%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO548^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 03:23:51 PM UTC 2025
% Result : Theorem 20.19s 20.48s
% Output : Proof 20.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 30 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 21 ~; 5 |; 0 &; 19 @)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 1 ^; 10 !; 0 ?; 15 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__55,type,
eigen__55: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__55,definition,
( eigen__55
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ! [X2: $i] : ( X1 @ X2 )
=> ~ ( X1
@ @+[X2: $i] :
~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__55])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ! [X1: $i] : ( eigen__55 @ X1 )
=> ~ ( eigen__55
@ @+[X1: $i] :
~ ( eigen__55 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( eigen__55 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( $i > $o ) > $i] :
~ ! [X2: $i > $o] :
( ~ ! [X3: $i] : ( X2 @ X3 )
=> ~ ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__55
@ @+[X1: $i] :
~ ( eigen__55 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] : ( X1 @ X2 )
=> ~ ( X1
@ @+[X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(choicecomp,conjecture,
~ sP3 ).
thf(h1,negated_conjecture,
sP3,
inference(assume_negation,[status(cth)],[choicecomp]) ).
thf(1,plain,
( ~ sP4
| sP2 ),
inference(choice_rule,[status(thm)],[]) ).
thf(2,plain,
( sP1
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP1
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__55]) ).
thf(5,plain,
( ~ sP3
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
~ sP3,
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO548^1 : TPTP v9.2.0. Released v5.2.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 01:01:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 20.19/20.48 % SZS status Theorem
% 20.19/20.48 % Mode: cade22grackle2x798d
% 20.19/20.48 % Steps: 7582
% 20.19/20.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------