TSTP Solution File: LCL863^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL863^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 Aug 31 08:05:22 EDT 2023
% Result : Theorem 3.59s 3.77s
% Output : Proof 5.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL863^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 05:17:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.59/3.77 % SZS status Theorem
% 3.59/3.77 % Mode: cade22grackle2xfee4
% 3.59/3.77 % Steps: 33207
% 3.59/3.77 % SZS output start Proof
% 3.59/3.77 thf(ty_eigen__13, type, eigen__13 : $i).
% 3.59/3.77 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 3.59/3.77 thf(ty_eigen__14, type, eigen__14 : $i).
% 3.59/3.77 thf(ty_eigen__15, type, eigen__15 : $i).
% 3.59/3.77 thf(ty_eigen__23, type, eigen__23 : $i).
% 3.59/3.77 thf(ty_eigen__16, type, eigen__16 : $i).
% 3.59/3.77 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 3.59/3.77 thf(eigendef_eigen__15, definition, eigen__15 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((~((((eigen__0 @ eigen__14) @ X1) => (~(((eigen__0 @ eigen__14) @ X2)))))) => ((eigen__0 @ X1) @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__15])])).
% 3.59/3.77 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3)))))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 3.59/3.77 thf(eigendef_eigen__23, definition, eigen__23 = (eps__0 @ (^[X1:$i]:(~((~(((eigen__0 @ eigen__13) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__23])])).
% 3.59/3.77 thf(eigendef_eigen__13, definition, eigen__13 = (eps__0 @ (^[X1:$i]:(~(((eigen__0 @ X1) @ X1))))), introduced(definition,[new_symbols(definition,[eigen__13])])).
% 3.59/3.77 thf(eigendef_eigen__16, definition, eigen__16 = (eps__0 @ (^[X1:$i]:(~(((~((((eigen__0 @ eigen__14) @ eigen__15) => (~(((eigen__0 @ eigen__14) @ X1)))))) => ((eigen__0 @ eigen__15) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__16])])).
% 3.59/3.77 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 3.59/3.77 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__14) @ X1) => (~(((eigen__0 @ eigen__14) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 3.59/3.77 thf(sP3,plain,sP3 <=> (((eigen__0 @ eigen__13) @ eigen__23) => ((eigen__0 @ eigen__23) @ eigen__13)),introduced(definition,[new_symbols(definition,[sP3])])).
% 3.59/3.77 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__15) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__15) @ X2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 3.59/3.77 thf(sP5,plain,sP5 <=> (![X1:$i]:(((eigen__0 @ eigen__14) @ X1) => ((eigen__0 @ X1) @ eigen__14))),introduced(definition,[new_symbols(definition,[sP5])])).
% 3.59/3.77 thf(sP6,plain,sP6 <=> (![X1:$i]:((~((((eigen__0 @ eigen__14) @ eigen__15) => (~(((eigen__0 @ eigen__14) @ X1)))))) => ((eigen__0 @ eigen__15) @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 3.59/3.77 thf(sP7,plain,sP7 <=> (![X1:$i]:((~((((eigen__0 @ eigen__13) @ eigen__23) => (~(((eigen__0 @ eigen__23) @ X1)))))) => ((eigen__0 @ eigen__13) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 3.59/3.77 thf(sP8,plain,sP8 <=> (![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 3.59/3.77 thf(sP9,plain,sP9 <=> ((eigen__0 @ eigen__23) @ eigen__13),introduced(definition,[new_symbols(definition,[sP9])])).
% 3.59/3.77 thf(sP10,plain,sP10 <=> (![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 3.59/3.77 thf(sP11,plain,sP11 <=> ((~((((eigen__0 @ eigen__13) @ eigen__23) => (~(sP9))))) => ((eigen__0 @ eigen__13) @ eigen__13)),introduced(definition,[new_symbols(definition,[sP11])])).
% 3.59/3.77 thf(sP12,plain,sP12 <=> (((eigen__0 @ eigen__14) @ eigen__15) => (~(((eigen__0 @ eigen__14) @ eigen__16)))),introduced(definition,[new_symbols(definition,[sP12])])).
% 3.59/3.77 thf(sP13,plain,sP13 <=> (![X1:$i]:((~((((eigen__0 @ eigen__15) @ eigen__14) => (~(((eigen__0 @ eigen__14) @ X1)))))) => ((eigen__0 @ eigen__15) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 3.59/3.77 thf(sP14,plain,sP14 <=> ((eigen__0 @ eigen__14) @ eigen__15),introduced(definition,[new_symbols(definition,[sP14])])).
% 3.59/3.77 thf(sP15,plain,sP15 <=> (((eigen__0 @ eigen__15) @ eigen__14) => (~(((eigen__0 @ eigen__14) @ eigen__16)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 3.59/3.77 thf(sP16,plain,sP16 <=> ((eigen__0 @ eigen__13) @ eigen__13),introduced(definition,[new_symbols(definition,[sP16])])).
% 3.59/3.77 thf(sP17,plain,sP17 <=> (![X1:$i]:(((eigen__0 @ eigen__13) @ X1) => ((eigen__0 @ X1) @ eigen__13))),introduced(definition,[new_symbols(definition,[sP17])])).
% 3.59/3.77 thf(sP18,plain,sP18 <=> (![X1:$i]:(~(((eigen__0 @ eigen__13) @ X1)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 3.59/3.77 thf(sP19,plain,sP19 <=> ((eigen__0 @ eigen__15) @ eigen__16),introduced(definition,[new_symbols(definition,[sP19])])).
% 3.59/3.77 thf(sP20,plain,sP20 <=> ((~(sP12)) => sP19),introduced(definition,[new_symbols(definition,[sP20])])).
% 3.59/3.77 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__13) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__13) @ X2)))),introduced(definition,[new_symbols(definition,[sP21])])).
% 3.59/3.77 thf(sP22,plain,sP22 <=> ((eigen__0 @ eigen__14) @ eigen__16),introduced(definition,[new_symbols(definition,[sP22])])).
% 3.59/3.77 thf(sP23,plain,sP23 <=> ((eigen__0 @ eigen__13) @ eigen__23),introduced(definition,[new_symbols(definition,[sP23])])).
% 3.59/3.77 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 3.59/3.77 thf(sP25,plain,sP25 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP25])])).
% 3.59/3.77 thf(sP26,plain,sP26 <=> (sP25 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP26])])).
% 3.59/3.77 thf(sP27,plain,sP27 <=> ((eigen__0 @ eigen__15) @ eigen__14),introduced(definition,[new_symbols(definition,[sP27])])).
% 3.59/3.77 thf(sP28,plain,sP28 <=> (sP14 => sP27),introduced(definition,[new_symbols(definition,[sP28])])).
% 3.59/3.77 thf(sP29,plain,sP29 <=> ((~(sP15)) => sP19),introduced(definition,[new_symbols(definition,[sP29])])).
% 3.59/3.77 thf(sP30,plain,sP30 <=> (sP23 => (~(sP9))),introduced(definition,[new_symbols(definition,[sP30])])).
% 3.59/3.77 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 3.59/3.77 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 3.59/3.77 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 3.59/3.77 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 3.59/3.77 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 3.59/3.77 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 3.59/3.77 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 3.59/3.77 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 3.59/3.77 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 3.59/3.77 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 3.59/3.77 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 3.59/3.77 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 3.59/3.77 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 3.59/3.77 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 3.59/3.77 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 3.59/3.77 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 3.59/3.77 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 3.59/3.77 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 3.59/3.77 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 3.59/3.77 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 3.59/3.77 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X3) @ X4))) @ ((X1 @ X2) @ X4)))))))).
% 3.59/3.77 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((X1 @ X3) @ X4)))))))).
% 3.59/3.77 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (X3 = X4)))))))).
% 3.59/3.77 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:(((X1 @ X2) @ X3) & (![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X4)) @ (X3 = X4))))))))).
% 3.59/3.77 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X3)) @ (?[X5:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 3.59/3.77 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 3.59/3.77 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (?[X5:$i]:(((X1 @ X3) @ X5) & ((X1 @ X4) @ X5)))))))))).
% 3.59/3.77 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 3.59/3.77 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 3.59/3.77 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 3.59/3.77 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 3.59/3.77 thf(conj,conjecture,(![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))) => (~((![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2)))))))))))).
% 3.59/3.77 thf(h1,negated_conjecture,(~((![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))) => (~((![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 3.59/3.77 thf(h2,assumption,(~(((~(sP26)) = (~(((~((sP8 => (~(sP24))))) => (~(sP10)))))))),introduced(assumption,[])).
% 3.59/3.77 thf(h3,assumption,(~((sP8 => (~(sP24))))),introduced(assumption,[])).
% 3.59/3.77 thf(h4,assumption,sP10,introduced(assumption,[])).
% 3.59/3.77 thf(h5,assumption,sP8,introduced(assumption,[])).
% 3.59/3.77 thf(h6,assumption,sP24,introduced(assumption,[])).
% 3.59/3.77 thf(1,plain,((~(sP30) | ~(sP23)) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(2,plain,((~(sP11) | sP30) | sP16),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(3,plain,(~(sP7) | sP11),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(4,plain,((~(sP3) | ~(sP23)) | sP9),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(5,plain,(~(sP17) | sP3),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(6,plain,(~(sP21) | sP7),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(7,plain,((~(sP15) | ~(sP27)) | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(8,plain,((~(sP29) | sP15) | sP19),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(9,plain,(~(sP13) | sP29),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(10,plain,(~(sP4) | sP13),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(11,plain,((~(sP28) | ~(sP14)) | sP27),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(12,plain,(~(sP24) | sP4),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(13,plain,(~(sP5) | sP28),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(14,plain,(~(sP10) | sP5),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(15,plain,(sP18 | sP23),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__23])).
% 3.59/3.77 thf(16,plain,(~(sP10) | sP17),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(17,plain,(~(sP8) | ~(sP18)),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(18,plain,(~(sP24) | sP21),inference(all_rule,[status(thm)],[])).
% 3.59/3.77 thf(19,plain,(sP12 | sP22),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(20,plain,(sP12 | sP14),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(21,plain,(sP20 | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(22,plain,(sP20 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 thf(23,plain,(sP6 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16])).
% 3.59/3.77 thf(24,plain,(sP2 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15])).
% 3.59/3.77 thf(25,plain,(sP1 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14])).
% 3.59/3.77 thf(26,plain,(sP25 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13])).
% 3.59/3.77 thf(27,plain,((~(sP26) | ~(sP25)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 3.59/3.77 1:562: Could not find hyp name
% 3.59/3.77 s = imp (Pi:$i (\_:$i.__0 ^0 ^0)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))) False)
% 3.59/3.77 hyp:
% 3.59/3.77 [567] h5: Pi:$i (\_:$i.imp (Pi:$i (\_:$i.imp (__0 ^1 ^0) False)) False)
% 3.59/3.77 [573] h6: Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^1 ^0) False)) False) (__0 ^2 ^0))))
% 3.59/3.77 [576] h3: imp (imp (Pi:$i (\_:$i.imp (Pi:$i (\_:$i.imp (__0 ^1 ^0) False)) False)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^1 ^0) False)) False) (__0 ^2 ^0))))) False)) False
% 3.59/3.77 [580] h4: Pi:$i (\_:$i.Pi:$i (\_:$i.imp (__0 ^1 ^0) (__0 ^0 ^1)))
% 3.59/3.77 [585] h2: imp (eq:$o (imp (imp (Pi:$i (\_:$i.__0 ^0 ^0)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))) False)) False) (imp (imp (imp (imp (Pi:$i (\_:$i.imp (Pi:$i (\_:$i.imp (__0 ^1 ^0) False)) False)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^1 ^0) False)) False) (__0 ^2 ^0))))) False)) False) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.imp (__0 ^1 ^0) (__0 ^0 ^1)))) False)) False)) False
% 3.59/3.77 [544] h1: imp (Pi:$i>$i>$o (\_:$i>$i>$o.eq:$o (imp (imp (Pi:$i (\_:$i.^1 ^0 ^0)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (^3 ^2 ^1) (imp (^3 ^2 ^0) False)) False) (^3 ^1 ^0))))) False)) False) (imp (imp (imp (imp (Pi:$i (\_:$i.imp (Pi:$i (\_:$i.imp (^2 ^1 ^0) False)) False)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (^3 ^2 ^1) (imp (^3 ^1 ^0) False)) False) (^3 ^2 ^0))))) False)) False) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.imp (^2 ^1 ^0) (^2 ^0 ^1)))) False)) False))) False
% 3.59/3.77 [42254] h0: Pi:$i>$o (\_:$i>$o.Pi:$i (\_:$i.imp (^1 ^0) (^1 (eps__0 ^1))))
% 3.59/3.77 % SZS status Error
% 3.59/3.77 Exception: Failure("Could not find hyp name")
% 5.45/5.81 % SZS status Theorem
% 5.45/5.81 % Mode: cade22grackle2x798d
% 5.45/5.81 % Steps: 25238
% 5.45/5.81 % SZS output start Proof
% 5.45/5.81 thf(ty_eigen__10, type, eigen__10 : $i).
% 5.45/5.81 thf(ty_eigen__2, type, eigen__2 : $i).
% 5.45/5.81 thf(ty_eigen__6, type, eigen__6 : $i).
% 5.45/5.81 thf(ty_eigen__13, type, eigen__13 : $i).
% 5.45/5.81 thf(ty_eigen__9, type, eigen__9 : $i).
% 5.45/5.81 thf(ty_eigen__8, type, eigen__8 : $i).
% 5.45/5.81 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 5.45/5.81 thf(ty_eigen__1, type, eigen__1 : $i).
% 5.45/5.81 thf(ty_eigen__5, type, eigen__5 : $i).
% 5.45/5.81 thf(ty_eigen__7, type, eigen__7 : $i).
% 5.45/5.81 thf(ty_eigen__3, type, eigen__3 : $i).
% 5.45/5.81 thf(ty_eigen__12, type, eigen__12 : $i).
% 5.45/5.81 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 5.45/5.81 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 5.45/5.81 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((eigen__0 @ X1) @ X1))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 5.45/5.81 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((~((![X2:$i]:(~(((eigen__0 @ X1) @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 5.45/5.81 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((~((((eigen__0 @ eigen__7) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__7) @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 5.45/5.81 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:$i]:(~(((~((((eigen__0 @ eigen__7) @ eigen__10) => (~(((eigen__0 @ eigen__10) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__12])])).
% 5.45/5.81 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ X1) @ eigen__3)))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 5.45/5.81 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3)))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 5.45/5.81 thf(eigendef_eigen__13, definition, eigen__13 = (eps__0 @ (^[X1:$i]:(~((~(((eigen__0 @ eigen__1) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__13])])).
% 5.45/5.81 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~(((~((((eigen__0 @ eigen__2) @ eigen__5) => (~(((eigen__0 @ eigen__2) @ X1)))))) => ((eigen__0 @ eigen__5) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__9])])).
% 5.45/5.81 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 5.45/5.81 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((~((((eigen__0 @ eigen__2) @ X1) => (~(((eigen__0 @ eigen__2) @ X2)))))) => ((eigen__0 @ X1) @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 5.45/5.81 thf(sP1,plain,sP1 <=> (((eigen__0 @ eigen__2) @ eigen__5) => ((eigen__0 @ eigen__5) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP1])])).
% 5.45/5.81 thf(sP2,plain,sP2 <=> ((![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))) => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 5.45/5.81 thf(sP3,plain,sP3 <=> (((eigen__0 @ eigen__7) @ eigen__10) => (~(((eigen__0 @ eigen__10) @ eigen__12)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 5.45/5.81 thf(sP4,plain,sP4 <=> ((eigen__0 @ eigen__5) @ eigen__2),introduced(definition,[new_symbols(definition,[sP4])])).
% 5.45/5.81 thf(sP5,plain,sP5 <=> ((~((((eigen__0 @ eigen__10) @ eigen__7) => (~(((eigen__0 @ eigen__10) @ eigen__12)))))) => ((eigen__0 @ eigen__7) @ eigen__12)),introduced(definition,[new_symbols(definition,[sP5])])).
% 5.45/5.81 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 5.45/5.81 thf(sP7,plain,sP7 <=> ((eigen__0 @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP7])])).
% 5.45/5.81 thf(sP8,plain,sP8 <=> ((eigen__0 @ eigen__6) @ eigen__6),introduced(definition,[new_symbols(definition,[sP8])])).
% 5.45/5.81 thf(sP9,plain,sP9 <=> (((eigen__0 @ eigen__1) @ eigen__13) => ((eigen__0 @ eigen__13) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP9])])).
% 5.45/5.81 thf(sP10,plain,sP10 <=> ((~(sP3)) => ((eigen__0 @ eigen__7) @ eigen__12)),introduced(definition,[new_symbols(definition,[sP10])])).
% 5.45/5.81 thf(sP11,plain,sP11 <=> ((eigen__0 @ eigen__2) @ eigen__9),introduced(definition,[new_symbols(definition,[sP11])])).
% 5.45/5.81 thf(sP12,plain,sP12 <=> (sP4 => (~(sP11))),introduced(definition,[new_symbols(definition,[sP12])])).
% 5.45/5.81 thf(sP13,plain,sP13 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__3) @ X1) => (~(((eigen__0 @ eigen__3) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 5.45/5.81 thf(sP14,plain,sP14 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP14])])).
% 5.45/5.81 thf(sP15,plain,sP15 <=> (![X1:$i]:(~(((eigen__0 @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 5.45/5.81 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__1) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 5.45/5.81 thf(sP17,plain,sP17 <=> (![X1:$i]:((~((((eigen__0 @ eigen__10) @ eigen__7) => (~(((eigen__0 @ eigen__10) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 5.45/5.81 thf(sP18,plain,sP18 <=> ((~((((eigen__0 @ eigen__1) @ eigen__13) => (~(((eigen__0 @ eigen__13) @ eigen__1)))))) => ((eigen__0 @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP18])])).
% 5.45/5.81 thf(sP19,plain,sP19 <=> ((eigen__0 @ eigen__10) @ eigen__12),introduced(definition,[new_symbols(definition,[sP19])])).
% 5.45/5.81 thf(sP20,plain,sP20 <=> ((eigen__0 @ eigen__1) @ eigen__13),introduced(definition,[new_symbols(definition,[sP20])])).
% 5.45/5.81 thf(sP21,plain,sP21 <=> ((eigen__0 @ eigen__8) @ eigen__3),introduced(definition,[new_symbols(definition,[sP21])])).
% 5.45/5.81 thf(sP22,plain,sP22 <=> ((~((((eigen__0 @ eigen__3) @ eigen__8) => (~(sP7))))) => sP21),introduced(definition,[new_symbols(definition,[sP22])])).
% 5.45/5.81 thf(sP23,plain,sP23 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP23])])).
% 5.45/5.81 thf(sP24,plain,sP24 <=> ((eigen__0 @ eigen__7) @ eigen__10),introduced(definition,[new_symbols(definition,[sP24])])).
% 5.45/5.81 thf(sP25,plain,sP25 <=> ((eigen__0 @ eigen__7) @ eigen__12),introduced(definition,[new_symbols(definition,[sP25])])).
% 5.45/5.81 thf(sP26,plain,sP26 <=> (((eigen__0 @ eigen__3) @ eigen__8) => sP21),introduced(definition,[new_symbols(definition,[sP26])])).
% 5.45/5.81 thf(sP27,plain,sP27 <=> (![X1:$i]:((~((sP4 => (~(((eigen__0 @ eigen__2) @ X1)))))) => ((eigen__0 @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP27])])).
% 5.45/5.81 thf(sP28,plain,sP28 <=> ((eigen__0 @ eigen__5) @ eigen__9),introduced(definition,[new_symbols(definition,[sP28])])).
% 5.45/5.81 thf(sP29,plain,sP29 <=> (![X1:$i]:(((eigen__0 @ eigen__7) @ X1) => ((eigen__0 @ X1) @ eigen__7))),introduced(definition,[new_symbols(definition,[sP29])])).
% 5.45/5.81 thf(sP30,plain,sP30 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__5) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__5) @ X2)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 5.45/5.81 thf(sP31,plain,sP31 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ X1) @ eigen__3))),introduced(definition,[new_symbols(definition,[sP31])])).
% 5.45/5.81 thf(sP32,plain,sP32 <=> (![X1:$i]:((~((((eigen__0 @ eigen__3) @ eigen__8) => (~(((eigen__0 @ eigen__3) @ X1)))))) => ((eigen__0 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP32])])).
% 5.45/5.81 thf(sP33,plain,sP33 <=> (![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP33])])).
% 5.45/5.81 thf(sP34,plain,sP34 <=> ((eigen__0 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP34])])).
% 5.45/5.81 thf(sP35,plain,sP35 <=> ((eigen__0 @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP35])])).
% 5.45/5.81 thf(sP36,plain,sP36 <=> ((eigen__0 @ eigen__2) @ eigen__5),introduced(definition,[new_symbols(definition,[sP36])])).
% 5.45/5.81 thf(sP37,plain,sP37 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP37])])).
% 5.45/5.81 thf(sP38,plain,sP38 <=> (sP24 => ((eigen__0 @ eigen__10) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP38])])).
% 5.45/5.81 thf(sP39,plain,sP39 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__7) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__7) @ X2)))),introduced(definition,[new_symbols(definition,[sP39])])).
% 5.45/5.81 thf(sP40,plain,sP40 <=> (sP14 => (~(sP23))),introduced(definition,[new_symbols(definition,[sP40])])).
% 5.45/5.81 thf(sP41,plain,sP41 <=> (![X1:$i]:((~((sP20 => (~(((eigen__0 @ eigen__13) @ X1)))))) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP41])])).
% 5.45/5.81 thf(sP42,plain,sP42 <=> ((~((sP36 => (~(sP11))))) => sP28),introduced(definition,[new_symbols(definition,[sP42])])).
% 5.45/5.81 thf(sP43,plain,sP43 <=> ((~(sP40)) = (~(((~(sP2)) => (~((![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP43])])).
% 5.45/5.81 thf(sP44,plain,sP44 <=> ((eigen__0 @ eigen__13) @ eigen__1),introduced(definition,[new_symbols(definition,[sP44])])).
% 5.45/5.81 thf(sP45,plain,sP45 <=> (sP35 => (~(sP7))),introduced(definition,[new_symbols(definition,[sP45])])).
% 5.45/5.81 thf(sP46,plain,sP46 <=> (((eigen__0 @ eigen__10) @ eigen__7) => (~(sP19))),introduced(definition,[new_symbols(definition,[sP46])])).
% 5.45/5.81 thf(sP47,plain,sP47 <=> (![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP47])])).
% 5.45/5.81 thf(sP48,plain,sP48 <=> (![X1:$i]:(((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP48])])).
% 5.45/5.81 thf(sP49,plain,sP49 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__2) @ X1) => (~(((eigen__0 @ eigen__2) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP49])])).
% 5.45/5.81 thf(sP50,plain,sP50 <=> (sP36 => (~(sP11))),introduced(definition,[new_symbols(definition,[sP50])])).
% 5.45/5.81 thf(sP51,plain,sP51 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__10) @ X1) => (~(((eigen__0 @ eigen__10) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP51])])).
% 5.45/5.81 thf(sP52,plain,sP52 <=> (![X1:$i]:(~(((eigen__0 @ eigen__6) @ X1)))),introduced(definition,[new_symbols(definition,[sP52])])).
% 5.45/5.81 thf(sP53,plain,sP53 <=> (![X1:$i]:((~((sP36 => (~(((eigen__0 @ eigen__2) @ X1)))))) => ((eigen__0 @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP53])])).
% 5.45/5.81 thf(sP54,plain,sP54 <=> ((~(sP2)) => (~(sP47))),introduced(definition,[new_symbols(definition,[sP54])])).
% 5.45/5.81 thf(sP55,plain,sP55 <=> (sP20 => (~(sP44))),introduced(definition,[new_symbols(definition,[sP55])])).
% 5.45/5.81 thf(sP56,plain,sP56 <=> ((eigen__0 @ eigen__10) @ eigen__7),introduced(definition,[new_symbols(definition,[sP56])])).
% 5.45/5.81 thf(sP57,plain,sP57 <=> (![X1:$i]:((~((sP24 => (~(((eigen__0 @ eigen__10) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1))),introduced(definition,[new_symbols(definition,[sP57])])).
% 5.45/5.81 thf(sP58,plain,sP58 <=> ((~(sP12)) => sP28),introduced(definition,[new_symbols(definition,[sP58])])).
% 5.45/5.81 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 5.45/5.81 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 5.45/5.81 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 5.45/5.81 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 5.45/5.81 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 5.45/5.81 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 5.45/5.81 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 5.45/5.81 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 5.45/5.81 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 5.45/5.81 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 5.45/5.81 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 5.45/5.81 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 5.45/5.81 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 5.45/5.81 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 5.45/5.81 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 5.45/5.81 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 5.45/5.81 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 5.45/5.81 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 5.45/5.81 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 5.45/5.81 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 5.45/5.81 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X3) @ X4))) @ ((X1 @ X2) @ X4)))))))).
% 5.45/5.81 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((X1 @ X3) @ X4)))))))).
% 5.45/5.81 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (X3 = X4)))))))).
% 5.45/5.81 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:(((X1 @ X2) @ X3) & (![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X4)) @ (X3 = X4))))))))).
% 5.45/5.81 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X3)) @ (?[X5:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 5.45/5.81 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 5.45/5.81 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (?[X5:$i]:(((X1 @ X3) @ X5) & ((X1 @ X4) @ X5)))))))))).
% 5.45/5.81 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 5.45/5.81 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 5.45/5.81 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 5.45/5.81 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 5.45/5.81 thf(conj,conjecture,(![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))) => (~((![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2)))))))))))).
% 5.45/5.81 thf(h1,negated_conjecture,(~((![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))) => (~((![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 5.45/5.81 thf(h2,assumption,(~(sP43)),introduced(assumption,[])).
% 5.45/5.81 thf(1,plain,((~(sP55) | ~(sP20)) | ~(sP44)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(2,plain,((~(sP46) | ~(sP56)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(3,plain,((~(sP18) | sP55) | sP34),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(4,plain,((~(sP5) | sP46) | sP25),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(5,plain,(~(sP41) | sP18),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(6,plain,((~(sP9) | ~(sP20)) | sP44),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(7,plain,(~(sP17) | sP5),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(8,plain,((~(sP12) | ~(sP4)) | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(9,plain,(~(sP16) | sP41),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(10,plain,(~(sP37) | sP9),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(11,plain,((~(sP45) | ~(sP35)) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(12,plain,((~(sP38) | ~(sP24)) | sP56),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(13,plain,(~(sP51) | sP17),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(14,plain,((~(sP58) | sP12) | sP28),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(15,plain,((~(sP1) | ~(sP36)) | sP4),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(16,plain,((~(sP22) | sP45) | sP21),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(17,plain,(~(sP29) | sP38),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(18,plain,(~(sP23) | sP51),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(19,plain,(~(sP27) | sP58),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(20,plain,(~(sP48) | sP1),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(21,plain,(~(sP32) | sP22),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(22,plain,(~(sP47) | sP29),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(23,plain,(~(sP30) | sP27),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(24,plain,(~(sP47) | sP48),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(25,plain,(~(sP13) | sP32),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(26,plain,(~(sP6) | sP30),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(27,plain,(sP15 | sP20),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13])).
% 5.45/5.81 thf(28,plain,(~(sP14) | sP7),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(29,plain,(~(sP23) | sP13),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(30,plain,(~(sP14) | sP8),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(31,plain,(~(sP52) | ~(sP8)),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(32,plain,(~(sP47) | sP37),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(33,plain,(~(sP33) | ~(sP15)),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(34,plain,(~(sP6) | sP16),inference(all_rule,[status(thm)],[])).
% 5.45/5.81 thf(35,plain,(sP3 | sP19),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(36,plain,(sP3 | sP24),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(37,plain,(sP10 | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(38,plain,(sP10 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(39,plain,(sP50 | sP11),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(40,plain,(sP50 | sP36),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(41,plain,(sP57 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])).
% 5.45/5.81 thf(42,plain,(sP42 | ~(sP28)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(43,plain,(sP42 | ~(sP50)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(44,plain,(sP26 | ~(sP21)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(45,plain,(sP26 | sP35),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(46,plain,(sP39 | ~(sP57)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])).
% 5.45/5.81 thf(47,plain,(sP53 | ~(sP42)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])).
% 5.45/5.81 thf(48,plain,(sP31 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 5.45/5.81 thf(49,plain,(sP6 | ~(sP39)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 5.45/5.81 thf(50,plain,(sP33 | sP52),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 5.45/5.81 thf(51,plain,(sP49 | ~(sP53)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])).
% 5.45/5.81 thf(52,plain,(sP47 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 5.45/5.81 thf(53,plain,((~(sP2) | ~(sP33)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(54,plain,(sP23 | ~(sP49)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 5.45/5.81 thf(55,plain,(sP14 | ~(sP34)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 5.45/5.81 thf(56,plain,(sP2 | sP6),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(57,plain,(sP2 | sP33),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(58,plain,((~(sP54) | sP2) | ~(sP47)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(59,plain,((~(sP40) | ~(sP14)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(60,plain,(sP54 | sP47),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(61,plain,(sP54 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(62,plain,(sP40 | sP23),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(63,plain,(sP40 | sP14),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(64,plain,((sP43 | sP40) | sP54),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(65,plain,((sP43 | ~(sP40)) | ~(sP54)),inference(prop_rule,[status(thm)],[])).
% 5.45/5.81 thf(66,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,h2])).
% 5.45/5.81 thf(67,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,66,h2])).
% 5.45/5.81 thf(68,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0])).
% 5.45/5.81 thf(0,theorem,(![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))) => (~((![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[67,h1])).
% 5.45/5.81 % SZS output end Proof
%------------------------------------------------------------------------------