TSTP Solution File: SEU716^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU716^2 : 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 : 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 : 600s
% DateTime : Tue Jul 19 13:58:37 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 52
% Syntax : Number of formulae : 65 ( 20 unt; 7 typ; 3 def)
% Number of atoms : 165 ( 3 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 306 ( 25 ~; 16 |; 0 &; 179 @)
% ( 16 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 24 con; 0-2 aty)
% Number of variables : 43 ( 1 ^ 42 !; 0 ?; 43 :)
% 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_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__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( subset @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ( sP9
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(def_powersetE,definition,
powersetE = sP5 ).
thf(def_subsetI2,definition,
subsetI2 = sP4 ).
thf(subsetTI,conjecture,
( sP5
=> ( sP4
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ( sP4
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[subsetTI]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP4
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP4,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP15
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) )
=> ( subset @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) )
=> ( subset @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ( sP1
=> sP11 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
in @ eigen__2 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| ~ sP15
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP2
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(10,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP8
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| ~ sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h4,h8,h13,h14]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,13,h13,h14]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,14,h11,h12]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,15,h10]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,16,h8,h9]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,17,h7]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,18,h6]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,19,h4,h5]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
( sP5
=> ( sP4
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[21,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU716^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 00:27:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 12
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------