%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU522^2 : 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 : n011.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 02:43:24 PM UTC 2025
% Result : Theorem 1.05s 1.25s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of formulae : 38 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 102 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 147 ( 24 ~; 16 |; 0 &; 72 @)
% ( 14 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 20 con; 0-2 aty)
% Number of variables : 20 ( 3 ^; 17 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_setunion,type,
setunion: $i > $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(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ eigen__1 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
= ( ~ ! [X3: $i] :
( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( ( in @ eigen__2 @ eigen__0 )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
= ( ~ ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP4 = ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_setunionAx,definition,
setunionAx = sP1 ).
thf(setunionI,conjecture,
sP11 ).
thf(h1,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[setunionI]) ).
thf(1,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| ~ sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( sP12
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP12
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP6
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP5
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(11,plain,
( sP14
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(12,plain,
( sP10
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(13,plain,
( sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP11
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU522^2 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Wed Oct 8 21:26:38 EDT 2025
% 0.12/0.31 % CPUTime :
% 1.05/1.25 % SZS status Theorem
% 1.05/1.25 % Mode: mode506
% 1.05/1.25 % Inferences: 19
% 1.05/1.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------