%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU782^2 : 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 02:49:40 PM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 67
% Syntax : Number of formulae : 80 ( 23 unt; 0 typ; 6 def)
% Number of atoms : 209 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 452 ( 36 ~; 27 |; 0 &; 286 @)
% ( 26 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 37 con; 0-2 aty)
% Number of variables : 54 ( 5 ^; 49 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
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_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( in @ eigen__3 @ eigen__2 )
=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) )
=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( in @ eigen__3 @ eigen__2 )
=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $o] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X1 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X1 @ eigen__2 )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( subset @ eigen__1 @ X1 )
=> ( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( binunion @ eigen__1 @ eigen__2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o] :
( ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ eigen__3 @ eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__3 @ eigen__2 )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP1
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( subset @ ( binunion @ eigen__1 @ eigen__2 ) @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( sP1
=> ( ( in @ X1 @ eigen__2 )
=> ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP2
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( subset @ eigen__2 @ X1 )
=> ( ( in @ X2 @ eigen__2 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( in @ eigen__3 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i,X3: $i,X4: $o] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X3 @ X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(def_subsetI1,definition,
subsetI1 = sP11 ).
thf(def_subsetE,definition,
subsetE = sP5 ).
thf(def_binunionEcases,definition,
binunionEcases = sP26 ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).
thf(breln1unionprop,conjecture,
( sP11
=> ( sP5
=> ( sP26
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP11
=> ( sP5
=> ( sP26
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1unionprop]) ).
thf(h2,assumption,
sP11,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP5
=> ( sP26
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP26
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP26,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( subset @ ( binunion @ X1 @ X2 ) @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP17
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( subset @ ( binunion @ eigen__1 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP17,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( subset @ ( binunion @ eigen__1 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> sP20 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP23
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP21
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| ~ sP17
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP15
| ~ sP25
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| ~ sP4
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| ~ sP7
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP26
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( sP13
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP13
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP2
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(19,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP14
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP22
| ~ sP2
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h2,h4,h6,h10,h13,h14]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,22,h13,h14]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h11,23,h12]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,24,h10,h11]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,25,h9]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,26,h8]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,27,h6,h7]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,28,h4,h5]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,29,h2,h3]) ).
thf(31,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[30,h0]) ).
thf(0,theorem,
( sP11
=> ( sP5
=> ( sP26
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset @ ( binunion @ X2 @ X3 ) @ ( cartprod @ X1 @ X1 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[30,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU782^2 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 20:58:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % Mode: mode213
% 0.14/0.38 % Inferences: 15
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------