%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN991^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 03:17:33 PM UTC 2025
% Result : Unsatisfiable 0.15s 0.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 6
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 1 def)
% Number of atoms : 11 ( 1 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 3 ~; 2 |; 0 &; 4 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $i > $o,X2: $i] : ( X1 @ X2 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax,axiom,
sP2 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm)],[1,2,ax]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.14 % Problem : SYN991^1 : TPTP v9.2.0. Released v3.7.0.
% 0.15/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Oct 8 15:05:38 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.40 % SZS status Unsatisfiable
% 0.15/0.40 % Mode: cade22grackle2xfee4
% 0.15/0.40 % Steps: 13
% 0.15/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------