TSTP Solution File: LCL860^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL860^1 : 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 : 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 : 300s
% DateTime : Thu Aug 31 08:05:21 EDT 2023
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL860^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % 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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 18:10:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % Mode: cade22grackle2xfee4
% 0.19/0.46 % Steps: 2405
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 0.19/0.46 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.46 thf(sP2,plain,sP2 <=> ((![X1:$i]:((eigen__0 @ X1) @ X1)) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.46 thf(sP3,plain,sP3 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.46 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.19/0.46 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.19/0.46 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 0.19/0.46 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 0.19/0.46 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.19/0.46 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 0.19/0.46 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.19/0.46 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.19/0.46 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.19/0.46 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.19/0.46 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.19/0.46 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.46 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.46 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 0.19/0.46 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.19/0.46 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 0.19/0.46 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.19/0.46 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.19/0.46 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 0.19/0.46 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 0.19/0.46 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)))))))).
% 0.19/0.46 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)))))))).
% 0.19/0.46 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)))))))).
% 0.19/0.46 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))))))))).
% 0.19/0.46 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:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 0.19/0.46 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 0.19/0.46 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$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)))))))))).
% 0.19/0.46 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 0.19/0.46 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 0.19/0.46 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 0.19/0.46 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 0.19/0.46 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]:((X1 @ X2) @ X2)) => (~((![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))))))))))))).
% 0.19/0.46 thf(h0,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]:((X1 @ X2) @ X2)) => (~((![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])).
% 0.19/0.46 thf(h1,assumption,(~(((~(sP2)) = (~(((~(((~((sP3 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))))) => (~((![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1))))))))) => (~(sP1)))))))),introduced(assumption,[])).
% 0.19/0.46 thf(h2,assumption,(~(((~((sP3 => (~((![X1:$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(assumption,[])).
% 0.19/0.46 thf(h3,assumption,sP1,introduced(assumption,[])).
% 0.19/0.46 thf(h4,assumption,(~((sP3 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))))),introduced(assumption,[])).
% 0.19/0.46 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(assumption,[])).
% 0.19/0.46 thf(h6,assumption,sP3,introduced(assumption,[])).
% 0.19/0.46 thf(h7,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(assumption,[])).
% 0.19/0.46 thf(1,plain,((~(sP2) | ~(sP3)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.46 1:564: Could not find hyp name
% 0.19/0.46 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)
% 0.19/0.46 hyp:
% 0.19/0.46 [550] h6: Pi:$i (\_:$i.__0 ^0 ^0)
% 0.19/0.46 [572] h7: Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^1 ^0) False)) False) (__0 ^2 ^0))))
% 0.19/0.46 [575] h4: 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 ^1 ^0) False)) False) (__0 ^2 ^0))))) False)) False
% 0.19/0.46 [579] h5: Pi:$i (\_:$i.Pi:$i (\_:$i.imp (__0 ^1 ^0) (__0 ^0 ^1)))
% 0.19/0.46 [582] h2: imp (imp (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 ^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
% 0.19/0.46 [562] h3: Pi:$i (\_:$i.Pi:$i (\_:$i.Pi:$i (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))
% 0.19/0.46 [586] h1: 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 (\_:$i.__0 ^0 ^0)) (imp (Pi:$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 (\_:$i.imp (imp (imp (__0 ^2 ^1) (imp (__0 ^2 ^0) False)) False) (__0 ^1 ^0))))) False)) False)) False
% 0.19/0.46 [546] h0: imp (Pi:$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.^1 ^0 ^0)) (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
% 0.19/0.46 % SZS status Error
% 0.19/0.46 Exception: Failure("Could not find hyp name")
% 0.76/0.94 % SZS status Theorem
% 0.76/0.94 % Mode: cade22grackle2x798d
% 0.76/0.94 % Steps: 6973
% 0.76/0.94 % SZS output start Proof
% 0.76/0.94 thf(ty_eigen__10, type, eigen__10 : $i).
% 0.76/0.94 thf(ty_eigen__9, type, eigen__9 : $i).
% 0.76/0.94 thf(ty_eigen__8, type, eigen__8 : $i).
% 0.76/0.94 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 0.76/0.94 thf(ty_eigen__5, type, eigen__5 : $i).
% 0.76/0.94 thf(ty_eigen__7, type, eigen__7 : $i).
% 0.76/0.94 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.76/0.94 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~(((~((((eigen__0 @ eigen__7) @ eigen__9) => (~(((eigen__0 @ eigen__9) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 0.76/0.94 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__5) @ X1) => ((eigen__0 @ X1) @ eigen__5)))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 0.76/0.94 thf(eigendef_eigen__9, definition, eigen__9 = (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__9])])).
% 0.76/0.94 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 0.76/0.94 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 0.76/0.94 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__7) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__7) @ X2)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.76/0.94 thf(sP2,plain,sP2 <=> (![X1:$i]:((~((((eigen__0 @ eigen__5) @ eigen__8) => (~(((eigen__0 @ eigen__5) @ X1)))))) => ((eigen__0 @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.76/0.94 thf(sP3,plain,sP3 <=> ((~(((![X1:$i]:((eigen__0 @ X1) @ X1)) => (~((![X1:$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,[sP3])])).
% 0.76/0.94 thf(sP4,plain,sP4 <=> ((eigen__0 @ eigen__7) @ eigen__10),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.76/0.94 thf(sP5,plain,sP5 <=> ((eigen__0 @ eigen__9) @ eigen__10),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.76/0.94 thf(sP6,plain,sP6 <=> (((eigen__0 @ eigen__7) @ eigen__9) => ((eigen__0 @ eigen__9) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.76/0.94 thf(sP7,plain,sP7 <=> ((~((((eigen__0 @ eigen__7) @ eigen__9) => (~(sP5))))) => sP4),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.76/0.94 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__9) @ X1) => (~(((eigen__0 @ eigen__9) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.76/0.94 thf(sP9,plain,sP9 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.76/0.94 thf(sP10,plain,sP10 <=> ((eigen__0 @ eigen__7) @ eigen__9),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.76/0.94 thf(sP11,plain,sP11 <=> ((eigen__0 @ eigen__8) @ eigen__5),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.76/0.94 thf(sP12,plain,sP12 <=> (sP10 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.76/0.94 thf(sP13,plain,sP13 <=> ((eigen__0 @ eigen__5) @ eigen__8),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.76/0.94 thf(sP14,plain,sP14 <=> ((~((((eigen__0 @ eigen__9) @ eigen__7) => (~(sP5))))) => sP4),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.76/0.94 thf(sP15,plain,sP15 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.76/0.94 thf(sP16,plain,sP16 <=> (((eigen__0 @ eigen__9) @ eigen__7) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.76/0.94 thf(sP17,plain,sP17 <=> ((~((sP13 => (~(((eigen__0 @ eigen__5) @ eigen__5)))))) => sP11),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.76/0.94 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.76/0.94 thf(sP19,plain,sP19 <=> (![X1:$i]:((~((sP10 => (~(((eigen__0 @ eigen__9) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1))),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.76/0.94 thf(sP20,plain,sP20 <=> (sP13 => sP11),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.76/0.94 thf(sP21,plain,sP21 <=> (sP9 => (~(sP15))),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.76/0.94 thf(sP22,plain,sP22 <=> ((eigen__0 @ eigen__5) @ eigen__5),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.76/0.94 thf(sP23,plain,sP23 <=> ((eigen__0 @ eigen__9) @ eigen__7),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.76/0.94 thf(sP24,plain,sP24 <=> ((~(sP21)) = (~(((~(sP3)) => (~(sP15)))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.76/0.94 thf(sP25,plain,sP25 <=> (sP9 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.76/0.94 thf(sP26,plain,sP26 <=> (sP13 => (~(sP22))),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.76/0.94 thf(sP27,plain,sP27 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.76/0.94 thf(sP28,plain,sP28 <=> (![X1:$i]:(((eigen__0 @ eigen__7) @ X1) => ((eigen__0 @ X1) @ eigen__7))),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.76/0.94 thf(sP29,plain,sP29 <=> (![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__5) @ X1) => (~(((eigen__0 @ eigen__5) @ X2)))))) => ((eigen__0 @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.76/0.94 thf(sP30,plain,sP30 <=> (![X1:$i]:(((eigen__0 @ eigen__5) @ X1) => ((eigen__0 @ X1) @ eigen__5))),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.76/0.94 thf(sP31,plain,sP31 <=> ((~(sP3)) => (~(sP15))),introduced(definition,[new_symbols(definition,[sP31])])).
% 0.76/0.94 thf(sP32,plain,sP32 <=> (![X1:$i]:((~((sP23 => (~(((eigen__0 @ eigen__9) @ X1)))))) => ((eigen__0 @ eigen__7) @ X1))),introduced(definition,[new_symbols(definition,[sP32])])).
% 0.76/0.94 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.76/0.94 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.76/0.94 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 0.76/0.94 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 0.76/0.94 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.76/0.94 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 0.76/0.94 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.76/0.94 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.76/0.94 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.76/0.94 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.76/0.94 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.76/0.94 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.76/0.94 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.76/0.94 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 0.76/0.94 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.76/0.94 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 0.76/0.94 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.76/0.94 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.76/0.94 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 0.76/0.94 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 0.76/0.94 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)))))))).
% 0.76/0.94 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)))))))).
% 0.76/0.94 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)))))))).
% 0.76/0.94 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))))))))).
% 0.76/0.94 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:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 0.76/0.94 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 0.76/0.94 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$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)))))))))).
% 0.76/0.94 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 0.76/0.94 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 0.76/0.94 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 0.76/0.94 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 0.76/0.94 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]:((X1 @ X2) @ X2)) => (~((![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))))))))))))).
% 0.76/0.94 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]:((X1 @ X2) @ X2)) => (~((![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])).
% 0.76/0.94 thf(h2,assumption,(~(sP24)),introduced(assumption,[])).
% 0.76/0.94 thf(1,plain,((~(sP16) | ~(sP23)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(2,plain,((~(sP14) | sP16) | sP4),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(3,plain,(~(sP32) | sP14),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(4,plain,((~(sP26) | ~(sP13)) | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(5,plain,((~(sP6) | ~(sP10)) | sP23),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(6,plain,(~(sP8) | sP32),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(7,plain,((~(sP17) | sP26) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(8,plain,(~(sP28) | sP6),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(9,plain,(~(sP15) | sP8),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(10,plain,(~(sP2) | sP17),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(11,plain,(~(sP18) | sP28),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(12,plain,(~(sP29) | sP2),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(13,plain,(~(sP9) | sP22),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(14,plain,(~(sP15) | sP29),inference(all_rule,[status(thm)],[])).
% 0.76/0.94 thf(15,plain,(sP12 | sP5),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(16,plain,(sP12 | sP10),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(17,plain,(sP7 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(18,plain,(sP7 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(19,plain,(sP19 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])).
% 0.76/0.94 thf(20,plain,(sP20 | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(21,plain,(sP20 | sP13),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(22,plain,(sP1 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])).
% 0.76/0.94 thf(23,plain,(sP30 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 0.76/0.94 thf(24,plain,(sP27 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 0.76/0.94 thf(25,plain,(sP18 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])).
% 0.76/0.94 thf(26,plain,((~(sP25) | ~(sP9)) | ~(sP27)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(27,plain,(sP25 | sP9),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(28,plain,((~(sP3) | sP25) | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(29,plain,(sP3 | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(30,plain,((~(sP31) | sP3) | ~(sP15)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(31,plain,((~(sP21) | ~(sP9)) | ~(sP15)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(32,plain,(sP31 | sP15),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(33,plain,(sP31 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(34,plain,(sP21 | sP15),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(35,plain,(sP21 | sP9),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(36,plain,((sP24 | sP21) | sP31),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(37,plain,((sP24 | ~(sP21)) | ~(sP31)),inference(prop_rule,[status(thm)],[])).
% 0.76/0.94 thf(38,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,h2])).
% 0.76/0.94 thf(39,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,38,h2])).
% 0.76/0.94 thf(40,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[39,h0])).
% 0.76/0.94 thf(0,theorem,(![X1:$i>$i>$o]:((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))))) = (~(((~(((~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$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])],[39,h1])).
% 0.76/0.94 % SZS output end Proof
%------------------------------------------------------------------------------