TSTP Solution File: SEU759^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU759^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 : 600s
% DateTime : Tue Jul 19 14:01:57 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 66
% Syntax : Number of formulae : 82 ( 26 unt; 9 typ; 4 def)
% Number of atoms : 195 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 401 ( 31 ~; 19 |; 0 &; 255 @)
% ( 19 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 29 con; 0-2 aty)
% Number of variables : 55 ( 1 ^ 54 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
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_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_powerset,type,
powerset: $i > $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__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__1 @ X1 ) )
=> ( in @ X2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ eigen__3 ) )
=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( subset @ eigen__1 @ X1 )
=> ( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( sP2
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ eigen__4 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP16
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP16
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_subsetI1,definition,
subsetI1 = sP15 ).
thf(def_subsetE,definition,
subsetE = sP3 ).
thf(def_binintersectEL,definition,
binintersectEL = sP6 ).
thf(woz13rule1,conjecture,
( sP15
=> ( sP3
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP15
=> ( sP3
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[woz13rule1]) ).
thf(h2,assumption,
sP15,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP3
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP6
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ eigen__0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( ( subset @ eigen__1 @ X2 )
=> ( subset @ ( binintersect @ eigen__1 @ X1 ) @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
in @ eigen__1 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( ( subset @ eigen__1 @ X2 )
=> ( subset @ ( binintersect @ eigen__1 @ X1 ) @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( subset @ eigen__1 @ X1 )
=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
in @ eigen__2 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( subset @ eigen__1 @ X1 )
=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ( in @ eigen__3 @ ( powerset @ eigen__0 ) )
=> ( sP2
=> sP14 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
in @ eigen__3 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP2
=> sP14 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP18
| ~ sP2
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| ~ sP7
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP19
| ~ sP16
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP17
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP17
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP9
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(13,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP4
| ~ sP9
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h15,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,h2,h4,h6,h18,h19]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,16,h18,h19]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,17,h16,h17]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h14,18,h15]) ).
thf(20,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])],[h12,19,h13,h14]) ).
thf(21,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)],[h11,20,h12]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,21,h10,h11]) ).
thf(23,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)],[h8,22,h9]) ).
thf(24,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)],[h7,23,h8]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,24,h6,h7]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,25,h4,h5]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,26,h2,h3]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
( sP15
=> ( sP3
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU759^2 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n008.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 : 600
% 0.13/0.34 % DateTime : Mon Jun 20 08:54:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 16
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------