:$i]:(((reli @ eigen__7) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => ((princ_inj @ eigen__0) @ X2))) => (eigen__2 @ X1))))))),introduced(assumption,[])).
% 12.80/13.02 thf(h19,assumption,sP31,introduced(assumption,[])).
% 12.80/13.02 thf(h20,assumption,(~((![X1:$i]:(((reli @ eigen__7) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => ((princ_inj @ eigen__0) @ X2))) => (eigen__2 @ X1)))))),introduced(assumption,[])).
% 12.80/13.02 thf(h21,assumption,(~((sP25 => (sP1 => sP26)))),introduced(assumption,[])).
% 12.80/13.02 thf(h22,assumption,sP25,introduced(assumption,[])).
% 12.80/13.02 thf(h23,assumption,(~((sP1 => sP26))),introduced(assumption,[])).
% 12.80/13.02 thf(h24,assumption,sP1,introduced(assumption,[])).
% 12.80/13.02 thf(h25,assumption,(~(sP26)),introduced(assumption,[])).
% 12.80/13.02 thf(1,plain,(~(sP27) | sP9),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(2,plain,((~(sP9) | ~(sP23)) | sP8),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(3,plain,(~(sP30) | sP27),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(4,plain,(~(sP13) | sP12),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(5,plain,((~(sP12) | ~(sP7)) | sP5),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(6,plain,(~(sP29) | sP19),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(7,plain,((~(sP19) | ~(sP3)) | sP13),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(8,plain,(~(sP22) | sP16),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(9,plain,(~(sP16) | sP11),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(10,plain,((~(sP11) | ~(sP28)) | sP29),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(11,plain,((~(sP8) | ~(sP15)) | sP26),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(12,plain,(~(sP4) | sP18),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(13,plain,((~(sP18) | ~(sP25)) | sP14),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(14,plain,((~(sP14) | ~(sP1)) | sP23),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(15,plain,(~(sP5) | sP6),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(16,plain,((~(sP6) | ~(sP31)) | sP4),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(17,plain,(~(sP32) | sP2),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(18,plain,((~(sP2) | ~(sP25)) | sP10),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(19,plain,((~(sP10) | ~(sP1)) | sP15),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(20,plain,(~(sP24) | sP21),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(21,plain,((~(sP21) | ~(sP31)) | sP32),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(22,plain,(~(sP17) | sP20),inference(all_rule,[status(thm)],[])).
% 12.80/13.02 thf(23,plain,((~(sP20) | ~(sP7)) | sP24),inference(prop_rule,[status(thm)],[])).
% 12.80/13.02 thf(refl_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ X1)))).
% 12.80/13.02 thf(24,plain,sP30,inference(preprocess,[status(thm)],[refl_axiom_i]).
% 12.80/13.02 thf(trans_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ ((mbox @ reli) @ ((mbox @ reli) @ X1)))))).
% 12.80/13.02 thf(25,plain,sP22,inference(preprocess,[status(thm)],[trans_axiom_i]).
% 12.80/13.02 thf(26,plain,$false,inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h23,h21,h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h8,h11,h13,h16,h19,h22,h24,h25])).
% 12.80/13.02 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,26,h24,h25])).
% 12.80/13.02 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,27,h22,h23])).
% 12.80/13.02 thf(29,plain,$false,inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__8)],[h20,28,h21])).
% 12.80/13.02 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,29,h19,h20])).
% 12.80/13.02 thf(31,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__7)],[h17,30,h18])).
% 12.80/13.02 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,31,h16,h17])).
% 12.80/13.02 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__6)],[h14,32,h15])).
% 12.80/13.02 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,33,h13,h14])).
% 12.80/13.02 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,34,h11,h12])).
% 12.80/13.02 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[h9,35,h10])).
% 12.80/13.02 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,36,h8,h9])).
% 12.80/13.02 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,37,h6,h7])).
% 12.80/13.02 thf(39,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__4)],[h4,38,h5])).
% 12.80/13.02 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,39,h4])).
% 12.80/13.02 thf(41,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,40,h3])).
% 12.80/13.02 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,41,h2])).
% 12.80/13.02 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,42,h1])).
% 12.80/13.02 thf(0,theorem,(![X1:individuals]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:(![X5:$i]:(((reli @ X4) @ X5) => ((~((~((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => ((~((~((![X9:$i]:(((reli @ X8) @ X9) => ((princ_inj @ X1) @ X9))))))) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((X2 @ X9))))) => (X3 @ X9))))))))))))))) => (![X6:$i]:(((reli @ X5) @ X6) => ((~((~((![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))))))) => (X2 @ X9)))))))))))) => (![X7:$i]:(((reli @ X6) @ X7) => (![X8:$i]:(((relr @ X7) @ X8) => (![X9:$i]:(((reli @ X8) @ X9) => ((~((~((![X10:$i]:(((reli @ X9) @ X10) => ((princ_inj @ X1) @ X10))))))) => (X3 @ X9)))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[43,h0])).
% 12.80/13.02 % SZS output end Proof
%------------------------------------------------------------------------------