TSTP Solution File: LCL864^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL864^1 : 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 : n031.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 11.47s 11.46s
% Output : Proof 13.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL864^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:01:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 11.47/11.46 % SZS status Theorem
% 11.47/11.46 % Mode: cade22grackle2xfee4
% 11.47/11.46 % Steps: 158826
% 11.47/11.46 % SZS output start Proof
% 11.47/11.46 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 11.47/11.46 thf(ty_eigen__32, type, eigen__32 : $i).
% 11.47/11.46 thf(ty_eigen__19, type, eigen__19 : $i).
% 11.47/11.46 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 11.47/11.46 thf(eigendef_eigen__32, definition, eigen__32 = (eps__0 @ (^[X1:$i]:(~((~(((eigen__0 @ eigen__19) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__32])])).
% 11.47/11.46 thf(eigendef_eigen__19, definition, eigen__19 = (eps__0 @ (^[X1:$i]:(~(((eigen__0 @ X1) @ X1))))), introduced(definition,[new_symbols(definition,[eigen__19])])).
% 11.47/11.46 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 11.47/11.46 thf(sP2,plain,sP2 <=> ((~((((eigen__0 @ eigen__19) @ eigen__32) => (~(((eigen__0 @ eigen__32) @ eigen__19)))))) => ((eigen__0 @ eigen__19) @ eigen__19)),introduced(definition,[new_symbols(definition,[sP2])])).
% 11.47/11.46 thf(sP3,plain,sP3 <=> (![X1:$i]:(~(((eigen__0 @ eigen__19) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 11.47/11.46 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__19) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__19) @ X2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 11.47/11.46 thf(sP5,plain,sP5 <=> ((eigen__0 @ eigen__19) @ eigen__32),introduced(definition,[new_symbols(definition,[sP5])])).
% 11.47/11.46 thf(sP6,plain,sP6 <=> (sP5 => (~(((eigen__0 @ eigen__32) @ eigen__19)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 11.47/11.46 thf(sP7,plain,sP7 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 11.47/11.46 thf(sP8,plain,sP8 <=> ((eigen__0 @ eigen__19) @ eigen__19),introduced(definition,[new_symbols(definition,[sP8])])).
% 11.47/11.46 thf(sP9,plain,sP9 <=> ((eigen__0 @ eigen__32) @ eigen__19),introduced(definition,[new_symbols(definition,[sP9])])).
% 11.47/11.46 thf(sP10,plain,sP10 <=> (![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 11.47/11.46 thf(sP11,plain,sP11 <=> (sP5 => sP9),introduced(definition,[new_symbols(definition,[sP11])])).
% 11.47/11.46 thf(sP12,plain,sP12 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP12])])).
% 11.47/11.46 thf(sP13,plain,sP13 <=> (sP12 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 11.47/11.46 thf(sP14,plain,sP14 <=> (![X1:$i]:(((eigen__0 @ eigen__19) @ X1) => ((eigen__0 @ X1) @ eigen__19))),introduced(definition,[new_symbols(definition,[sP14])])).
% 11.47/11.46 thf(sP15,plain,sP15 <=> (![X1:$i]:((~((sP5 => (~(((eigen__0 @ eigen__32) @ X1)))))) => ((eigen__0 @ eigen__19) @ X1))),introduced(definition,[new_symbols(definition,[sP15])])).
% 11.47/11.46 thf(sP16,plain,sP16 <=> (![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 11.47/11.46 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 11.47/11.46 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 11.47/11.46 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 11.47/11.46 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 11.47/11.46 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 11.47/11.46 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 11.47/11.46 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 11.47/11.46 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 11.47/11.46 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 11.47/11.46 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 11.47/11.46 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 11.47/11.46 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 11.47/11.46 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 11.47/11.46 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 11.47/11.46 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 11.47/11.46 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 11.47/11.46 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 11.47/11.46 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 11.47/11.46 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 11.47/11.46 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 11.47/11.46 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)))))))).
% 11.47/11.46 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)))))))).
% 11.47/11.46 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)))))))).
% 11.47/11.46 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))))))))).
% 11.47/11.46 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:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 11.47/11.46 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 11.47/11.46 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$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)))))))))).
% 11.47/11.46 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 11.47/11.46 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 11.47/11.46 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 11.47/11.46 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 11.47/11.46 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))))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))))))))).
% 11.47/11.46 thf(h1,negated_conjecture,(~((![X1:$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:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 11.47/11.46 thf(h2,assumption,(~(((~(sP13)) = (~(((~(((~((sP16 => (~(sP7))))) => (~(sP10))))) => (~(sP1)))))))),introduced(assumption,[])).
% 11.47/11.46 thf(h3,assumption,(~(((~((sP16 => (~(sP7))))) => (~(sP10))))),introduced(assumption,[])).
% 11.47/11.46 thf(h4,assumption,sP1,introduced(assumption,[])).
% 11.47/11.46 thf(h5,assumption,(~((sP16 => (~(sP7))))),introduced(assumption,[])).
% 11.47/11.46 thf(h6,assumption,sP10,introduced(assumption,[])).
% 11.47/11.46 thf(h7,assumption,sP16,introduced(assumption,[])).
% 11.47/11.46 thf(h8,assumption,sP7,introduced(assumption,[])).
% 11.47/11.46 thf(1,plain,((~(sP6) | ~(sP5)) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 11.47/11.46 thf(2,plain,((~(sP2) | sP6) | sP8),inference(prop_rule,[status(thm)],[])).
% 11.47/11.46 thf(3,plain,(~(sP15) | sP2),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(4,plain,((~(sP11) | ~(sP5)) | sP9),inference(prop_rule,[status(thm)],[])).
% 11.47/11.46 thf(5,plain,(~(sP14) | sP11),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(6,plain,(~(sP4) | sP15),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(7,plain,(sP3 | sP5),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__32])).
% 11.47/11.46 thf(8,plain,(~(sP10) | sP14),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(9,plain,(~(sP16) | ~(sP3)),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(10,plain,(~(sP7) | sP4),inference(all_rule,[status(thm)],[])).
% 11.47/11.46 thf(11,plain,(sP12 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19])).
% 11.47/11.46 thf(12,plain,((~(sP13) | ~(sP12)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 11.47/11.46 1:564: Could not find hyp name
% 11.47/11.46 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)
% 11.47/11.46 hyp:
% 11.47/11.46 [569] h7: Pi:$i (\_:$i.imp (Pi:$i (\_:$i.imp (__0 ^1 ^0) False)) False)
% 11.47/11.46 [575] h8: Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^1 ^0) False)) False) (__0 ^2 ^0))))
% 11.47/11.46 [578] h5: 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
% 11.47/11.46 [582] h6: Pi:$i (\_:$i.Pi:$i (\_:$i.imp (__0 ^1 ^0) (__0 ^0 ^1)))
% 11.47/11.46 [585] h3: 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
% 11.47/11.46 [562] h4: Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))
% 11.47/11.46 [589] h2: imp (eq:$o (imp (imp (Pi:$i (\_:$i.__0 ^0 ^0)) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))) False)) False) (imp (imp (imp (imp (imp (imp (Pi:$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 (\_:$i.imp (__0 ^1 ^0) (__0 ^0 ^1)))) False)) False) (imp (Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))) False)) False)) False
% 11.47/11.46 [546] h1: imp (Pi:$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 (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) (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))) False
% 11.47/11.46 [204631] h0: Pi:$i>$o (\_:$i>$o.Pi:$i (\_:$i.imp (^1 ^0) (^1 (eps__0 ^1))))
% 11.47/11.46 % SZS status Error
% 11.47/11.46 Exception: Failure("Could not find hyp name")
% 13.11/13.06 % SZS status Theorem
% 13.11/13.06 % Mode: cade22grackle2x798d
% 13.11/13.06 % Steps: 26840
% 13.11/13.06 % SZS output start Proof
% 13.11/13.06 thf(ty_eigen__13, type, eigen__13 : $i).
% 13.11/13.06 thf(ty_eigen__9, type, eigen__9 : $i).
% 13.11/13.06 thf(ty_eigen__8, type, eigen__8 : $i).
% 13.11/13.06 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 13.11/13.06 thf(ty_eigen__11, type, eigen__11 : $i).
% 13.11/13.06 thf(ty_eigen__1, type, eigen__1 : $i).
% 13.11/13.06 thf(ty_eigen__5, type, eigen__5 : $i).
% 13.11/13.06 thf(ty_eigen__7, type, eigen__7 : $i).
% 13.11/13.06 thf(ty_eigen__12, type, eigen__12 : $i).
% 13.11/13.06 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 13.11/13.06 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((~((((eigen__0 @ eigen__8) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__8) @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__11])])).
% 13.11/13.06 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((eigen__0 @ X1) @ X1))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 13.11/13.06 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:$i]:(~(((~((((eigen__0 @ eigen__8) @ eigen__11) => (~(((eigen__0 @ eigen__11) @ X1)))))) => ((eigen__0 @ eigen__8) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__12])])).
% 13.11/13.07 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 13.11/13.07 thf(eigendef_eigen__13, definition, eigen__13 = (eps__0 @ (^[X1:$i]:(~((~(((eigen__0 @ eigen__1) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__13])])).
% 13.11/13.07 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__5) @ X1) => ((eigen__0 @ X1) @ eigen__5)))))), introduced(definition,[new_symbols(definition,[eigen__9])])).
% 13.11/13.07 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((~((![X2:$i]:(~(((eigen__0 @ X1) @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 13.11/13.07 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 13.11/13.07 thf(sP1,plain,sP1 <=> ((~(((![X1:$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)))))))))) => (~((![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 13.11/13.07 thf(sP2,plain,sP2 <=> (![X1:$i]:(~(((eigen__0 @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 13.11/13.07 thf(sP3,plain,sP3 <=> ((eigen__0 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])).
% 13.11/13.07 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__11) @ X1) => (~(((eigen__0 @ eigen__11) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 13.11/13.07 thf(sP5,plain,sP5 <=> (((eigen__0 @ eigen__5) @ eigen__9) => (~(((eigen__0 @ eigen__5) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 13.11/13.07 thf(sP6,plain,sP6 <=> ((eigen__0 @ eigen__9) @ eigen__5),introduced(definition,[new_symbols(definition,[sP6])])).
% 13.11/13.07 thf(sP7,plain,sP7 <=> (((eigen__0 @ eigen__1) @ eigen__13) => (~(((eigen__0 @ eigen__13) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 13.11/13.07 thf(sP8,plain,sP8 <=> ((eigen__0 @ eigen__7) @ eigen__7),introduced(definition,[new_symbols(definition,[sP8])])).
% 13.11/13.07 thf(sP9,plain,sP9 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP9])])).
% 13.11/13.07 thf(sP10,plain,sP10 <=> (((eigen__0 @ eigen__8) @ eigen__11) => (~(((eigen__0 @ eigen__11) @ eigen__12)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 13.11/13.07 thf(sP11,plain,sP11 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__1) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 13.11/13.07 thf(sP12,plain,sP12 <=> ((eigen__0 @ eigen__5) @ eigen__5),introduced(definition,[new_symbols(definition,[sP12])])).
% 13.11/13.07 thf(sP13,plain,sP13 <=> (![X1:$i]:(~(((eigen__0 @ eigen__7) @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 13.11/13.07 thf(sP14,plain,sP14 <=> (((eigen__0 @ eigen__8) @ eigen__11) => ((eigen__0 @ eigen__11) @ eigen__8)),introduced(definition,[new_symbols(definition,[sP14])])).
% 13.11/13.07 thf(sP15,plain,sP15 <=> (((eigen__0 @ eigen__1) @ eigen__13) => ((eigen__0 @ eigen__13) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP15])])).
% 13.11/13.07 thf(sP16,plain,sP16 <=> ((eigen__0 @ eigen__8) @ eigen__12),introduced(definition,[new_symbols(definition,[sP16])])).
% 13.11/13.07 thf(sP17,plain,sP17 <=> ((eigen__0 @ eigen__8) @ eigen__11),introduced(definition,[new_symbols(definition,[sP17])])).
% 13.11/13.07 thf(sP18,plain,sP18 <=> ((~(sP10)) => sP16),introduced(definition,[new_symbols(definition,[sP18])])).
% 13.11/13.07 thf(sP19,plain,sP19 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 13.11/13.07 thf(sP20,plain,sP20 <=> ((~((((eigen__0 @ eigen__11) @ eigen__8) => (~(((eigen__0 @ eigen__11) @ eigen__12)))))) => sP16),introduced(definition,[new_symbols(definition,[sP20])])).
% 13.11/13.07 thf(sP21,plain,sP21 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP21])])).
% 13.11/13.07 thf(sP22,plain,sP22 <=> ((eigen__0 @ eigen__5) @ eigen__9),introduced(definition,[new_symbols(definition,[sP22])])).
% 13.11/13.07 thf(sP23,plain,sP23 <=> (![X1:$i]:((~((((eigen__0 @ eigen__11) @ eigen__8) => (~(((eigen__0 @ eigen__11) @ X1)))))) => ((eigen__0 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP23])])).
% 13.11/13.07 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 13.11/13.07 thf(sP25,plain,sP25 <=> (![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP25])])).
% 13.11/13.07 thf(sP26,plain,sP26 <=> ((eigen__0 @ eigen__11) @ eigen__12),introduced(definition,[new_symbols(definition,[sP26])])).
% 13.11/13.07 thf(sP27,plain,sP27 <=> ((~(sP5)) => sP6),introduced(definition,[new_symbols(definition,[sP27])])).
% 13.11/13.07 thf(sP28,plain,sP28 <=> (![X1:$i]:((~((((eigen__0 @ eigen__1) @ eigen__13) => (~(((eigen__0 @ eigen__13) @ X1)))))) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP28])])).
% 13.11/13.07 thf(sP29,plain,sP29 <=> ((eigen__0 @ eigen__13) @ eigen__1),introduced(definition,[new_symbols(definition,[sP29])])).
% 13.11/13.07 thf(sP30,plain,sP30 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__5) @ X1) => (~(((eigen__0 @ eigen__5) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 13.11/13.07 thf(sP31,plain,sP31 <=> (sP22 => sP6),introduced(definition,[new_symbols(definition,[sP31])])).
% 13.11/13.07 thf(sP32,plain,sP32 <=> (((eigen__0 @ eigen__11) @ eigen__8) => (~(sP26))),introduced(definition,[new_symbols(definition,[sP32])])).
% 13.11/13.07 thf(sP33,plain,sP33 <=> (sP9 => (~(sP19))),introduced(definition,[new_symbols(definition,[sP33])])).
% 13.11/13.07 thf(sP34,plain,sP34 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__8) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__8) @ X2)))),introduced(definition,[new_symbols(definition,[sP34])])).
% 13.11/13.07 thf(sP35,plain,sP35 <=> ((~(sP33)) = (~(((~(sP1)) => (~(sP19)))))),introduced(definition,[new_symbols(definition,[sP35])])).
% 13.11/13.07 thf(sP36,plain,sP36 <=> ((![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))) => (~(sP24))),introduced(definition,[new_symbols(definition,[sP36])])).
% 13.11/13.07 thf(sP37,plain,sP37 <=> ((eigen__0 @ eigen__1) @ eigen__13),introduced(definition,[new_symbols(definition,[sP37])])).
% 13.11/13.07 thf(sP38,plain,sP38 <=> (![X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP38])])).
% 13.11/13.07 thf(sP39,plain,sP39 <=> (![X1:$i]:((~((sP17 => (~(((eigen__0 @ eigen__11) @ X1)))))) => ((eigen__0 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP39])])).
% 13.11/13.07 thf(sP40,plain,sP40 <=> (![X1:$i]:((~((sP22 => (~(((eigen__0 @ eigen__5) @ X1)))))) => ((eigen__0 @ eigen__9) @ X1))),introduced(definition,[new_symbols(definition,[sP40])])).
% 13.11/13.07 thf(sP41,plain,sP41 <=> (![X1:$i]:(((eigen__0 @ eigen__8) @ X1) => ((eigen__0 @ X1) @ eigen__8))),introduced(definition,[new_symbols(definition,[sP41])])).
% 13.11/13.07 thf(sP42,plain,sP42 <=> ((eigen__0 @ eigen__11) @ eigen__8),introduced(definition,[new_symbols(definition,[sP42])])).
% 13.11/13.07 thf(sP43,plain,sP43 <=> (![X1:$i]:(((eigen__0 @ eigen__5) @ X1) => ((eigen__0 @ X1) @ eigen__5))),introduced(definition,[new_symbols(definition,[sP43])])).
% 13.11/13.07 thf(sP44,plain,sP44 <=> ((~(sP1)) => (~(sP19))),introduced(definition,[new_symbols(definition,[sP44])])).
% 13.11/13.07 thf(sP45,plain,sP45 <=> ((~(sP7)) => sP3),introduced(definition,[new_symbols(definition,[sP45])])).
% 13.11/13.07 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 13.11/13.07 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 13.11/13.07 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 13.11/13.07 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 13.11/13.07 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 13.11/13.07 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 13.11/13.07 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 13.11/13.07 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 13.11/13.07 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 13.11/13.07 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 13.11/13.07 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 13.11/13.07 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 13.11/13.07 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 13.11/13.07 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 13.11/13.07 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 13.11/13.07 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 13.11/13.07 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 13.11/13.07 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 13.11/13.07 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 13.11/13.07 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 13.11/13.07 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)))))))).
% 13.11/13.07 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)))))))).
% 13.11/13.07 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)))))))).
% 13.11/13.07 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))))))))).
% 13.11/13.07 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:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 13.11/13.07 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 13.11/13.07 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$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)))))))))).
% 13.11/13.07 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 13.11/13.07 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 13.11/13.07 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 13.11/13.07 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 13.11/13.07 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))))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))))))))).
% 13.11/13.07 thf(h1,negated_conjecture,(~((![X1:$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:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 13.11/13.07 thf(h2,assumption,(~(sP35)),introduced(assumption,[])).
% 13.11/13.07 thf(1,plain,((~(sP32) | ~(sP42)) | ~(sP26)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(2,plain,((~(sP7) | ~(sP37)) | ~(sP29)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(3,plain,((~(sP20) | sP32) | sP16),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(4,plain,((~(sP45) | sP7) | sP3),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(5,plain,(~(sP23) | sP20),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(6,plain,(~(sP28) | sP45),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(7,plain,((~(sP15) | ~(sP37)) | sP29),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(8,plain,((~(sP5) | ~(sP22)) | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(9,plain,((~(sP14) | ~(sP17)) | sP42),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(10,plain,(~(sP4) | sP23),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(11,plain,(~(sP11) | sP28),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(12,plain,(~(sP21) | sP15),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(13,plain,((~(sP27) | sP5) | sP6),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(14,plain,(~(sP41) | sP14),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(15,plain,(~(sP19) | sP4),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(16,plain,(~(sP40) | sP27),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(17,plain,(~(sP25) | sP41),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(18,plain,(~(sP30) | sP40),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(19,plain,(~(sP9) | sP12),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(20,plain,(~(sP19) | sP30),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(21,plain,(~(sP9) | sP8),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(22,plain,(~(sP13) | ~(sP8)),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(23,plain,(sP2 | sP37),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13])).
% 13.11/13.07 thf(24,plain,(sP10 | sP26),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(25,plain,(sP10 | sP17),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(26,plain,(~(sP25) | sP21),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(27,plain,(~(sP38) | ~(sP2)),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(28,plain,(~(sP24) | sP11),inference(all_rule,[status(thm)],[])).
% 13.11/13.07 thf(29,plain,(sP18 | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(30,plain,(sP18 | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(31,plain,(sP39 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])).
% 13.11/13.07 thf(32,plain,(sP31 | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(33,plain,(sP31 | sP22),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(34,plain,(sP34 | ~(sP39)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])).
% 13.11/13.07 thf(35,plain,(sP43 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])).
% 13.11/13.07 thf(36,plain,(sP24 | ~(sP34)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 13.11/13.07 thf(37,plain,(sP38 | sP13),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 13.11/13.07 thf(38,plain,(sP25 | ~(sP43)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])).
% 13.11/13.07 thf(39,plain,((~(sP36) | ~(sP38)) | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(40,plain,(sP36 | sP38),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(41,plain,((~(sP1) | sP36) | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(42,plain,(sP9 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 13.11/13.07 thf(43,plain,(sP1 | sP25),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(44,plain,(sP1 | ~(sP36)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(45,plain,((~(sP44) | sP1) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(46,plain,((~(sP33) | ~(sP9)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(47,plain,(sP44 | sP19),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(48,plain,(sP44 | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(49,plain,(sP33 | sP19),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(50,plain,(sP33 | sP9),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(51,plain,((sP35 | sP33) | sP44),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(52,plain,((sP35 | ~(sP33)) | ~(sP44)),inference(prop_rule,[status(thm)],[])).
% 13.11/13.07 thf(53,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,h2])).
% 13.11/13.07 thf(54,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,53,h2])).
% 13.11/13.07 thf(55,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[54,h0])).
% 13.11/13.07 thf(0,theorem,(![X1:$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:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))))) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[54,h1])).
% 13.11/13.07 % SZS output end Proof
%------------------------------------------------------------------------------