%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV243^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 Oct 9 02:55:20 PM UTC 2025
% Result : Theorem 181.23s 181.44s
% Output : Proof 181.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 85
% Syntax : Number of formulae : 100 ( 24 unt; 0 typ; 4 def)
% Number of atoms : 282 ( 9 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 645 ( 141 ~; 45 |; 0 &; 288 @)
% ( 37 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 44 con; 0-2 aty)
% Number of variables : 146 ( 27 ^; 119 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(ty_eigen__30,type,
eigen__30: a ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__9,type,
eigen__9: a ).
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__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ 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__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__2 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__30,definition,
( eigen__30
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__30])]) ).
thf(sP1,plain,
( sP1
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK
@ ^ [X3: a] :
~ ! [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( cK
@ ( cK
@ ^ [X3: a] :
~ ! [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ( eigen__2 @ X1 )
=> ( cK @ eigen__2 @ X1 ) )
=> ~ ( eigen__2 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__2 @ eigen__1 )
=> ( cK @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cK @ eigen__2 @ eigen__1 )
=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: a] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [X1: a] :
( ( cK @ eigen__2 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cK @ eigen__10 @ eigen__0 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__10 @ eigen__30 )
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__30 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cK @ eigen__10 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__10 @ eigen__0 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: a] :
( ( eigen__10 @ X1 )
=> ( cK @ eigen__10 @ X1 ) )
=> ~ ( eigen__10 @ eigen__30 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( cK @ eigen__10 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__10 @ eigen__30 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__30 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a] :
( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( cK
@ ^ [X3: a] :
~ ! [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cK @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ( cK @ eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
=> ( cK @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP8
=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( cK @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP16
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP22
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__10 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a] :
( ( cK @ eigen__2 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(cTHM116_C_pme,conjecture,
( sP27
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ( sP27
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM116_C_pme]) ).
thf(h3,assumption,
sP27,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP1 != ( ~ sP28 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
sP28,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP20
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP22
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP25
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP29
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP29
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP36
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP32
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(8,plain,
( ~ sP6
| ~ sP32
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP19
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP4
| ~ sP34
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP22
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP26
| ~ sP30
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| ~ sP37
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP31
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP31
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP8
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(18,plain,
( sP23
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP23
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP30
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(21,plain,
( ~ sP27
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP27
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP28
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,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,h3,h6,h7]) ).
thf(h10,assumption,
~ ( sP21
=> ~ sP33 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP21,
introduced(assumption,[]) ).
thf(h12,assumption,
sP33,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP7
| ~ sP10
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP13
| ~ sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP17
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( sP9
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP9
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( sP35
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__30]) ).
thf(32,plain,
( ~ sP18
| ~ sP35
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP27
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP11
| ~ sP33
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP21
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h5,h3,h4,h2,h1,h0])],[25,26,27,28,29,30,31,32,33,34,35,36,h3,h8,h11,h12]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,37,h11,h12]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__10)],[h9,38,h10]) ).
thf(40,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,24,39,h6,h7,h8,h9]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,40,h5]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,41,h3,h4]) ).
thf(43,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[42,h1]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[43,h0]) ).
thf(0,theorem,
( sP27
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[42,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV243^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 19:39:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 181.23/181.44 % SZS status Theorem
% 181.23/181.44 % Mode: cade22grackle2x2d0b
% 181.23/181.44 % Steps: 326
% 181.23/181.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------