TSTP Solution File: SYO544^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO544^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : Fri Sep 1 04:47:26 EDT 2023
% Result : Theorem 0.65s 0.89s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO544^1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.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 : Sat Aug 26 07:23:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.65/0.89 % SZS status Theorem
% 0.65/0.89 % Mode: cade22grackle2xfee4
% 0.65/0.89 % Steps: 1834
% 0.65/0.89 % SZS output start Proof
% 0.65/0.89 thf(ty_eigen__13, type, eigen__13 : $o).
% 0.65/0.89 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.65/0.89 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.65/0.89 thf(ty_f2, type, f2 : ($o>$o)).
% 0.65/0.89 thf(ty_f3, type, f3 : ($o>$o)).
% 0.65/0.89 thf(ty_eigen__10, type, eigen__10 : $o).
% 0.65/0.89 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.65/0.89 thf(ty_eigen__4, type, eigen__4 : $o).
% 0.65/0.89 thf(ty_f0, type, f0 : ($o>$o)).
% 0.65/0.89 thf(ty_eigen__16, type, eigen__16 : $o).
% 0.65/0.89 thf(ty_eps, type, eps : (($i>$o)>$i)).
% 0.65/0.89 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.65/0.89 thf(ty_eigen__7, type, eigen__7 : $o).
% 0.65/0.89 thf(ty_f1, type, f1 : ($o>$o)).
% 0.65/0.89 thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.65/0.89 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$o]:(~((~((f0 @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 0.65/0.89 thf(eigendef_eigen__13, definition, eigen__13 = (eps__0 @ (^[X1:$o]:(~(((f2 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__13])])).
% 0.65/0.89 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 0.65/0.89 thf(eigendef_eigen__16, definition, eigen__16 = (eps__0 @ (^[X1:$o]:(~(((f3 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__16])])).
% 0.65/0.89 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~(X1))))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 0.65/0.89 thf(sP1,plain,sP1 <=> (![X1:$i]:(~(((~(((~((((f0 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.65/0.89 thf(sP2,plain,sP2 <=> (f0 @ (~($false))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.65/0.89 thf(sP3,plain,sP3 <=> (sP2 = (~($false))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.65/0.89 thf(sP4,plain,sP4 <=> (f0 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.65/0.89 thf(sP5,plain,sP5 <=> ((~((f0 = (^[X1:$o]:$false)))) => (~((sP4 => (~((eigen__0 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.65/0.89 thf(sP6,plain,sP6 <=> (![X1:$o]:((f2 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.65/0.89 thf(sP7,plain,sP7 <=> (![X1:$o]:((f0 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.65/0.89 thf(sP8,plain,sP8 <=> (f3 @ $false),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.65/0.89 thf(sP9,plain,sP9 <=> ((f0 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f0 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.65/0.89 thf(sP10,plain,sP10 <=> ((f2 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.65/0.89 thf(sP11,plain,sP11 <=> (![X1:$o]:((f0 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.65/0.89 thf(sP12,plain,sP12 <=> ((f1 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.65/0.89 thf(sP13,plain,sP13 <=> (f3 @ eigen__16),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.65/0.89 thf(sP14,plain,sP14 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~((eigen__2 = eigen__0)))) => (~(((f2 = (^[X1:$o]:(~(X1)))) => (~((eigen__2 = eigen__1))))))))) => (f2 = (^[X1:$o]:X1))))) => (~(((f2 = (^[X1:$o]:(~($false)))) => (~((eigen__2 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.65/0.89 thf(sP15,plain,sP15 <=> ((~((((eps @ (^[X1:$i]:((~(((~((((f0 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.65/0.89 thf(sP16,plain,sP16 <=> (![X1:$o]:((f0 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.65/0.89 thf(sP17,plain,sP17 <=> ((f1 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.65/0.89 thf(sP18,plain,sP18 <=> (![X1:$o]:((f1 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.65/0.89 thf(sP19,plain,sP19 <=> (f1 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.65/0.89 thf(sP20,plain,sP20 <=> ((f1 @ eigen__7) = (~(eigen__7))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.65/0.89 thf(sP21,plain,sP21 <=> (f2 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.65/0.89 thf(sP22,plain,sP22 <=> ((f2 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.65/0.89 thf(sP23,plain,sP23 <=> (![X1:$o]:((f3 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.65/0.89 thf(sP24,plain,sP24 <=> (f1 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.65/0.89 thf(sP25,plain,sP25 <=> ((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP24 => (~((X1 = eigen__1))))))))) => (~((sP19 => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.65/0.89 thf(sP26,plain,sP26 <=> (f1 @ eigen__7),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.65/0.89 thf(sP27,plain,sP27 <=> (f2 @ $false),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.65/0.89 thf(sP28,plain,sP28 <=> ((f0 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.65/0.89 thf(sP29,plain,sP29 <=> (f1 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.65/0.89 thf(sP30,plain,sP30 <=> (![X1:$o]:(~((f2 @ X1)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.65/0.89 thf(sP31,plain,sP31 <=> (((f2 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f2 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP31])])).
% 0.65/0.89 thf(sP32,plain,sP32 <=> ((~($false)) = eigen__16),introduced(definition,[new_symbols(definition,[sP32])])).
% 0.65/0.89 thf(sP33,plain,sP33 <=> ((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP33])])).
% 0.65/0.89 thf(sP34,plain,sP34 <=> (![X1:$i]:(~(((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP24 => (~((X1 = eigen__1))))))))) => (~((sP19 => (~((X1 = eigen__2))))))))) => (~((sP29 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 0.65/0.89 thf(sP35,plain,sP35 <=> (f2 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP35])])).
% 0.65/0.89 thf(sP36,plain,sP36 <=> (f2 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP36])])).
% 0.65/0.89 thf(sP37,plain,sP37 <=> (![X1:$o]:((f3 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP37])])).
% 0.65/0.89 thf(sP38,plain,sP38 <=> (f0 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP38])])).
% 0.65/0.89 thf(sP39,plain,sP39 <=> (![X1:$o]:(~((f3 @ X1)))),introduced(definition,[new_symbols(definition,[sP39])])).
% 0.65/0.89 thf(sP40,plain,sP40 <=> ((~(((sP38 => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP4 => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f0 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP40])])).
% 0.65/0.89 thf(sP41,plain,sP41 <=> (![X1:$o]:((f3 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP41])])).
% 0.65/0.89 thf(sP42,plain,sP42 <=> ((f2 @ eigen__13) = eigen__13),introduced(definition,[new_symbols(definition,[sP42])])).
% 0.65/0.89 thf(sP43,plain,sP43 <=> eigen__13,introduced(definition,[new_symbols(definition,[sP43])])).
% 0.65/0.89 thf(sP44,plain,sP44 <=> (f2 @ (~($false))),introduced(definition,[new_symbols(definition,[sP44])])).
% 0.65/0.89 thf(sP45,plain,sP45 <=> (f3 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP45])])).
% 0.65/0.89 thf(sP46,plain,sP46 <=> eigen__4,introduced(definition,[new_symbols(definition,[sP46])])).
% 0.65/0.89 thf(sP47,plain,sP47 <=> ((f3 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP47])])).
% 0.65/0.89 thf(sP48,plain,sP48 <=> (f0 @ eigen__10),introduced(definition,[new_symbols(definition,[sP48])])).
% 0.65/0.89 thf(sP49,plain,sP49 <=> (sP35 => (~(((eps @ (^[X1:$i]:((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP49])])).
% 0.65/0.89 thf(sP50,plain,sP50 <=> (eigen__10 = (~($false))),introduced(definition,[new_symbols(definition,[sP50])])).
% 0.65/0.89 thf(sP51,plain,sP51 <=> (f0 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP51])])).
% 0.65/0.89 thf(sP52,plain,sP52 <=> (sP19 => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP24 => (~((X1 = eigen__1))))))))) => (~((sP19 => (~((X1 = eigen__2))))))))) => (~((sP29 => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP52])])).
% 0.65/0.89 thf(sP53,plain,sP53 <=> ((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP24 => (~((X1 = eigen__1))))))))) => (~((sP19 => (~((X1 = eigen__2))))))))) => (~((sP29 => (~((X1 = eigen__3))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP53])])).
% 0.65/0.89 thf(sP54,plain,sP54 <=> ((~(((~(sP31)) => (~(sP10))))) => (~((sP21 => (~(((eps @ (^[X1:$i]:((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP54])])).
% 0.65/0.89 thf(sP55,plain,sP55 <=> (sP21 => (~(((eps @ (^[X1:$i]:((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP55])])).
% 0.65/0.89 thf(sP56,plain,sP56 <=> (f2 @ sP43),introduced(definition,[new_symbols(definition,[sP56])])).
% 0.65/0.89 thf(sP57,plain,sP57 <=> eigen__16,introduced(definition,[new_symbols(definition,[sP57])])).
% 0.65/0.89 thf(sP58,plain,sP58 <=> ((~(((~(((sP45 => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP47))))) => (~(sP33))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP58])])).
% 0.65/0.89 thf(sP59,plain,sP59 <=> ((~(sP15)) => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP59])])).
% 0.65/0.89 thf(sP60,plain,sP60 <=> ((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3),introduced(definition,[new_symbols(definition,[sP60])])).
% 0.65/0.89 thf(sP61,plain,sP61 <=> (![X1:$o]:(~((f1 @ X1)))),introduced(definition,[new_symbols(definition,[sP61])])).
% 0.65/0.89 thf(sP62,plain,sP62 <=> (f3 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP62])])).
% 0.65/0.89 thf(sP63,plain,sP63 <=> (![X1:$o]:((f1 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP63])])).
% 0.65/0.89 thf(sP64,plain,sP64 <=> (![X1:$o]:(~((f0 @ X1)))),introduced(definition,[new_symbols(definition,[sP64])])).
% 0.65/0.89 thf(sP65,plain,sP65 <=> ((~(sP5)) => (~(((f0 = (^[X1:$o]:X1)) => (~((eigen__0 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP65])])).
% 0.65/0.89 thf(sP66,plain,sP66 <=> ((~(((~(((sP45 => (~((eigen__3 = eigen__0)))) => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~((eigen__3 = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~((eigen__3 = eigen__2))))))))) => sP62),introduced(definition,[new_symbols(definition,[sP66])])).
% 0.65/0.89 thf(sP67,plain,sP67 <=> eigen__10,introduced(definition,[new_symbols(definition,[sP67])])).
% 0.65/0.89 thf(sP68,plain,sP68 <=> (sP36 => (~(((eps @ (^[X1:$i]:((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP68])])).
% 0.65/0.89 thf(sP69,plain,sP69 <=> (((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => sP24),introduced(definition,[new_symbols(definition,[sP69])])).
% 0.65/0.89 thf(sP70,plain,sP70 <=> (![X1:$o]:((f2 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP70])])).
% 0.65/0.89 thf(sP71,plain,sP71 <=> ((~(sP40)) => (~(sP9))),introduced(definition,[new_symbols(definition,[sP71])])).
% 0.65/0.89 thf(sP72,plain,sP72 <=> (f1 @ sP46),introduced(definition,[new_symbols(definition,[sP72])])).
% 0.65/0.89 thf(sP73,plain,sP73 <=> ((~(((sP45 => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP62 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP47))))) => (~(sP33))),introduced(definition,[new_symbols(definition,[sP73])])).
% 0.65/0.89 thf(sP74,plain,sP74 <=> ((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP51 => (~((X1 = eigen__3))))))))) = eigen__0),introduced(definition,[new_symbols(definition,[sP74])])).
% 0.65/0.89 thf(sP75,plain,sP75 <=> (f1 @ $false),introduced(definition,[new_symbols(definition,[sP75])])).
% 0.65/0.89 thf(sP76,plain,sP76 <=> (![X1:$o]:((f2 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP76])])).
% 0.65/0.89 thf(sP77,plain,sP77 <=> ((~(((~((sP25 => (~(sP17))))) => (~(sP52))))) => (~(sP12))),introduced(definition,[new_symbols(definition,[sP77])])).
% 0.65/0.89 thf(sP78,plain,sP78 <=> ((sP38 => (~(sP74))) => (~((sP4 => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP51 => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP78])])).
% 0.65/0.89 thf(sP79,plain,sP79 <=> (f0 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP79])])).
% 0.65/0.89 thf(sP80,plain,sP80 <=> ((~(((sP35 => (~((eigen__2 = eigen__0)))) => (~((sP36 => (~((eigen__2 = eigen__1))))))))) => (f2 = (^[X1:$o]:X1))),introduced(definition,[new_symbols(definition,[sP80])])).
% 0.65/0.89 thf(sP81,plain,sP81 <=> (f0 @ $false),introduced(definition,[new_symbols(definition,[sP81])])).
% 0.65/0.89 thf(sP82,plain,sP82 <=> (sP79 => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~((sP79 => (~((X1 = eigen__2))))))))) => (~((sP51 => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP82])])).
% 0.65/0.89 thf(sP83,plain,sP83 <=> (sP45 => (~(((eps @ (^[X1:$i]:((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP62 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP83])])).
% 0.65/0.89 thf(sP84,plain,sP84 <=> ((~((sP25 => (~(sP17))))) => (~(sP52))),introduced(definition,[new_symbols(definition,[sP84])])).
% 0.65/0.89 thf(sP85,plain,sP85 <=> (eigen__7 = sP46),introduced(definition,[new_symbols(definition,[sP85])])).
% 0.65/0.89 thf(sP86,plain,sP86 <=> (f1 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP86])])).
% 0.65/0.89 thf(sP87,plain,sP87 <=> (f3 @ (~($false))),introduced(definition,[new_symbols(definition,[sP87])])).
% 0.65/0.89 thf(sP88,plain,sP88 <=> ((~(sP69)) => (~((sP19 => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP88])])).
% 0.65/0.89 thf(sP89,plain,sP89 <=> (sP13 = (~($false))),introduced(definition,[new_symbols(definition,[sP89])])).
% 0.65/0.89 thf(sP90,plain,sP90 <=> (f2 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP90])])).
% 0.65/0.89 thf(sP91,plain,sP91 <=> (![X1:$i]:(~(((~(((~(((sP45 => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP62 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP91])])).
% 0.65/0.89 thf(sP92,plain,sP92 <=> ((~(sP31)) => (~(sP10))),introduced(definition,[new_symbols(definition,[sP92])])).
% 0.65/0.89 thf(sP93,plain,sP93 <=> eigen__7,introduced(definition,[new_symbols(definition,[sP93])])).
% 0.65/0.89 thf(sP94,plain,sP94 <=> (f3 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP94])])).
% 0.65/0.89 thf(sP95,plain,sP95 <=> (sP38 => (~(sP74))),introduced(definition,[new_symbols(definition,[sP95])])).
% 0.65/0.89 thf(sP96,plain,sP96 <=> (sP25 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP96])])).
% 0.65/0.89 thf(sP97,plain,sP97 <=> ((eps @ (^[X1:$i]:((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~((sP90 => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP97])])).
% 0.65/0.89 thf(sP98,plain,sP98 <=> (sP74 => (~(sP53))),introduced(definition,[new_symbols(definition,[sP98])])).
% 0.65/0.89 thf(sP99,plain,sP99 <=> ((~(sP65)) => (~((sP51 => (~((eigen__0 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP99])])).
% 0.65/0.89 thf(sP100,plain,sP100 <=> (f3 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP100])])).
% 0.65/0.89 thf(sP101,plain,sP101 <=> ((~($false)) = sP43),introduced(definition,[new_symbols(definition,[sP101])])).
% 0.65/0.89 thf(sP102,plain,sP102 <=> $false,introduced(definition,[new_symbols(definition,[sP102])])).
% 0.65/0.89 thf(sP103,plain,sP103 <=> (f1 @ (~(sP102))),introduced(definition,[new_symbols(definition,[sP103])])).
% 0.65/0.89 thf(sP104,plain,sP104 <=> ((~(sP88)) => (~((sP29 => (~((eigen__1 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP104])])).
% 0.65/0.89 thf(sP105,plain,sP105 <=> (sP83 => (~(sP47))),introduced(definition,[new_symbols(definition,[sP105])])).
% 0.65/0.89 thf(sP106,plain,sP106 <=> (![X1:$o]:((f1 @ X1) = (~(sP102)))),introduced(definition,[new_symbols(definition,[sP106])])).
% 0.65/0.89 thf(sP107,plain,sP107 <=> (sP62 => (~(sP60))),introduced(definition,[new_symbols(definition,[sP107])])).
% 0.65/0.89 thf(sP108,plain,sP108 <=> (sP103 = (~(sP102))),introduced(definition,[new_symbols(definition,[sP108])])).
% 0.65/0.89 thf(sP109,plain,sP109 <=> (sP4 => (~(((eps @ (^[X1:$i]:((~(((~(((sP38 => (~((X1 = eigen__0)))) => (~((sP4 => (~((X1 = eigen__1))))))))) => (~((sP79 => (~((X1 = eigen__2))))))))) => (~((sP51 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP109])])).
% 0.65/0.89 thf(sP110,plain,sP110 <=> (sP72 = (~(sP102))),introduced(definition,[new_symbols(definition,[sP110])])).
% 0.65/0.89 thf(sP111,plain,sP111 <=> (![X1:$i]:(~(((~(((~(((sP35 => (~((X1 = eigen__0)))) => (~((sP36 => (~((X1 = eigen__1))))))))) => (~((sP90 => (~((X1 = eigen__2))))))))) => (~((sP21 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP111])])).
% 0.65/0.89 thf(def_case,definition,(case = (^[X1:$o>$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(eps @ (^[X6:$i]:(((((X1 = (^[X7:$o]:sP102)) & (X6 = X2)) | ((X1 = (~)) & (X6 = X3))) | ((X1 = (^[X7:$o]:X7)) & (X6 = X4))) | ((X1 = (^[X7:$o]:$true)) & (X6 = X5)))))))))))).
% 0.65/0.89 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP38 => (~((X5 = X1)))) => (~((sP4 => (~((X5 = X2))))))))) => (~((sP79 => (~((X5 = X3))))))))) => (~((sP51 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP86 => (~((X5 = X1)))) => (~((sP24 => (~((X5 = X2))))))))) => (~((sP19 => (~((X5 = X3))))))))) => (~((sP29 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP35 => (~((X5 = X1)))) => (~((sP36 => (~((X5 = X2))))))))) => (~((sP90 => (~((X5 = X3))))))))) => (~((sP21 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP45 => (~((X5 = X1)))) => (~((sP100 => (~((X5 = X2))))))))) => (~((sP94 => (~((X5 = X3))))))))) => (~((sP62 => (~((X5 = X4))))))))) = X4))))))))))).
% 0.65/0.89 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP38 => (~((X5 = X1)))) => (~((sP4 => (~((X5 = X2))))))))) => (~((sP79 => (~((X5 = X3))))))))) => (~((sP51 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP86 => (~((X5 = X1)))) => (~((sP24 => (~((X5 = X2))))))))) => (~((sP19 => (~((X5 = X3))))))))) => (~((sP29 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP35 => (~((X5 = X1)))) => (~((sP36 => (~((X5 = X2))))))))) => (~((sP90 => (~((X5 = X3))))))))) => (~((sP21 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP45 => (~((X5 = X1)))) => (~((sP100 => (~((X5 = X2))))))))) => (~((sP94 => (~((X5 = X3))))))))) => (~((sP62 => (~((X5 = X4))))))))) = X4)))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.65/0.89 thf(h2,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(~(((~(((~((((eps @ (^[X4:$i]:((~(((~(((sP38 => (~((X4 = eigen__0)))) => (~((sP4 => (~((X4 = X1))))))))) => (~((sP79 => (~((X4 = X2))))))))) => (~((sP51 => (~((X4 = X3))))))))) = eigen__0) => (~(((eps @ (^[X4:$i]:((~(((~(((sP86 => (~((X4 = eigen__0)))) => (~((sP24 => (~((X4 = X1))))))))) => (~((sP19 => (~((X4 = X2))))))))) => (~((sP29 => (~((X4 = X3))))))))) = X1)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP35 => (~((X4 = eigen__0)))) => (~((sP36 => (~((X4 = X1))))))))) => (~((sP90 => (~((X4 = X2))))))))) => (~((sP21 => (~((X4 = X3))))))))) = X2)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP45 => (~((X4 = eigen__0)))) => (~((sP100 => (~((X4 = X1))))))))) => (~((sP94 => (~((X4 = X2))))))))) => (~((sP62 => (~((X4 = X3))))))))) = X3))))))))))),introduced(assumption,[])).
% 0.65/0.89 thf(h3,assumption,(~((![X1:$i]:(![X2:$i]:(~(((~(((~((((eps @ (^[X3:$i]:((~(((~(((sP38 => (~((X3 = eigen__0)))) => (~((sP4 => (~((X3 = eigen__1))))))))) => (~((sP79 => (~((X3 = X1))))))))) => (~((sP51 => (~((X3 = X2))))))))) = eigen__0) => (~(((eps @ (^[X3:$i]:((~(((~(((sP86 => (~((X3 = eigen__0)))) => (~((sP24 => (~((X3 = eigen__1))))))))) => (~((sP19 => (~((X3 = X1))))))))) => (~((sP29 => (~((X3 = X2))))))))) = eigen__1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP35 => (~((X3 = eigen__0)))) => (~((sP36 => (~((X3 = eigen__1))))))))) => (~((sP90 => (~((X3 = X1))))))))) => (~((sP21 => (~((X3 = X2))))))))) = X1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP45 => (~((X3 = eigen__0)))) => (~((sP100 => (~((X3 = eigen__1))))))))) => (~((sP94 => (~((X3 = X1))))))))) => (~((sP62 => (~((X3 = X2))))))))) = X2)))))))))),introduced(assumption,[])).
% 0.65/0.89 thf(h4,assumption,(~((![X1:$i]:(~(((~(((~((((eps @ (^[X2:$i]:((~(((~(((sP38 => (~((X2 = eigen__0)))) => (~((sP4 => (~((X2 = eigen__1))))))))) => (~((sP79 => (~((X2 = eigen__2))))))))) => (~((sP51 => (~((X2 = X1))))))))) = eigen__0) => (~(((eps @ (^[X2:$i]:((~(((~(((sP86 => (~((X2 = eigen__0)))) => (~((sP24 => (~((X2 = eigen__1))))))))) => (~((sP19 => (~((X2 = eigen__2))))))))) => (~((sP29 => (~((X2 = X1))))))))) = eigen__1)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP35 => (~((X2 = eigen__0)))) => (~((sP36 => (~((X2 = eigen__1))))))))) => (~((sP90 => (~((X2 = eigen__2))))))))) => (~((sP21 => (~((X2 = X1))))))))) = eigen__2)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP45 => (~((X2 = eigen__0)))) => (~((sP100 => (~((X2 = eigen__1))))))))) => (~((sP94 => (~((X2 = eigen__2))))))))) => (~((sP62 => (~((X2 = X1))))))))) = X1))))))))),introduced(assumption,[])).
% 0.65/0.89 thf(h5,assumption,sP59,introduced(assumption,[])).
% 0.65/0.89 thf(h6,assumption,sP87,introduced(assumption,[])).
% 0.65/0.89 thf(h7,assumption,(~(sP102)),introduced(assumption,[])).
% 0.65/0.89 thf(h8,assumption,(~(sP87)),introduced(assumption,[])).
% 0.65/0.89 thf(h9,assumption,sP102,introduced(assumption,[])).
% 0.65/0.89 thf(h10,assumption,sP8,introduced(assumption,[])).
% 0.65/0.89 thf(h11,assumption,(~(sP8)),introduced(assumption,[])).
% 0.65/0.89 thf(h12,assumption,sP44,introduced(assumption,[])).
% 0.65/0.89 thf(h13,assumption,(~(sP44)),introduced(assumption,[])).
% 0.65/0.89 thf(h14,assumption,sP75,introduced(assumption,[])).
% 0.65/0.89 thf(h15,assumption,(~(sP75)),introduced(assumption,[])).
% 0.65/0.89 thf(1,plain,((~(sP56) | sP27) | sP43),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(2,plain,((sP50 | ~(sP67)) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(3,plain,((~(sP48) | sP81) | sP67),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(4,plain,((~(sP48) | sP2) | ~(sP50)),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(5,plain,((sP85 | ~(sP93)) | ~(sP46)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(6,plain,((~(sP26) | sP72) | ~(sP85)),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(7,plain,(sP66 | ~(sP62)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(8,plain,(~(sP91) | ~(sP66)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(9,plain,(sP80 | ~(sP90)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(10,plain,(sP14 | ~(sP80)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(11,plain,(~(sP111) | ~(sP14)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(12,plain,(sP69 | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(13,plain,(sP88 | ~(sP69)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(14,plain,(sP104 | ~(sP88)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(15,plain,(~(sP34) | ~(sP104)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(16,plain,((sP32 | sP102) | ~(sP57)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(17,plain,((~(sP8) | sP13) | sP57),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(18,plain,((~(sP87) | sP13) | ~(sP32)),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(19,plain,((sP101 | sP102) | ~(sP43)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(20,plain,((~(sP44) | sP56) | ~(sP101)),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(21,plain,((~(sP75) | sP26) | sP93),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(22,plain,((~(sP75) | sP72) | sP46),inference(mating_rule,[status(thm)],[])).
% 0.65/0.89 thf(23,plain,((sP89 | ~(sP13)) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(24,plain,(sP41 | ~(sP89)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16])).
% 0.65/0.89 thf(25,plain,(sP62 | ~(sP41)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(26,plain,((sP42 | ~(sP56)) | ~(sP43)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(27,plain,((sP42 | sP56) | sP43),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(28,plain,(sP76 | ~(sP42)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13])).
% 0.65/0.89 thf(29,plain,(sP90 | ~(sP76)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(30,plain,(sP64 | sP48),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])).
% 0.65/0.89 thf(31,plain,(sP38 | ~(sP64)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(32,plain,(sP5 | ~(sP38)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(33,plain,(sP65 | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(34,plain,(sP99 | ~(sP65)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(35,plain,((sP20 | ~(sP26)) | sP93),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(36,plain,((sP20 | sP26) | ~(sP93)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(37,plain,(sP63 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 0.65/0.89 thf(38,plain,(sP24 | ~(sP63)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(39,plain,((sP110 | ~(sP72)) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(40,plain,(sP106 | ~(sP110)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])).
% 0.65/0.89 thf(41,plain,(~(sP1) | ~(sP99)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(42,plain,(sP17 | sP53),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(43,plain,(~(sP61) | ~(sP75)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(44,plain,(~(sP86) | sP61),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(45,plain,(sP25 | sP86),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(46,plain,(~(sP18) | ~(sP75)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(47,plain,(~(sP19) | sP18),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(48,plain,(sP52 | sP19),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(49,plain,((~(sP96) | ~(sP25)) | ~(sP17)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(50,plain,((~(sP84) | sP96) | ~(sP52)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(51,plain,(~(sP7) | sP28),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(52,plain,(~(sP4) | sP7),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(53,plain,(sP109 | sP4),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(54,plain,(sP95 | sP74),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(55,plain,(~(sP11) | sP3),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(56,plain,(~(sP79) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(57,plain,(sP82 | sP79),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(58,plain,((~(sP78) | ~(sP95)) | ~(sP109)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(59,plain,((~(sP40) | sP78) | ~(sP82)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(60,plain,(~(sP70) | ~(sP44)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(61,plain,(~(sP36) | sP70),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(62,plain,(sP68 | sP36),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(63,plain,(~(sP30) | ~(sP44)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(64,plain,(~(sP35) | sP30),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(65,plain,(sP49 | sP35),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(66,plain,(sP10 | sP97),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(67,plain,((~(sP31) | ~(sP49)) | ~(sP68)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(68,plain,((~(sP92) | sP31) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(69,plain,(~(sP23) | ~(sP87)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(70,plain,(~(sP100) | sP23),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(71,plain,(sP47 | sP100),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(72,plain,(~(sP39) | ~(sP87)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(73,plain,(~(sP45) | sP39),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(74,plain,(sP83 | sP45),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(75,plain,(~(sP37) | ~(sP8)),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(76,plain,(~(sP94) | sP37),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(77,plain,(sP33 | sP94),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(78,plain,((~(sP105) | ~(sP83)) | ~(sP47)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(79,plain,((~(sP73) | sP105) | ~(sP33)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(80,plain,((~(sP108) | sP103) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(81,plain,(~(sP106) | sP108),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(82,plain,(~(sP29) | sP106),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(83,plain,(sP12 | sP29),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(84,plain,((~(sP77) | sP84) | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(85,plain,((~(sP28) | sP81) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(86,plain,((~(sP3) | sP2) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(87,plain,(~(sP16) | sP3),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(88,plain,(~(sP51) | sP16),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(89,plain,(sP9 | sP51),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(90,plain,((~(sP71) | sP40) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(91,plain,((~(sP22) | sP27) | sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(92,plain,(~(sP6) | sP22),inference(all_rule,[status(thm)],[])).
% 0.65/0.89 thf(93,plain,(~(sP21) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(94,plain,(sP55 | sP21),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(95,plain,((~(sP54) | sP92) | ~(sP55)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(96,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(97,plain,(sP107 | sP60),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(98,plain,((~(sP58) | sP73) | ~(sP107)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
% 0.65/0.89 thf(99,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[99]).
% 0.65/0.89 thf(100,plain,(sP77 | sP34),inference(choice_rule,[status(thm)],[99])).
% 0.65/0.89 thf(101,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[101]).
% 0.65/0.89 thf(102,plain,(sP71 | sP1),inference(choice_rule,[status(thm)],[101])).
% 0.65/0.89 thf(103,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[103]).
% 0.65/0.89 thf(104,plain,(sP54 | sP111),inference(choice_rule,[status(thm)],[103])).
% 0.65/0.89 thf(105,plain,((~(sP98) | ~(sP74)) | ~(sP53)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(106,plain,((~(sP15) | sP98) | ~(sP97)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(107,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[107]).
% 0.65/0.89 thf(108,plain,(sP58 | sP91),inference(choice_rule,[status(thm)],[107])).
% 0.65/0.89 thf(109,plain,((~(sP59) | sP15) | ~(sP60)),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(f2f,axiom,(~(sP27))).
% 0.65/0.89 thf(f1t,axiom,(~(sP103))).
% 0.65/0.89 thf(f0t,axiom,(~(sP2))).
% 0.65/0.89 thf(f0f,axiom,(~(sP81))).
% 0.65/0.89 thf(110,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h7,h12,h7,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,100,102,104,105,106,108,109,h5,h6,h10,h12,f2f,f1t,h14,f0t,f0f])).
% 0.65/0.89 thf(111,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(112,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h9,h12,h7,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[111,h9])).
% 0.65/0.89 thf(f1f,axiom,(sP75 = (~(sP102)))).
% 0.65/0.89 thf(113,plain,$false,inference(tab_bq,[status(thm),assumptions([h12,h7,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h14,h7]),tab_bq(discharge,[h15,h9])],[f1f,110,112,h14,h7,h15,h9])).
% 0.65/0.89 thf(114,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(115,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h7,h13,h9,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[114,h9])).
% 0.65/0.89 thf(116,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(117,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h9,h13,h9,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[116,h9])).
% 0.65/0.89 thf(118,plain,$false,inference(tab_bq,[status(thm),assumptions([h13,h9,h10,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h14,h7]),tab_bq(discharge,[h15,h9])],[f1f,115,117,h14,h7,h15,h9])).
% 0.65/0.89 thf(f2t,axiom,(sP44 = (~(sP102)))).
% 0.65/0.89 thf(119,plain,$false,inference(tab_bq,[status(thm),assumptions([h10,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h12,h7]),tab_bq(discharge,[h13,h9])],[f2t,113,118,h12,h7,h13,h9])).
% 0.65/0.89 thf(120,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(121,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h7,h12,h7,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[120,h9])).
% 0.65/0.89 thf(122,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(123,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h9,h12,h7,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[122,h9])).
% 0.65/0.89 thf(124,plain,$false,inference(tab_bq,[status(thm),assumptions([h12,h7,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h14,h7]),tab_bq(discharge,[h15,h9])],[f1f,121,123,h14,h7,h15,h9])).
% 0.65/0.89 thf(125,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(126,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h7,h13,h9,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[125,h9])).
% 0.65/0.89 thf(127,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(128,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h9,h13,h9,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[127,h9])).
% 0.65/0.89 thf(129,plain,$false,inference(tab_bq,[status(thm),assumptions([h13,h9,h11,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h14,h7]),tab_bq(discharge,[h15,h9])],[f1f,126,128,h14,h7,h15,h9])).
% 0.65/0.89 thf(130,plain,$false,inference(tab_bq,[status(thm),assumptions([h11,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h12,h7]),tab_bq(discharge,[h13,h9])],[f2t,124,129,h12,h7,h13,h9])).
% 0.65/0.89 thf(f3f,axiom,(sP8 = (~(sP102)))).
% 0.65/0.89 thf(131,plain,$false,inference(tab_bq,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h10,h7]),tab_bq(discharge,[h11,h9])],[f3f,119,130,h10,h7,h11,h9])).
% 0.65/0.89 thf(132,plain,~(sP102),inference(prop_rule,[status(thm)],[])).
% 0.65/0.89 thf(133,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0])],[132,h9])).
% 0.65/0.89 thf(f3t,axiom,(sP87 = (~(sP102)))).
% 0.65/0.89 thf(134,plain,$false,inference(tab_bq,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_bq(discharge,[h6,h7]),tab_bq(discharge,[h8,h9])],[f3t,131,133,h6,h7,h8,h9])).
% 0.65/0.89 thf(135,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,134,h5])).
% 0.65/0.89 thf(136,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,135,h4])).
% 0.65/0.89 thf(137,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,136,h3])).
% 0.65/0.89 thf(138,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,137,h2])).
% 0.65/0.89 thf(139,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[138,h0])).
% 0.65/0.89 thf(0,theorem,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP38 => (~((X5 = X1)))) => (~((sP4 => (~((X5 = X2))))))))) => (~((sP79 => (~((X5 = X3))))))))) => (~((sP51 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP86 => (~((X5 = X1)))) => (~((sP24 => (~((X5 = X2))))))))) => (~((sP19 => (~((X5 = X3))))))))) => (~((sP29 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP35 => (~((X5 = X1)))) => (~((sP36 => (~((X5 = X2))))))))) => (~((sP90 => (~((X5 = X3))))))))) => (~((sP21 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP45 => (~((X5 = X1)))) => (~((sP100 => (~((X5 = X2))))))))) => (~((sP94 => (~((X5 = X3))))))))) => (~((sP62 => (~((X5 = X4))))))))) = X4)))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[138,h1])).
% 0.65/0.89 % SZS output end Proof
%------------------------------------------------------------------------------