%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU557^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:32:09 PM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of formulae : 50 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 152 ( 70 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 355 ( 74 ~; 5 |; 1 &; 143 @)
% ( 6 <=>; 126 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 129 ( 15 ^; 113 !; 1 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_descr,type,
descr: ( $i > $o ) > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__4 = X1 )
=> ( ( eigen__0 @ eigen__4 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( eigen__0 @ X1 )
= ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__4 )
= ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( descr @ eigen__0 )
= ( descr @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ).
thf(def_exuEu,definition,
( exuEu
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ) ).
thf(def_descrp,definition,
( descrp
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ).
thf(descr__Cong,conjecture,
( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) )
=> ( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) )
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X2 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) )
=> ( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) )
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[descr__Cong]) ).
thf(h2,assumption,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) )
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( eigen__0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( X2 = X3 ) ) )
=> ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( ( descr @ eigen__0 )
= ( descr @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP3
=> ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) )
=> sP6 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) )
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) )
=> sP6 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( eigen__0 @ eigen__2 )
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
eigen__0 @ eigen__2,
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__2 = X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ( eigen__1 @ eigen__3 )
=> ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__3 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
eigen__1 @ eigen__3,
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__3 = X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP1
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(4,plain,
( sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP6
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,h8,h16]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,6,h18,h19]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__3)],[h15,7,h17]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h11,8,h15,h16]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,9,h13,h14]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h10,10,h12]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,11,h10,h11]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,12,h8,h9]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,13,h7]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,15,h4,h5]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,16,h2,h3]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) )
=> ( ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) )
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X2 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU557^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 21:11:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % Mode: cade22grackle2xfee4
% 0.20/0.43 % Steps: 113
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------