TSTP Solution File: SEU634^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU634^2 : 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 : n004.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 13:54:48 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 57
% Syntax : Number of formulae : 67 ( 18 unt; 8 typ; 5 def)
% Number of atoms : 141 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 241 ( 34 ~; 21 |; 0 &; 134 @)
% ( 20 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 25 ( 2 ^ 23 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ( in @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ( eigen__2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ( subset @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__1 @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> ~ ( in @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( subset @ ( setunion @ ( setadjoin @ eigen__0 @ emptyset ) ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP10
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP7
=> ~ ( in @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_uniqinunit,definition,
uniqinunit = sP19 ).
thf(def_subsetI2,definition,
subsetI2 = sP13 ).
thf(def_setunionE2,definition,
setunionE2 = sP1 ).
thf(setunionsingleton1,conjecture,
( sP19
=> ( sP13
=> ( sP1
=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP19
=> ( sP13
=> ( sP1
=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[setunionsingleton1]) ).
thf(h2,assumption,
sP19,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP13
=> ( sP1
=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP13,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
sP17,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP4
| ~ sP17
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP19
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP18
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP18
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(9,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP16
| ~ sP10
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP5
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(15,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| ~ sP5
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h2,h4,h6,h8]) ).
thf(19,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)],[h7,18,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,19,h6,h7]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,21,h2,h3]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
( sP19
=> ( sP13
=> ( sP1
=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU634^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 20:46:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 65
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------