%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO360^5 : 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 : n009.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 03:23:18 PM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_j,type,
j: a > a ).
thf(ty_f,type,
f: ( a > a ) > a > a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_g,type,
g: ( a > a ) > a > a ).
thf(ty_h,type,
h: a > a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( g @ h @ eigen__0 )
= ( g @ j @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( f @ h @ X1 )
= ( g @ h @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ h @ eigen__0 )
= ( g @ h @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( h = j ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > a,X2: a] :
( ( f @ X1 @ X2 )
= ( g @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( f @ h @ eigen__0 )
= ( g @ j @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cEDEC1,conjecture,
( ~ ( sP7
=> ~ sP1 )
=> ( ( f @ h )
= ( g @ j ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP7
=> ~ sP1 )
=> ( ( f @ h )
= ( g @ j ) ) ),
inference(assume_negation,[status(cth)],[cEDEC1]) ).
thf(h1,assumption,
~ ( sP7
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( f @ h )
!= ( g @ j ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( f @ h @ X1 )
= ( g @ j @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP2
| sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
~ sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP8
| sP3
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h3,h4,h6]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,7,h6]) ).
thf(9,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_fe(discharge,[h5])],[h2,8,h5]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( ~ ( sP7
=> ~ sP1 )
=> ( ( f @ h )
= ( g @ j ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO360^5 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n009.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 : Thu Oct 9 01:14:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % Mode: cade22grackle2xfee4
% 0.21/0.40 % Steps: 56
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------