TSTP Solution File: SEU621^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU621^2 : 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 : n031.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 17:19:56 EDT 2023
% Result : Theorem 20.69s 20.91s
% Output : Proof 20.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 46
% Syntax : Number of formulae : 56 ( 16 unt; 7 typ; 3 def)
% Number of atoms : 113 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 194 ( 21 ~; 15 |; 0 &; 114 @)
% ( 15 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 23 con; 0-2 aty)
% Number of variables : 34 ( 7 ^; 27 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
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 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( setadjoin @ eigen__1 @ emptyset ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__4 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( in @ eigen__4 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__4 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__4 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> ( subset @ ( setadjoin @ eigen__1 @ emptyset ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( subset @ ( setadjoin @ eigen__1 @ emptyset ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ eigen__4 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(def_uniqinunit,definition,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
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(singletonsubset,conjecture,
( sP15
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP15
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[singletonsubset]) ).
thf(h2,assumption,
sP15,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP6 ),
inference(symeq,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP14
| sP2
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(10,plain,
( ~ sP9
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h9]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,13,h8,h9]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,15,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,16,h4,h5]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
( sP15
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU621^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 21:23:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 20.69/20.91 % SZS status Theorem
% 20.69/20.91 % Mode: cade22grackle2x798d
% 20.69/20.91 % Steps: 7420
% 20.69/20.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------