%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:25 PM UTC 2026
% Result : Theorem 20.14s 20.50s
% Output : Proof 20.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 37
% Syntax : Number of formulae : 45 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 96 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 163 ( 48 ~; 19 |; 0 &; 57 @)
% ( 17 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 20 con; 0-2 aty)
% Number of variables : 45 ( 5 ^; 33 !; 0 ?; 45 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__69,type,
eigen__69: a > $o ).
thf(ty_eigen__1,type,
eigen__1: ( a > $o ) > $o ).
thf(ty_eigen__68,type,
eigen__68: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__68,definition,
( eigen__68
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( eigen__1 @ X1 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__68])]) ).
thf(h1,assumption,
! [X1: ( ( a > $o ) > $o ) > $o,X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: ( a > $o ) > $o] :
~ ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( a > $o ) > a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__69,definition,
( eigen__69
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__69])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__68 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1
@ ^ [X1: a] : $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ( eigen__68
@ @+[X1: a] : ( eigen__68 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ( eigen__1 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
~ ( eigen__69 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__68
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__69
@ @+[X1: a] : ( eigen__69 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ sP10 )
= ( ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( a > $o ) > a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ( eigen__1 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
~ ( eigen__68 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( a > $o ) > a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP7
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__68
@ @+[X1: a] : ( eigen__68 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ( eigen__1 @ X1 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM541,conjecture,
sP11 ).
thf(h2,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[cTHM541]) ).
thf(1,plain,
( sP9
| sP7 ),
inference(choice_rule,[status(thm)],[]) ).
thf(2,plain,
( sP16
| sP13 ),
inference(choice_rule,[status(thm)],[]) ).
thf(3,plain,
( sP8
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP3
| ~ sP8 ),
inference(mating_rule,[status(thm)],[]) ).
thf(5,plain,
( sP15
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP15
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP5
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP5
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP4
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__69]) ).
thf(10,plain,
( sP17
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__68]) ).
thf(11,plain,
( ~ sP10
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP12
| ~ sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( sP6
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP6
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP14
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(17,plain,
( sP11
| sP10
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h2]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h2])],[18,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 21:56:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 20.14/20.50 % SZS status Theorem
% 20.14/20.50 % Mode: cade22grackle2x798d
% 20.14/20.50 % Steps: 2535
% 20.14/20.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------