%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO114^5 : 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 : 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 03:22:46 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 58
% Syntax : Number of formulae : 66 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 184 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 311 ( 133 ~; 34 |; 0 &; 63 @)
% ( 27 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 35 con; 0-2 aty)
% Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_c,type,
c: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_a,type,
a: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_d,type,
d: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ~ ( ~ ( ~ ( ~ ( cP @ b )
=> ~ ( cQ @ b ) )
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ c ) )
=> ~ ( cQ @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ~ ( ~ ( ~ ( ~ ( cP @ a )
=> ~ ( cQ @ a ) )
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ c ) )
=> ~ ( cQ @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ~ ( ~ ( ~ ( ~ ( cP @ X1 )
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ X2 ) )
=> ~ ( cQ @ c ) )
=> ~ ( cQ @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( cP @ b )
=> ~ ( cQ @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( cP @ c )
=> ( cR @ c ) )
=> ~ ( cQ @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ( cP @ a )
=> ( cR @ a ) )
=> ~ ( cQ @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cP @ b ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2
=> ~ ( cQ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ sP5
=> ( cR @ b ) )
=> ~ ( cQ @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ ( cP @ d )
=> ( cR @ d ) )
=> ~ ( cQ @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP6
=> ~ ( cQ @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ~ ( ~ ( cP @ a )
=> ~ ( cQ @ a ) )
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ c ) )
=> ~ ( cQ @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cQ @ d ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cQ @ a ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ~ ( ~ ( cP @ a )
=> ~ sP13 )
=> ~ sP11 )
=> ~ ( cQ @ c ) )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP9
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ~ sP2
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ c ) )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( cP @ a )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cQ @ b ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
~ ( ( ~ ( cP @ X1 )
=> ( cR @ X1 ) )
=> ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( cP @ a )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ~ ( cP @ eigen__1 )
=> ( cR @ eigen__1 ) )
=> ~ ( cQ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ~ sP17
=> ~ sP11 )
=> ~ ( cQ @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cQ @ c ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP17
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ~ ( cP @ eigen__0 )
=> ( cR @ eigen__0 ) )
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cQ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cP @ a ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(cTHM119,conjecture,
( ~ ( sP19
=> ~ sP1 )
=> ~ sP20 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP19
=> ~ sP1 )
=> ~ sP20 ),
inference(assume_negation,[status(cth)],[cTHM119]) ).
thf(h2,assumption,
~ ( sP19
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP20,
introduced(assumption,[]) ).
thf(h4,assumption,
sP19,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP21
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP19
| ~ sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP25
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| ~ sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP8
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP19
| ~ sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP3
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP19
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP5
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP6
| sP2
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP9
| sP6
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP15
| sP9
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP16
| sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(14,plain,
( sP7
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP19
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| ~ sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP17
| sP27
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP24
| sP17
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP22
| sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP14
| sP22
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP10
| sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(22,plain,
( sP4
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP19
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP1
| ~ sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP20
| ~ sP27
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,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,h4,h5,h3]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,26,h4,h5]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,27,h2,h3]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
( ~ ( sP19
=> ~ sP1 )
=> ~ sP20 ),
inference(contra,[status(thm),contra(discharge,[h1])],[28,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO114^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -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 : Thu Oct 9 00:46:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 113
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------