TSTP Solution File: SEU623^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU623^2 : 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 : n005.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 13:54:31 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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_emptyset,type,
emptyset: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( subset @ eigen__0 @ ( binunion @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__2 @ ( binunion @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( subset @ eigen__0 @ X1 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( in @ ( setadjoin @ eigen__2 @ emptyset ) @ ( powerset @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( subset @ eigen__0 @ ( binunion @ eigen__0 @ eigen__1 ) )
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( subset @ eigen__0 @ ( binunion @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ ( setadjoin @ eigen__2 @ emptyset ) @ ( powerset @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ eigen__0 @ eigen__1 ) )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_subsetE,definition,
subsetE = sP5 ).
thf(def_powersetsubset,definition,
( powersetsubset
= ( ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ) ) ) ).
thf(def_binunionLsub,definition,
binunionLsub = sP13 ).
thf(def_singletoninpowerset,definition,
singletoninpowerset = sP9 ).
thf(singletoninpowunion,conjecture,
( sP5
=> ( ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
=> ( sP13
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ( ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
=> ( sP13
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[singletoninpowunion]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
=> ( sP13
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP13
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ eigen__0 @ eigen__1 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| ~ sP10
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,h1,h5,h7,h12,h13]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,11,h12,h13]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,12,h11]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,13,h10]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,14,h9]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,15,h7,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,17,h3,h4]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,18,h1,h2]) ).
thf(0,theorem,
( sP5
=> ( ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
=> ( sP13
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU623^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 06:47:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 18
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------