%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET616^5 : 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 : n005.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 02:24:26 PM UTC 2025
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1 @ eigen__2 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( sP1
=> ( eigen__1 @ eigen__2 ) ) )
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ^ [X1: a] :
~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cBOOL_PROP_90_pme,conjecture,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) )
=> ( X1 = X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) )
=> ( X1 = X2 ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_90_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ( eigen__0 = eigen__1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
eigen__0 != eigen__1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1 != sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,h3,h7,h8]) ).
thf(7,plain,
( ~ sP2
| ~ sP6
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP4
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h6,h5,h3,h4,h2,h1,h0])],[7,8,9,10,11,h3,h9,h10]) ).
thf(13,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,6,12,h7,h8,h9,h10]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,13,h6]) ).
thf(15,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,14,h5]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) )
=> ( X1 = X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET616^5 : 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 : n005.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 14:41:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % Mode: cade22grackle2xfee4
% 0.18/0.41 % Steps: 24
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------