%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN732^5 : 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 : n026.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 03:17:12 PM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 54 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 31 ~; 7 |; 0 &; 44 @)
% ( 7 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 1 ^; 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cQ,type,
cQ: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( ~ ( cP @ eigen__2 @ X1 )
=> ( cQ @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: $i] :
~ ( cP @ X1 @ eigen__2 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( cP @ X1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP3
=> ~ ! [X1: $i] :
~ ( ~ ( cP @ eigen__0 @ X1 )
=> ( cQ @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ( ~ ! [X2: $i] :
~ ( cP @ X2 @ X1 )
=> ~ ! [X2: $i] :
~ ( ~ ( cP @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP4
=> ( cQ @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cX3411,conjecture,
( ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ X1 )
=> ! [X2: $i] : ( cQ @ X2 @ X1 ) )
=> ~ sP6 ) ).
thf(h1,negated_conjecture,
~ ( ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ X1 )
=> ! [X2: $i] : ( cQ @ X2 @ X1 ) )
=> ~ sP6 ),
inference(assume_negation,[status(cth)],[cX3411]) ).
thf(h2,assumption,
! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ X1 )
=> ! [X2: $i] : ( cQ @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP2
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP3
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
( sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,h3]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,8,h2,h3]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
( ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ X1 )
=> ! [X2: $i] : ( cQ @ X2 @ X1 ) )
=> ~ sP6 ),
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN732^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n026.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 : Wed Oct 8 15:14:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22grackle2xfee4
% 0.20/0.42 % Steps: 43
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------