TSTP Solution File: SEU570^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU570^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 Aug 31 17:18:51 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 57
% Syntax : Number of formulae : 69 ( 18 unt; 6 typ; 3 def)
% Number of atoms : 162 ( 3 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 261 ( 29 ~; 21 |; 0 &; 138 @)
% ( 20 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 28 con; 0-2 aty)
% Number of variables : 51 ( 9 ^; 42 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $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 @ eigen__0 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ( subset @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( subset @ eigen__0 @ X1 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( subset @ eigen__0 @ eigen__1 )
=> ( sP3
=> ( in @ eigen__3 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( sP1
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__3 @ eigen__2 ) ),
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__0 @ eigen__1 )
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__2 ) )
=> ( subset @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( subset @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP1
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( subset @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP3
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_subsetI2,definition,
( subsetI2
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(def_subsetE,definition,
( subsetE
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( subset @ X1 @ X2 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) ) ) ) ) ).
thf(subsetTrans,conjecture,
( sP5
=> ( sP19
=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ( sP19
=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[subsetTrans]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP19
=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP19,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ eigen__0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( sP15
=> ( ( subset @ eigen__1 @ X1 )
=> ( subset @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP15
=> ( sP1
=> sP17 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP1
=> sP17 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP18
| ~ sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP15
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP16
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP19
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP14
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP14
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP20
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(13,plain,
( ~ sP11
| ~ sP20
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP12
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP19
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2,h4,h9,h11,h12]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,17,h11,h12]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,19,h8]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,20,h7]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,21,h6]) ).
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,
( sP5
=> ( sP19
=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU570^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 15:22:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % Mode: cade22grackle2xfee4
% 0.22/0.44 % Steps: 279
% 0.22/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------