TSTP Solution File: SET598^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET598^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 15:17:42 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET598^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 10:32:03 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.60 % SZS status Theorem
% 0.20/0.60 % Mode: cade22grackle2xfee4
% 0.20/0.60 % Steps: 2991
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 thf(ty_a, type, a : $tType).
% 0.20/0.60 thf(ty_eigen__0, type, eigen__0 : (a>$o)).
% 0.20/0.60 thf(ty_eigen__15, type, eigen__15 : a).
% 0.20/0.60 thf(ty_eigen__7, type, eigen__7 : a).
% 0.20/0.60 thf(ty_eigen__14, type, eigen__14 : a).
% 0.20/0.60 thf(ty_eigen__1, type, eigen__1 : (a>$o)).
% 0.20/0.60 thf(ty_eigen__2, type, eigen__2 : (a>$o)).
% 0.20/0.60 thf(h0, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.20/0.60 thf(eigendef_eigen__15, definition, eigen__15 = (eps__0 @ (^[X1:a]:(~(((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__2 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__15])])).
% 0.20/0.60 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:a]:(~(((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 0.20/0.60 thf(sP1,plain,sP1 <=> ((eigen__1 @ eigen__14) => (~((eigen__2 @ eigen__14)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.60 thf(sP2,plain,sP2 <=> (![X1:a]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.60 thf(sP3,plain,sP3 <=> ((eigen__1 @ eigen__7) => (~((eigen__2 @ eigen__7)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.60 thf(sP4,plain,sP4 <=> (![X1:a>$o]:((~(((![X2:a]:((X1 @ X2) => (eigen__1 @ X2))) => (~((![X2:a]:((X1 @ X2) => (eigen__2 @ X2)))))))) => (![X2:a]:((X1 @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.60 thf(sP5,plain,sP5 <=> (eigen__0 @ eigen__7),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.60 thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__7),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.60 thf(sP7,plain,sP7 <=> (eigen__1 @ eigen__14),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.60 thf(sP8,plain,sP8 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.60 thf(sP9,plain,sP9 <=> ((![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__1 @ X1))) => (~((![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__2 @ X1)))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.60 thf(sP10,plain,sP10 <=> ((~(sP3)) => sP5),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.20/0.60 thf(sP11,plain,sP11 <=> (sP5 => (eigen__1 @ eigen__7)),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.20/0.60 thf(sP12,plain,sP12 <=> (![X1:a]:((eigen__0 @ X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.20/0.60 thf(sP13,plain,sP13 <=> (sP5 => sP6),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.20/0.60 thf(sP14,plain,sP14 <=> ((~(((eigen__1 @ eigen__15) => (~((eigen__2 @ eigen__15)))))) => (eigen__2 @ eigen__15)),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.20/0.60 thf(sP15,plain,sP15 <=> ((eigen__1 @ eigen__15) => (~((eigen__2 @ eigen__15)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.20/0.60 thf(sP16,plain,sP16 <=> ((~(sP1)) => sP7),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.20/0.60 thf(sP17,plain,sP17 <=> ((~(sP9)) => sP8),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.20/0.60 thf(sP18,plain,sP18 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.20/0.60 thf(sP19,plain,sP19 <=> (eigen__1 @ eigen__7),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.20/0.60 thf(sP20,plain,sP20 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.20/0.60 thf(sP21,plain,sP21 <=> (eigen__2 @ eigen__15),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.20/0.60 thf(cBOOL_PROP_57_pme,conjecture,(![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((X1 = (^[X4:a]:(~(((X2 @ X4) => (~((X3 @ X4)))))))) = (~(((~(((![X4:a]:((X1 @ X4) => (X2 @ X4))) => (~((![X4:a]:((X1 @ X4) => (X3 @ X4)))))))) => (~((![X4:a>$o]:((~(((![X5:a]:((X4 @ X5) => (X2 @ X5))) => (~((![X5:a]:((X4 @ X5) => (X3 @ X5)))))))) => (![X5:a]:((X4 @ X5) => (X1 @ X5))))))))))))))).
% 0.20/0.60 thf(h1,negated_conjecture,(~((![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((X1 = (^[X4:a]:(~(((X2 @ X4) => (~((X3 @ X4)))))))) = (~(((~(((![X4:a]:((X1 @ X4) => (X2 @ X4))) => (~((![X4:a]:((X1 @ X4) => (X3 @ X4)))))))) => (~((![X4:a>$o]:((~(((![X5:a]:((X4 @ X5) => (X2 @ X5))) => (~((![X5:a]:((X4 @ X5) => (X3 @ X5)))))))) => (![X5:a]:((X4 @ X5) => (X1 @ X5)))))))))))))))),inference(assume_negation,[status(cth)],[cBOOL_PROP_57_pme])).
% 0.20/0.60 thf(h2,assumption,(~((![X1:a>$o]:(![X2:a>$o]:((eigen__0 = (^[X3:a]:(~(((X1 @ X3) => (~((X2 @ X3)))))))) = (~(((~(((![X3:a]:((eigen__0 @ X3) => (X1 @ X3))) => (~((![X3:a]:((eigen__0 @ X3) => (X2 @ X3)))))))) => (~((![X3:a>$o]:((~(((![X4:a]:((X3 @ X4) => (X1 @ X4))) => (~((![X4:a]:((X3 @ X4) => (X2 @ X4)))))))) => (![X4:a]:((X3 @ X4) => (eigen__0 @ X4))))))))))))))),introduced(assumption,[])).
% 0.20/0.60 thf(h3,assumption,(~((![X1:a>$o]:((eigen__0 = (^[X2:a]:(~(((eigen__1 @ X2) => (~((X1 @ X2)))))))) = (~(((~((sP12 => (~((![X2:a]:((eigen__0 @ X2) => (X1 @ X2)))))))) => (~((![X2:a>$o]:((~(((![X3:a]:((X2 @ X3) => (eigen__1 @ X3))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (![X3:a]:((X2 @ X3) => (eigen__0 @ X3)))))))))))))),introduced(assumption,[])).
% 0.20/0.60 thf(h4,assumption,(~(((eigen__0 = (^[X1:a]:(~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))) = (~(((~((sP12 => (~(sP2))))) => (~(sP4)))))))),introduced(assumption,[])).
% 0.20/0.60 thf(h5,assumption,(~((![X1:a]:((eigen__0 @ X1) = (~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))))),introduced(assumption,[])).
% 0.20/0.60 thf(h6,assumption,(~((sP5 = (~(sP3))))),introduced(assumption,[])).
% 0.20/0.60 thf(h7,assumption,sP5,introduced(assumption,[])).
% 0.20/0.60 thf(h8,assumption,(~(sP3)),introduced(assumption,[])).
% 0.20/0.60 thf(h9,assumption,(~(sP5)),introduced(assumption,[])).
% 0.20/0.60 thf(h10,assumption,sP3,introduced(assumption,[])).
% 0.20/0.60 thf(h11,assumption,(~((sP12 => (~(sP2))))),introduced(assumption,[])).
% 0.20/0.60 thf(h12,assumption,sP4,introduced(assumption,[])).
% 0.20/0.60 thf(h13,assumption,sP12,introduced(assumption,[])).
% 0.20/0.60 thf(h14,assumption,sP2,introduced(assumption,[])).
% 0.20/0.60 thf(1,plain,((~(sP13) | ~(sP5)) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.20/0.60 thf(2,plain,((~(sP11) | ~(sP5)) | sP19),inference(prop_rule,[status(thm)],[])).
% 0.20/0.60 thf(3,plain,(~(sP2) | sP13),inference(all_rule,[status(thm)],[])).
% 0.20/0.60 thf(4,plain,(~(sP12) | sP11),inference(all_rule,[status(thm)],[])).
% 0.20/0.60 thf(5,plain,((~(sP3) | ~(sP19)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.60 thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,h7,h8,h13,h14])).
% 0.20/0.60 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,6,h13,h14])).
% 0.20/0.60 7:377: Could not find hyp name
% 0.20/0.60 s = imp (imp (imp (imp (Pi:a (\_:a.imp (__0 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (__0 ^0) (__2 ^0))) False)) False) (imp (Pi:a>$o (\_:a>$o.imp (imp (imp (Pi:a (\_:a.imp (^1 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (^1 ^0) (__2 ^0))) False)) False) (Pi:a (\_:a.imp (^1 ^0) (__0 ^0))))) False)) False
% 0.20/0.60 hyp:
% 0.20/0.60 [467] h7: __0 __7
% 0.20/0.60 [471] h8: imp (__1 __7) (imp (__2 __7) False)
% 0.20/0.60 [474] h6: imp (eq:$o (__0 __7) (imp (imp (__1 __7) (imp (__2 __7) False)) False)) False
% 0.20/0.60 [465] h5: imp (Pi:a (\_:a.eq:$o (__0 ^0) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False))) False
% 0.20/0.60 [379] h4: imp (eq:$o (eq:a>$o __0 (\_:a.imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (imp (imp (imp (imp (Pi:a (\_:a.imp (__0 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (__0 ^0) (__2 ^0))) False)) False) (imp (Pi:a>$o (\_:a>$o.imp (imp (imp (Pi:a (\_:a.imp (^1 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (^1 ^0) (__2 ^0))) False)) False) (Pi:a (\_:a.imp (^1 ^0) (__0 ^0))))) False)) False)) False
% 0.20/0.60 [355] h3: imp (Pi:a>$o (\_:a>$o.eq:$o (eq:a>$o __0 (\_:a.imp (imp (__1 ^0) (imp (^1 ^0) False)) False)) (imp (imp (imp (imp (Pi:a (\_:a.imp (__0 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (__0 ^0) (^1 ^0))) False)) False) (imp (Pi:a>$o (\_:a>$o.imp (imp (imp (Pi:a (\_:a.imp (^1 ^0) (__1 ^0))) (imp (Pi:a (\_:a.imp (^1 ^0) (^2 ^0))) False)) False) (Pi:a (\_:a.imp (^1 ^0) (__0 ^0))))) False)) False))) False
% 0.20/0.60 [333] h2: imp (Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.eq:$o (eq:a>$o __0 (\_:a.imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (imp (imp (imp (imp (Pi:a (\_:a.imp (__0 ^0) (^2 ^0))) (imp (Pi:a (\_:a.imp (__0 ^0) (^1 ^0))) False)) False) (imp (Pi:a>$o (\_:a>$o.imp (imp (imp (Pi:a (\_:a.imp (^1 ^0) (^3 ^0))) (imp (Pi:a (\_:a.imp (^1 ^0) (^2 ^0))) False)) False) (Pi:a (\_:a.imp (^1 ^0) (__0 ^0))))) False)) False)))) False
% 0.20/0.60 [312] h1: imp (Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.eq:$o (eq:a>$o ^2 (\_:a.imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (imp (imp (imp (imp (Pi:a (\_:a.imp (^3 ^0) (^2 ^0))) (imp (Pi:a (\_:a.imp (^3 ^0) (^1 ^0))) False)) False) (imp (Pi:a>$o (\_:a>$o.imp (imp (imp (Pi:a (\_:a.imp (^1 ^0) (^3 ^0))) (imp (Pi:a (\_:a.imp (^1 ^0) (^2 ^0))) False)) False) (Pi:a (\_:a.imp (^1 ^0) (^4 ^0))))) False)) False))))) False
% 0.20/0.60 [2278] h0: Pi:a>$o (\_:a>$o.Pi:a (\_:a.imp (^1 ^0) (^1 (eps__0 ^1))))
% 0.20/0.60 % SZS status Error
% 0.20/0.60 Exception: Failure("Could not find hyp name")
% 0.20/0.63 % SZS status Theorem
% 0.20/0.63 % Mode: cade22grackle2x798d
% 0.20/0.63 % Steps: 453
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 thf(ty_a, type, a : $tType).
% 0.20/0.63 thf(ty_eigen__0, type, eigen__0 : (a>$o)).
% 0.20/0.63 thf(ty_eigen__3, type, eigen__3 : a).
% 0.20/0.63 thf(ty_eigen__4, type, eigen__4 : (a>$o)).
% 0.20/0.63 thf(ty_eigen__11, type, eigen__11 : a).
% 0.20/0.63 thf(ty_eigen__7, type, eigen__7 : a).
% 0.20/0.63 thf(ty_eigen__1, type, eigen__1 : (a>$o)).
% 0.20/0.63 thf(ty_eigen__6, type, eigen__6 : a).
% 0.20/0.63 thf(ty_eigen__10, type, eigen__10 : a).
% 0.20/0.63 thf(ty_eigen__12, type, eigen__12 : a).
% 0.20/0.63 thf(ty_eigen__2, type, eigen__2 : (a>$o)).
% 0.20/0.63 thf(h0, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.20/0.63 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:a]:(~(((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__11])])).
% 0.20/0.63 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:a]:(~(((eigen__0 @ X1) = (~(((eigen__1 @ X1) => (~((eigen__2 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 0.20/0.63 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:a]:(~(((eigen__0 @ X1) => (eigen__1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 0.20/0.63 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:a]:(~(((eigen__4 @ X1) => (eigen__0 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 0.20/0.63 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:a]:(~(((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__2 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__12])])).
% 0.20/0.63 thf(h1, assumption, (![X1:(a>$o)>$o]:(![X2:a>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 0.20/0.63 thf(eigendef_eigen__4, definition, eigen__4 = (eps__1 @ (^[X1:a>$o]:(~(((~(((![X2:a]:((X1 @ X2) => (eigen__1 @ X2))) => (~((![X2:a]:((X1 @ X2) => (eigen__2 @ X2)))))))) => (![X2:a]:((X1 @ X2) => (eigen__0 @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 0.20/0.63 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:a]:(~(((eigen__0 @ X1) => (eigen__2 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 0.20/0.63 thf(sP1,plain,sP1 <=> (eigen__1 @ eigen__6),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.63 thf(sP2,plain,sP2 <=> (![X1:a]:((eigen__4 @ X1) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.63 thf(sP3,plain,sP3 <=> ((eigen__1 @ eigen__7) => (~((eigen__2 @ eigen__7)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.63 thf(sP4,plain,sP4 <=> ((![X1:a]:((eigen__0 @ X1) => (eigen__1 @ X1))) => (~((![X1:a]:((eigen__0 @ X1) => (eigen__2 @ X1)))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.63 thf(sP5,plain,sP5 <=> ((eigen__1 @ eigen__12) => (~((eigen__2 @ eigen__12)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.63 thf(sP6,plain,sP6 <=> (![X1:a]:((eigen__4 @ X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.63 thf(sP7,plain,sP7 <=> ((eigen__4 @ eigen__10) => (eigen__1 @ eigen__10)),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.63 thf(sP8,plain,sP8 <=> (![X1:a]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.63 thf(sP9,plain,sP9 <=> (eigen__0 @ eigen__6),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.63 thf(sP10,plain,sP10 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.20/0.63 thf(sP11,plain,sP11 <=> ((~(((eigen__1 @ eigen__3) => (~(sP10))))) => (eigen__0 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.20/0.63 thf(sP12,plain,sP12 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.20/0.63 thf(sP13,plain,sP13 <=> ((eigen__1 @ eigen__11) => (~((eigen__2 @ eigen__11)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.20/0.63 thf(sP14,plain,sP14 <=> (sP9 = (~((sP1 => (~((eigen__2 @ eigen__6))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.20/0.63 thf(sP15,plain,sP15 <=> ((eigen__0 @ eigen__3) => sP10),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.20/0.63 thf(sP16,plain,sP16 <=> (eigen__0 @ eigen__7),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.20/0.63 thf(sP17,plain,sP17 <=> (![X1:a]:((eigen__4 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.20/0.63 thf(sP18,plain,sP18 <=> (eigen__1 @ eigen__11),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.20/0.63 thf(sP19,plain,sP19 <=> ((eigen__1 @ eigen__10) => (~((eigen__2 @ eigen__10)))),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.20/0.63 thf(sP20,plain,sP20 <=> (sP6 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.20/0.63 thf(sP21,plain,sP21 <=> (sP1 => (~((eigen__2 @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.20/0.63 thf(sP22,plain,sP22 <=> ((eigen__4 @ eigen__10) => (eigen__0 @ eigen__10)),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.20/0.63 thf(sP23,plain,sP23 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.20/0.63 thf(sP24,plain,sP24 <=> ((eigen__0 @ eigen__10) = (~(sP19))),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.20/0.63 thf(sP25,plain,sP25 <=> (sP16 => (eigen__2 @ eigen__7)),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.20/0.63 thf(sP26,plain,sP26 <=> (![X1:a]:((eigen__0 @ X1) = (~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.20/0.63 thf(sP27,plain,sP27 <=> ((~(sP5)) => (eigen__2 @ eigen__12)),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.20/0.63 thf(sP28,plain,sP28 <=> (eigen__2 @ eigen__12),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.20/0.63 thf(sP29,plain,sP29 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.20/0.63 thf(sP30,plain,sP30 <=> (sP12 => (~(sP23))),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.20/0.63 thf(sP31,plain,sP31 <=> ((eigen__4 @ eigen__10) => (eigen__2 @ eigen__10)),introduced(definition,[new_symbols(definition,[sP31])])).
% 0.20/0.63 thf(sP32,plain,sP32 <=> (eigen__0 @ eigen__10),introduced(definition,[new_symbols(definition,[sP32])])).
% 0.20/0.63 thf(sP33,plain,sP33 <=> (![X1:a]:((eigen__0 @ X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP33])])).
% 0.20/0.63 thf(sP34,plain,sP34 <=> (sP9 => sP1),introduced(definition,[new_symbols(definition,[sP34])])).
% 0.20/0.63 thf(sP35,plain,sP35 <=> ((~(sP20)) => sP2),introduced(definition,[new_symbols(definition,[sP35])])).
% 0.20/0.63 thf(sP36,plain,sP36 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP36])])).
% 0.20/0.63 thf(sP37,plain,sP37 <=> (eigen__0 = (^[X1:a]:(~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP37])])).
% 0.20/0.63 thf(sP38,plain,sP38 <=> (sP37 = (~(((~(sP4)) => (~((![X1:a>$o]:((~(((![X2:a]:((X1 @ X2) => (eigen__1 @ X2))) => (~((![X2:a]:((X1 @ X2) => (eigen__2 @ X2)))))))) => (![X2:a]:((X1 @ X2) => (eigen__0 @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP38])])).
% 0.20/0.63 thf(sP39,plain,sP39 <=> (sP16 = (~(sP3))),introduced(definition,[new_symbols(definition,[sP39])])).
% 0.20/0.63 thf(sP40,plain,sP40 <=> ((~(sP13)) => sP18),introduced(definition,[new_symbols(definition,[sP40])])).
% 0.20/0.63 thf(sP41,plain,sP41 <=> (eigen__2 @ eigen__7),introduced(definition,[new_symbols(definition,[sP41])])).
% 0.20/0.63 thf(sP42,plain,sP42 <=> (![X1:a>$o]:((~(((![X2:a]:((X1 @ X2) => (eigen__1 @ X2))) => (~((![X2:a]:((X1 @ X2) => (eigen__2 @ X2)))))))) => (![X2:a]:((X1 @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP42])])).
% 0.20/0.63 thf(sP43,plain,sP43 <=> ((~(sP30)) => (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP43])])).
% 0.20/0.63 thf(sP44,plain,sP44 <=> (eigen__2 @ eigen__10),introduced(definition,[new_symbols(definition,[sP44])])).
% 0.20/0.63 thf(sP45,plain,sP45 <=> (sP36 => sP29),introduced(definition,[new_symbols(definition,[sP45])])).
% 0.20/0.63 thf(sP46,plain,sP46 <=> (eigen__1 @ eigen__10),introduced(definition,[new_symbols(definition,[sP46])])).
% 0.20/0.63 thf(sP47,plain,sP47 <=> (sP36 = (~((sP29 => (~(sP10)))))),introduced(definition,[new_symbols(definition,[sP47])])).
% 0.20/0.63 thf(sP48,plain,sP48 <=> (eigen__4 @ eigen__10),introduced(definition,[new_symbols(definition,[sP48])])).
% 0.20/0.63 thf(sP49,plain,sP49 <=> ((~(sP4)) => (~(sP42))),introduced(definition,[new_symbols(definition,[sP49])])).
% 0.20/0.63 thf(sP50,plain,sP50 <=> (sP29 => (~(sP10))),introduced(definition,[new_symbols(definition,[sP50])])).
% 0.20/0.63 thf(sP51,plain,sP51 <=> (![X1:a]:((~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP51])])).
% 0.20/0.63 thf(cBOOL_PROP_57_pme,conjecture,(![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((X1 = (^[X4:a]:(~(((X2 @ X4) => (~((X3 @ X4)))))))) = (~(((~(((![X4:a]:((X1 @ X4) => (X2 @ X4))) => (~((![X4:a]:((X1 @ X4) => (X3 @ X4)))))))) => (~((![X4:a>$o]:((~(((![X5:a]:((X4 @ X5) => (X2 @ X5))) => (~((![X5:a]:((X4 @ X5) => (X3 @ X5)))))))) => (![X5:a]:((X4 @ X5) => (X1 @ X5))))))))))))))).
% 0.20/0.63 thf(h2,negated_conjecture,(~((![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((X1 = (^[X4:a]:(~(((X2 @ X4) => (~((X3 @ X4)))))))) = (~(((~(((![X4:a]:((X1 @ X4) => (X2 @ X4))) => (~((![X4:a]:((X1 @ X4) => (X3 @ X4)))))))) => (~((![X4:a>$o]:((~(((![X5:a]:((X4 @ X5) => (X2 @ X5))) => (~((![X5:a]:((X4 @ X5) => (X3 @ X5)))))))) => (![X5:a]:((X4 @ X5) => (X1 @ X5)))))))))))))))),inference(assume_negation,[status(cth)],[cBOOL_PROP_57_pme])).
% 0.20/0.63 thf(h3,assumption,(~((![X1:a>$o]:(![X2:a>$o]:((eigen__0 = (^[X3:a]:(~(((X1 @ X3) => (~((X2 @ X3)))))))) = (~(((~(((![X3:a]:((eigen__0 @ X3) => (X1 @ X3))) => (~((![X3:a]:((eigen__0 @ X3) => (X2 @ X3)))))))) => (~((![X3:a>$o]:((~(((![X4:a]:((X3 @ X4) => (X1 @ X4))) => (~((![X4:a]:((X3 @ X4) => (X2 @ X4)))))))) => (![X4:a]:((X3 @ X4) => (eigen__0 @ X4))))))))))))))),introduced(assumption,[])).
% 0.20/0.63 thf(h4,assumption,(~((![X1:a>$o]:((eigen__0 = (^[X2:a]:(~(((eigen__1 @ X2) => (~((X1 @ X2)))))))) = (~(((~((sP33 => (~((![X2:a]:((eigen__0 @ X2) => (X1 @ X2)))))))) => (~((![X2:a>$o]:((~(((![X3:a]:((X2 @ X3) => (eigen__1 @ X3))) => (~((![X3:a]:((X2 @ X3) => (X1 @ X3)))))))) => (![X3:a]:((X2 @ X3) => (eigen__0 @ X3)))))))))))))),introduced(assumption,[])).
% 0.20/0.63 thf(h5,assumption,(~(sP38)),introduced(assumption,[])).
% 0.20/0.63 thf(1,plain,((~(sP19) | ~(sP46)) | ~(sP44)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(2,plain,((~(sP24) | sP32) | sP19),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(3,plain,((~(sP7) | ~(sP48)) | sP46),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(4,plain,((~(sP31) | ~(sP48)) | sP44),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(5,plain,(sP3 | sP41),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(6,plain,(sP21 | sP1),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(7,plain,(~(sP26) | sP24),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(8,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(9,plain,(~(sP17) | sP31),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(10,plain,((~(sP39) | ~(sP16)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(11,plain,((~(sP45) | ~(sP36)) | sP29),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(12,plain,((~(sP15) | ~(sP36)) | sP10),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(13,plain,((~(sP11) | sP50) | sP36),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(14,plain,((~(sP14) | ~(sP9)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(15,plain,(~(sP26) | sP39),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(16,plain,(~(sP33) | sP45),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(17,plain,(~(sP8) | sP15),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(18,plain,(~(sP51) | sP11),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(19,plain,(~(sP26) | sP14),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(20,plain,(sP5 | sP28),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(21,plain,(sP13 | sP18),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(22,plain,(sP27 | ~(sP28)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(23,plain,(sP27 | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(24,plain,(sP40 | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(25,plain,(sP40 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(26,plain,(sP22 | ~(sP32)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(27,plain,(sP22 | sP48),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(28,plain,(sP23 | ~(sP27)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])).
% 0.20/0.63 thf(29,plain,(sP12 | ~(sP40)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])).
% 0.20/0.63 thf(30,plain,(sP2 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])).
% 0.20/0.63 thf(31,plain,(sP20 | sP17),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(32,plain,(sP20 | sP6),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(33,plain,(sP25 | ~(sP41)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(34,plain,(sP25 | sP16),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(35,plain,(sP34 | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(36,plain,(sP34 | sP9),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(37,plain,((~(sP50) | ~(sP29)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(38,plain,((~(sP30) | ~(sP12)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(39,plain,(sP35 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(40,plain,(sP35 | ~(sP20)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(41,plain,(sP8 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 0.20/0.63 thf(42,plain,(sP33 | ~(sP34)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 0.20/0.63 thf(43,plain,((sP47 | ~(sP36)) | sP50),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(44,plain,((sP47 | sP36) | ~(sP50)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(45,plain,((~(sP43) | sP30) | sP51),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(46,plain,(sP42 | ~(sP35)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4])).
% 0.20/0.63 thf(47,plain,((~(sP4) | ~(sP33)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(48,plain,(sP26 | ~(sP47)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 0.20/0.63 thf(49,plain,(~(sP42) | sP43),inference(all_rule,[status(thm)],[])).
% 0.20/0.63 thf(50,plain,(sP4 | sP8),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(51,plain,(sP4 | sP33),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(52,plain,((~(sP49) | sP4) | ~(sP42)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(53,plain,(sP37 | ~(sP26)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(54,plain,(sP49 | sP42),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(55,plain,(sP49 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(56,plain,(~(sP37) | sP26),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(57,plain,((sP38 | ~(sP37)) | sP49),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(58,plain,((sP38 | sP37) | ~(sP49)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.63 thf(59,plain,$false,inference(prop_unsat,[status(thm),assumptions([h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,h5])).
% 0.20/0.63 thf(60,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,59,h5])).
% 0.20/0.63 thf(61,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,60,h4])).
% 0.20/0.63 thf(62,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,61,h3])).
% 0.20/0.63 thf(63,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[62,h1])).
% 0.20/0.63 thf(64,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[63,h0])).
% 0.20/0.63 thf(0,theorem,(![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((X1 = (^[X4:a]:(~(((X2 @ X4) => (~((X3 @ X4)))))))) = (~(((~(((![X4:a]:((X1 @ X4) => (X2 @ X4))) => (~((![X4:a]:((X1 @ X4) => (X3 @ X4)))))))) => (~((![X4:a>$o]:((~(((![X5:a]:((X4 @ X5) => (X2 @ X5))) => (~((![X5:a]:((X4 @ X5) => (X3 @ X5)))))))) => (![X5:a]:((X4 @ X5) => (X1 @ X5)))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[62,h2])).
% 0.20/0.63 % SZS output end Proof
%------------------------------------------------------------------------------