%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV243^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 02:56:31 PM UTC 2025
% Result : Theorem 42.55s 42.72s
% Output : Proof 42.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 95
% Syntax : Number of formulae : 110 ( 24 unt; 0 typ; 4 def)
% Number of atoms : 325 ( 9 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 643 ( 136 ~; 52 |; 0 &; 286 @)
% ( 42 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 49 con; 0-2 aty)
% Number of variables : 133 ( 23 ^; 110 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__125,type,
eigen__125: a ).
thf(ty_eigen__111,type,
eigen__111: a > $o ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(ty_eigen__18,type,
eigen__18: a ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__125,definition,
( eigen__125
= ( eps__1
@ ^ [X1: a] :
~ ( ( cK @ eigen__111 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__125])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [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__2])]) ).
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] :
( ( eigen__10 @ X1 )
=> ( cK @ eigen__10 @ X1 ) )
=> ~ ( eigen__10 @ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__10 @ eigen__2 )
=> ( cK @ eigen__10 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__10 @ eigen__18 )
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__18 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__111 @ X1 )
=> ( cK @ eigen__111 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__125 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cK @ ( cK @ eigen__111 ) @ eigen__0 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a] :
( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [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,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cK @ eigen__111 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cK @ eigen__111 @ eigen__125 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__111 @ eigen__0 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( cK @ eigen__111 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [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,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cK @ eigen__10 @ eigen__2 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP15
=> ! [X1: a] :
( ( cK @ ( cK @ eigen__111 ) @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
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
<=> ( eigen__10 @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: a] :
( ( cK @ eigen__111 @ X1 )
=> ( cK @ ( cK @ eigen__111 ) @ X1 ) )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ eigen__111 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( cK @ ( cK @ eigen__111 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cK @ eigen__10 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP8
=> ! [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
<=> ( sP6
=> ! [X1: a] :
( ( cK @ eigen__111 @ X1 )
=> ( cK @ ( cK @ eigen__111 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP19
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP11
=> ( cK @ ( cK @ eigen__111 ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [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,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__10 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP12
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__111 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ( cK @ eigen__111 @ X1 )
=> ( cK @ ( cK @ eigen__111 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [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,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a] :
( ( cK @ ( cK @ eigen__111 ) @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cK @ ( cK @ eigen__111 ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP21
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP36
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [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,[sP42])]) ).
thf(cTHM116_C_pme,conjecture,
( sP30
=> ! [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,
~ ( sP30
=> ! [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,
sP30,
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 != ( ~ sP32 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
sP32,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP21
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP14
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP5
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP18
| ~ sP25
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP42
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP37
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18]) ).
thf(8,plain,
( ~ sP10
| ~ sP37
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP3
| ~ sP31
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP21
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( sP40
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP40
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP19
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(15,plain,
( sP28
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP28
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP26
| ~ sP8
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP17
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP8
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(20,plain,
( ~ sP41
| ~ sP36
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP30
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP30
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP32
| sP41 ),
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,
~ ( sP6
=> ~ sP34 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
sP34,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP23
| ~ sP35
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP7
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( sP33
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP33
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP29
| ~ sP11
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP9
| ~ sP39
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP35
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP38
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP27
| ~ sP6
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP15
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__125]) ).
thf(35,plain,
( ~ sP20
| ~ sP15
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP24
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP4
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP13
| ~ sP34
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP30
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP30
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP6
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h5,h3,h4,h2,h1,h0])],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,h3,h8,h11,h12]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,42,h11,h12]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__111)],[h9,43,h10]) ).
thf(45,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,24,44,h6,h7,h8,h9]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,45,h5]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,46,h3,h4]) ).
thf(48,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[47,h1]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[48,h0]) ).
thf(0,theorem,
( sP30
=> ! [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])],[47,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV243^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 19:39:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 42.55/42.72 % SZS status Theorem
% 42.55/42.72 % Mode: mode484
% 42.55/42.72 % Inferences: 62257
% 42.55/42.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------