TSTP Solution File: SEV019^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV019^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:32:20 EDT 2023
% Result : Theorem 0.21s 0.71s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 119
% Syntax : Number of formulae : 134 ( 17 unt; 11 typ; 9 def)
% Number of atoms : 348 ( 35 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 526 ( 145 ~; 64 |; 0 &; 199 @)
% ( 52 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 61 con; 0-2 aty)
% Number of variables : 78 ( 9 ^; 69 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cQ,type,
cQ: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__16,type,
eigen__16: a > $o ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__12,type,
eigen__12: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ( cQ @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( cQ @ eigen__1 @ X1 )
=> ( cQ @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( cQ @ eigen__3 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( cQ @ eigen__3 @ eigen__4 )
=> ~ ( cQ @ eigen__4 @ X1 ) )
=> ( cQ @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( cQ @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cQ @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__12 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__12 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__6 @ eigen__1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cQ @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ! [X1: a] :
~ ( eigen__6 @ X1 )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ! [X2: a] :
( ( eigen__6 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__16 @ eigen__0 )
= sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] : ( cQ @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP6
= ( cQ @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP6
=> ! [X1: a] :
( ( eigen__12 @ X1 )
= ( cQ @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__16 @ X1 )
= ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__6 @ eigen__2 )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( eigen__12 @ X1 )
= ( cQ @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__12 @ X1 )
=> ! [X2: a] :
( ( eigen__12 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__6 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ ! [X1: a] :
~ ( eigen__16 @ X1 )
=> ~ ! [X1: a] :
( ( eigen__16 @ X1 )
=> ! [X2: a] :
( ( eigen__16 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) )
=> ~ ( eigen__16 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a] :
( ( eigen__16 @ X1 )
=> ! [X2: a] :
( ( eigen__16 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
=> ! [X2: a] :
( ( eigen__6 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP7
= ( cQ @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__12 @ eigen__3 )
=> ! [X1: a] :
( ( eigen__12 @ X1 )
= ( cQ @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cQ @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP7
= ( cQ @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__6 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ( eigen__12 @ X1 )
= ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a] :
( ~ ( sP26
=> ~ ( cQ @ eigen__4 @ X1 ) )
=> ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP9
=> ( cQ @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cQ @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ! [X1: a] :
~ ( eigen__16 @ X1 )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP10
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ! [X1: a] :
~ ( eigen__12 @ X1 )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eigen__16 @ eigen__0 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( cQ @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP12
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP38
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__16 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP19 = sP32 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: a] :
( ( cQ @ eigen__1 @ X1 )
=> ( cQ @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__12 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a,X2: a] :
( ~ ( ( cQ @ eigen__3 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP26
=> ~ ( cQ @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP46
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP28
=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( cQ @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( cQ @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ sP35
=> ~ sP43 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( cQ @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(cTHM559_pme,conjecture,
( sP1
=> ~ sP39 ) ).
thf(h2,negated_conjecture,
~ ( sP1
=> ~ sP39 ),
inference(assume_negation,[status(cth)],[cTHM559_pme]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP39,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| ~ sP40
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP36
| ~ sP40
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP33
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP21
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP21
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP3
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16]) ).
thf(9,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP27
| ~ sP7
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP24
| sP7
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP29
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP6
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP29
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP14
| ~ sP6
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP25
| ~ sP43
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP18
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP35
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP51
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP51
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP45
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(24,plain,
( ~ sP1
| ~ sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP41
| ~ sP19
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP50
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP49
| ~ sP28
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP16
| sP28
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP23
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP2
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP8
| ~ sP19
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP23
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( sP10
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP34
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP34
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP4
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(37,plain,
( ~ sP1
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( sP46
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP46
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP47
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP47
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP30
| ~ sP47 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(43,plain,
( sP44
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(44,plain,
( sP48
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(45,plain,
( sP31
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP31
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP42
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(48,plain,
( sP20
| ~ sP42 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(49,plain,
( sP12
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(50,plain,
( ~ sP38
| ~ sP12
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP39
| sP38
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,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,h3,h4]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,52,h3,h4]) ).
thf(54,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[53,h1]) ).
thf(55,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[54,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP39 ),
inference(contra,[status(thm),contra(discharge,[h2])],[53,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV019^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 04:02:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.71 % SZS status Theorem
% 0.21/0.71 % Mode: cade22grackle2xfee4
% 0.21/0.71 % Steps: 3135
% 0.21/0.71 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------