%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU806^2 : 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 : n027.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 02:51:12 PM UTC 2025
% Result : Theorem 13.32s 13.20s
% Output : Proof 13.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 54
% Syntax : Number of formulae : 64 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 187 ( 39 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 294 ( 54 ~; 23 |; 0 &; 142 @)
% ( 21 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 30 con; 0-2 aty)
% Number of variables : 63 ( 1 ^; 62 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: $i] :
~ ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__2 )
=> ~ ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ( eigen__2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> ~ ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP15
=> ( eigen__0 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(def_foundationAx,definition,
foundationAx = sP7 ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP18 ).
thf(def_uniqinunit,definition,
uniqinunit = sP13 ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(notinself,conjecture,
( sP7
=> ( sP18
=> ( sP13
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP7
=> ( sP18
=> ( sP13
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[notinself]) ).
thf(h2,assumption,
sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP18
=> ( sP13
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP13
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP13,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
~ ( in @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP1
| ~ sP20
| ~ sP20 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP19
| ~ sP15
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP21
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
sP21,
inference(eq_sym,[status(thm)],[]) ).
thf(6,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| ~ sP11
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| ~ sP1
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP6
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP5
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(14,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP2
| sP10
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP10
| ~ sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP16
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP18
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2,h4,h6,h10]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,19,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,22,h4,h5]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,23,h2,h3]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
( sP7
=> ( sP18
=> ( sP13
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU806^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 20:44:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 13.32/13.20 % SZS status Theorem
% 13.32/13.20 % Mode: mode461
% 13.32/13.20 % Inferences: 37
% 13.32/13.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------