TSTP Solution File: SEV155^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV155^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : 600s
% DateTime : Tue Jul 19 18:05:07 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 164
% Syntax : Number of formulae : 212 ( 71 unt; 21 typ; 4 def)
% Number of atoms : 513 ( 4 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 3001 ( 657 ~; 48 |; 0 &;1535 @)
% ( 48 <=>; 713 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 211 ( 211 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 69 usr; 61 con; 0-2 aty)
% Number of variables : 717 ( 4 ^ 713 !; 0 ?; 717 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a > a > $o ).
thf(ty_eigen__12,type,
eigen__12: a > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__16,type,
eigen__16: a ).
thf(ty_eigen__7,type,
eigen__7: a > a > $o ).
thf(ty_eigen__30,type,
eigen__30: a > a > $o ).
thf(ty_eigen__35,type,
eigen__35: a > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__26,type,
eigen__26: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__27,type,
eigen__27: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__29,type,
eigen__29: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__13,type,
eigen__13: a > a > $o ).
thf(ty_eigen__28,type,
eigen__28: a ).
thf(ty_eigen__22,type,
eigen__22: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__16 @ X1 )
=> ( eigen__12 @ eigen__16 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( eigen__0 @ eigen__8 @ eigen__10 )
=> ( eigen__1 @ eigen__8 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__12 @ X1 @ X2 )
=> ~ ( eigen__12 @ X2 @ X3 ) )
=> ( eigen__12 @ X1 @ X3 ) ) )
=> ( eigen__12 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 @ eigen__16 @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__12 @ eigen__16 @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__1 @ eigen__8 @ X1 ) )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP7
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__12 @ X1 @ X2 )
=> ~ ( eigen__12 @ X2 @ X3 ) )
=> ( eigen__12 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__35 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__35 @ X1 @ X2 )
=> ~ ( eigen__35 @ X2 @ X3 ) )
=> ( eigen__35 @ X1 @ X3 ) ) )
=> ( eigen__35 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__29 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__29 @ X1 @ X2 )
=> ~ ( eigen__29 @ X2 @ X3 ) )
=> ( eigen__29 @ X1 @ X3 ) ) )
=> ( eigen__29 @ eigen__26 @ eigen__27 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ eigen__8 @ eigen__10 )
=> ( eigen__6 @ eigen__8 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__29 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__26 @ eigen__27 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__6 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP15
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__29 @ X1 @ X2 )
=> ~ ( eigen__29 @ X2 @ X3 ) )
=> ( eigen__29 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__6 @ eigen__8 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__27 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ~ ( eigen__0 @ eigen__16 @ eigen__22 )
=> sP5 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ~ ( ( eigen__29 @ eigen__26 @ eigen__27 )
=> ~ ( eigen__29 @ eigen__27 @ X1 ) )
=> ( eigen__29 @ eigen__26 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP1
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) )
=> ~ sP9 )
=> ( eigen__6 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__29 @ eigen__26 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__1 @ eigen__16 @ X1 )
=> ( eigen__12 @ eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__29 @ eigen__26 @ X1 )
=> ~ ( eigen__29 @ X1 @ X2 ) )
=> ( eigen__29 @ eigen__26 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__35 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ( ( eigen__29 @ eigen__26 @ eigen__27 )
=> ~ ( eigen__29 @ eigen__27 @ eigen__28 ) )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__35 @ X1 @ X2 )
=> ~ ( eigen__35 @ X2 @ X3 ) )
=> ( eigen__35 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__35 @ X1 @ X2 ) )
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__29 @ X1 @ X2 )
=> ~ ( eigen__29 @ X2 @ X3 ) )
=> ( eigen__29 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__0 @ eigen__8 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__29 @ eigen__27 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__35 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ ( eigen__0 @ eigen__16 @ eigen__22 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( eigen__29 @ eigen__26 @ eigen__27 )
=> ~ sP35 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__6 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__12 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP18
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__12 @ X1 @ X2 )
=> ~ ( eigen__12 @ X2 @ X3 ) )
=> ( eigen__12 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__16 @ X1 )
=> ( eigen__1 @ eigen__16 @ X1 ) )
=> ( eigen__12 @ eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__29 @ eigen__26 @ eigen__27 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(cTHM250D_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[cTHM250D_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X4 @ X5 ) )
=> ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X4 @ X6 ) ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X3 @ X4 ) )
=> ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( ~ ( ! [X2: a,X3: a] :
( ( ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X2 @ X3 ) )
=> ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) )
=> sP3 )
=> sP3 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) )
=> sP3 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP3,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__4 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__4 @ X1 ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( ~ sP2
=> sP43 )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__4 @ eigen__5 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ~ sP2
=> sP43 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__4 @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
sP43,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( sP17
=> ~ sP9 )
=> sP41 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP17
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(h21,assumption,
sP17,
introduced(assumption,[]) ).
thf(h22,assumption,
sP9,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__7 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) ) )
=> ( eigen__7 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__7 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( eigen__7 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h26,assumption,
! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__7 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP1
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP24
| ~ sP1
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP14
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP14
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP44
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(8,plain,
( sP37
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(9,plain,
( ~ sP2
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP25
| sP36
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP36
| ~ sP37
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h16,h21,h22,h20]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,12,h26,h27]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,13,h24,h25]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__7)],[h7,14,h23]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,15,h21,h22]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,16,h19,h20]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__6)],[h15,17,h18]) ).
thf(h28,assumption,
~ ( ~ ( sP22
=> ~ sP46 )
=> sP42 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( sP22
=> ~ sP46 ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP42,
introduced(assumption,[]) ).
thf(h31,assumption,
sP22,
introduced(assumption,[]) ).
thf(h32,assumption,
sP46,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__13 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__13 @ X1 @ X2 )
=> ~ ( eigen__13 @ X2 @ X3 ) )
=> ( eigen__13 @ X1 @ X3 ) ) )
=> ( eigen__13 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__13 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__13 @ X1 @ X2 )
=> ~ ( eigen__13 @ X2 @ X3 ) )
=> ( eigen__13 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( eigen__13 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h36,assumption,
! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__13 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__13 @ X1 @ X2 )
=> ~ ( eigen__13 @ X2 @ X3 ) )
=> ( eigen__13 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(19,plain,
( sP39
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP47
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP21
| ~ sP39
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP13
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP27
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__22]) ).
thf(26,plain,
( sP7
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(27,plain,
( ~ sP43
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP4
| sP10
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP10
| ~ sP7
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h36,h37,h34,h35,h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[19,20,21,22,23,24,25,26,27,28,29,h17,h31,h32,h30]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h34,30,h36,h37]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,31,h34,h35]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__13)],[h7,32,h33]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,33,h31,h32]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,34,h29,h30]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__12)],[h15,35,h28]) ).
thf(37,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,18,36,h16,h17]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,37,h14,h15]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__5)],[h12,38,h13]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__4)],[h10,39,h12]) ).
thf(h38,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ eigen__26 @ X1 ) )
=> ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ eigen__26 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ ! [X1: a] :
( ~ ( sP16
=> ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__27 @ X1 ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__26 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( ~ ( sP16
=> ~ sP20 )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__26 @ eigen__28 ) ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( sP16
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h42,assumption,
~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__26 @ eigen__28 ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
sP16,
introduced(assumption,[]) ).
thf(h44,assumption,
sP20,
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ sP18
=> sP26 ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h47,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h48,assumption,
sP15,
introduced(assumption,[]) ).
thf(h49,assumption,
sP33,
introduced(assumption,[]) ).
thf(h50,assumption,
~ ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__30 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__30 @ X1 @ X2 )
=> ~ ( eigen__30 @ X2 @ X3 ) )
=> ( eigen__30 @ X1 @ X3 ) ) )
=> ( eigen__30 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__30 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__30 @ X1 @ X2 )
=> ~ ( eigen__30 @ X2 @ X3 ) )
=> ( eigen__30 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h52,assumption,
~ ( eigen__30 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h53,assumption,
! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__30 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__30 @ X1 @ X2 )
=> ~ ( eigen__30 @ X2 @ X3 ) )
=> ( eigen__30 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(41,plain,
( ~ sP33
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP28
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP23
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP30
| sP40
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP40
| ~ sP48
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP12
| sP18
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP20
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP45
| sP18
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP18
| ~ sP15
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h53,h54,h51,h52,h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[41,42,43,44,45,46,47,48,49,50,h43,h44,h48,h49,h47]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h53,h54])],[h51,51,h53,h54]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h51,h52])],[h50,52,h51,h52]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h50]),tab_negall(eigenvar,eigen__30)],[h7,53,h50]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h48,h49])],[h46,54,h48,h49]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,55,h46,h47]) ).
thf(57,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__29)],[h42,56,h45]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,57,h43,h44]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h40,58,h41,h42]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__28)],[h39,59,h40]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h39]),tab_negall(eigenvar,eigen__27)],[h38,60,h39]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__26)],[h11,61,h38]) ).
thf(63,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,40,62,h10,h11]) ).
thf(h55,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h56,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h57,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h58,assumption,
sP38,
introduced(assumption,[]) ).
thf(h59,assumption,
sP31,
introduced(assumption,[]) ).
thf(64,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP11
| sP32
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP32
| ~ sP38
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h58,h59,h56,h57,h55,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[64,65,66,h9,h58,h59,h57]) ).
thf(68,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h56,h57,h55,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h58,h59])],[h56,67,h58,h59]) ).
thf(69,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h56,h57])],[h55,68,h56,h57]) ).
thf(70,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h55]),tab_negall(eigenvar,eigen__35)],[h7,69,h55]) ).
thf(71,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,63,70,h8,h9]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,71,h6,h7]) ).
thf(73,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,72,h5]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,73,h4]) ).
thf(75,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,74,h3]) ).
thf(76,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,75,h2]) ).
thf(77,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[76,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[76,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV155^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 03:21:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % Mode: mode213
% 0.19/0.51 % Inferences: 132
% 0.19/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------