%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO039^1 : 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 : n025.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 03:22:33 PM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 11
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 9 ~; 7 |; 0 &; 6 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $o > $i ).
thf(sP1,plain,
( sP1
<=> ( ( h @ $false )
= ( h @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ $false ) = sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( h @ sP1 )
= ( h @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( h @ ~ sP3 )
= ( h @ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(1,plain,
( sP2
| sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
~ sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP4
| ~ sP5
| sP3 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( sP4
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf('1_001',axiom,
~ sP4 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm)],[1,2,3,4,5,1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO039^1 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Oct 9 01:22:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % Mode: cade22grackle2xfee4
% 0.20/0.37 % Steps: 14
% 0.20/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------