%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL736^5 : 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 : n031.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 12:27:26 PM UTC 2026
% Result : Theorem 20.12s 20.49s
% Output : Proof 20.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 31 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 153 ( 51 ~; 5 |; 0 &; 72 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 1 ^; 41 !; 0 ?; 45 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__44,type,
eigen__44: b > $o ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__44,definition,
( eigen__44
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__44])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
~ ( eigen__44 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__44
@ @+[X1: b] : ( eigen__44 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(cX5310D,conjecture,
( ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
( ! [X3: b > $o] :
~ ! [X4: b,X5: b] :
~ ( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o] :
~ ! [X5: b] :
~ ( ~ ( X1 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X2 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP5 ) ).
thf(h1,negated_conjecture,
~ ( ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
( ! [X3: b > $o] :
~ ! [X4: b,X5: b] :
~ ( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o] :
~ ! [X5: b] :
~ ( ~ ( X1 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X2 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP5 ),
inference(assume_negation,[status(cth)],[cX5310D]) ).
thf(h2,assumption,
! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
( ! [X3: b > $o] :
~ ! [X4: b,X5: b] :
~ ( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o] :
~ ! [X5: b] :
~ ( ~ ( X1 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X2 @ X4 @ ( X3 @ X4 ) @ X5 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| sP1 ),
inference(choice_rule,[status(thm)],[]) ).
thf(2,plain,
( sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP4
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__44]) ).
thf(5,plain,
( ~ sP5
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,h3]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,6,h2,h3]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
( ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
( ! [X3: b > $o] :
~ ! [X4: b,X5: b] :
~ ( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o] :
~ ! [X5: b] :
~ ( ~ ( X1 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X2 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP5 ),
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL736^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.08/0.35 % Computer : n031.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 20:44:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 20.12/20.49 % SZS status Theorem
% 20.12/20.49 % Mode: cade22grackle2x798d
% 20.12/20.49 % Steps: 2539
% 20.12/20.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------