%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU896^5 : 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 : n029.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 02:42:06 PM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_x,type,
x: b ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_y,type,
y: b ).
thf(ty_g,type,
g: b > a ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
= ( g @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( g @ eigen__1 )
= ( g @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = x ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 = y ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( g @ eigen__1 )
= ( g @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP1
=> ( eigen__0
= ( g @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0
= ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0
= ( g @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b] :
( ( ( X1 != x )
=> ( X1 = y ) )
=> ( eigen__0
!= ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP4
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cTHM500_pme,conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
!= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM500_pme]) ).
thf(h1,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ~ sP10 ) != sP7 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP11
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP1
| sP2
| ~ sP3 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
~ sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP9
| sP2
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP11
| sP4
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h8,h9,h10,h11]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h4,7,h10,h11]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,8,h8,h9]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h3,9,h7]) ).
thf(11,plain,
( ~ sP10
| ~ sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP7
| sP1
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h2,h1,h0])],[11,12,13,h5,h6]) ).
thf(15,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,10,14,h3,h4,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,15,h2]) ).
thf(17,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,16,h1]) ).
thf(0,theorem,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU896^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 21:17:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % Mode: cade22grackle2xfee4
% 0.20/0.39 % Steps: 26
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------