TSTP Solution File: SEU819^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU819^2 : 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 : n002.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 17:35:43 EDT 2023
% Result : Theorem 0.55s 0.83s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 47
% Syntax : Number of formulae : 57 ( 21 unt; 8 typ; 7 def)
% Number of atoms : 265 ( 28 equ; 2 cnn)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 694 ( 111 ~; 16 |; 6 &; 382 @)
% ( 13 <=>; 166 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 26 con; 0-2 aty)
% Number of variables : 129 ( 32 ^; 96 !; 1 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
=> ( subset @ X1 @ eigen__5 ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__5 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__5 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__5 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__5 ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
=> ( subset @ X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( X2 != emptyset )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( subset @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(def_nonempty,definition,
( nonempty
= ( ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).
thf(def_transitiveset,definition,
( transitiveset
= ( ^ [X1: $i] :
! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( subset @ X2 @ X1 ) ) ) ) ).
thf(def_setunionTransitive,definition,
( setunionTransitive
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( transitiveset @ X2 ) )
@ ( transitiveset @ ( setunion @ X1 ) ) ) ) ) ).
thf(def_stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [X1: $i] :
( ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( in @ X2 @ X3 )
& ( in @ X3 @ X4 ) )
@ ( in @ X2 @ X4 ) ) ) ) )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ( X2 = X3 )
| ( in @ X2 @ X3 )
| ( in @ X3 @ X2 ) ) ) )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( (~) @ ( in @ X2 @ X2 ) ) ) ) ) ) ).
thf(def_wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [X1: $i] :
( ( stricttotalorderedByIn @ X1 )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( nonempty @ X2 )
@ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X2 )
@ ( ( X3 = X4 )
| ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).
thf(def_ordinal,definition,
( ordinal
= ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) ) ) ).
thf(setunionOrdinalLem1,conjecture,
( sP13
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) )
=> ( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ~ ( ( in @ X3 @ X4 )
=> ~ ( in @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ~ ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) )
=> ( in @ X4 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X3 ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( X3 != emptyset )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( ( X4 != X5 )
=> ( in @ X4 @ X5 ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP13
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) )
=> ( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ~ ( ( in @ X3 @ X4 )
=> ~ ( in @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ~ ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) )
=> ( in @ X4 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X3 ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( X3 != emptyset )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( ( X4 != X5 )
=> ( in @ X4 @ X5 ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[setunionOrdinalLem1]) ).
thf(h2,assumption,
sP13,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) )
=> ( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ~ ( ( in @ X3 @ X4 )
=> ~ ( in @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ~ ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) )
=> ( in @ X4 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X3 ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( X3 != emptyset )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( ( X4 != X5 )
=> ( in @ X4 @ X5 ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP9
=> sP8 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| ~ sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(7,plain,
( ~ sP12
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| ~ sP3
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2,h5,h8,h9]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,12,h7]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,13,h5,h6]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,14,h4]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,15,h2,h3]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
( sP13
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) )
=> ( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ~ ( ( in @ X3 @ X4 )
=> ~ ( in @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ~ ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) )
=> ( in @ X4 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X3 ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( X3 != emptyset )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( ( X4 != X5 )
=> ( in @ X4 @ X5 ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[16,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU819^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n002.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 16:19:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.55/0.83 % SZS status Theorem
% 0.55/0.83 % Mode: cade22grackle2xfee4
% 0.55/0.83 % Steps: 11431
% 0.55/0.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------