TSTP Solution File: SEU553^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU553^2 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 Aug 31 17:18:37 EDT 2023
% Result : Theorem 0.17s 0.33s
% Output : Proof 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( powerset @ eigen__0 )
= ( powerset @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(powerset__Cong,conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( powerset @ X1 )
= ( powerset @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( powerset @ X1 )
= ( powerset @ X2 ) ) ),
inference(assume_negation,[status(cth)],[powerset__Cong]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( ( powerset @ eigen__0 )
= ( powerset @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,h3,h4]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,2,h3,h4]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( powerset @ X1 )
= ( powerset @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU553^2 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 23 21:25:16 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.33 % SZS status Theorem
% 0.17/0.33 % Mode: cade22grackle2xfee4
% 0.17/0.33 % Steps: 2
% 0.17/0.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------