%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU564^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 02:43:41 PM UTC 2025
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ) ).
thf(subsetE,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ X4 @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ X4 @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[subsetE]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in @ X3 @ X1 ) )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( sP2
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP2
=> sP4 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h4,h6,h7]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,3,h6,h7]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,4,h4,h5]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,5,h3]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,6,h2]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ X4 @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU564^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 21:48:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % Mode: mode213
% 0.14/0.37 % Inferences: 3
% 0.14/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------