%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO233^5 : 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 : n025.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 03:23:05 PM UTC 2025
% Result : Theorem 20.21s 20.43s
% Output : Proof 20.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cM,type,
cM: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cN,type,
cN: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( cM @ X1 )
= ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cM @ eigen__0 )
= ( cN @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(cLEIBNIZ,conjecture,
( ! [X1: $i,X2: $i > $o] :
( ( X2 @ ( cM @ X1 ) )
=> ( X2 @ ( cN @ X1 ) ) )
=> ( cM = cN ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i,X2: $i > $o] :
( ( X2 @ ( cM @ X1 ) )
=> ( X2 @ ( cN @ X1 ) ) )
=> ( cM = cN ) ),
inference(assume_negation,[status(cth)],[cLEIBNIZ]) ).
thf(h1,assumption,
! [X1: $i,X2: $i > $o] :
( ( X2 @ ( cM @ X1 ) )
=> ( X2 @ ( cN @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
cM != cN,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h3,h1,h1,h2,h0])],[1,h1,h4]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,2,h4]) ).
thf(4,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h1,h2,h0]),tab_fe(discharge,[h3])],[h2,3,h3]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,4,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i,X2: $i > $o] :
( ( X2 @ ( cM @ X1 ) )
=> ( X2 @ ( cN @ X1 ) ) )
=> ( cM = cN ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYO233^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Oct 9 00:58:08 EDT 2025
% 0.15/0.37 % CPUTime :
% 20.21/20.43 % SZS status Theorem
% 20.21/20.43 % Mode: cade22grackle2x798d
% 20.21/20.43 % Steps: 10
% 20.21/20.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------