TSTP Solution File: SEU714^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU714^2 : 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 : n024.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 13:58:30 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setminus,type,
setminus: $i > $i > $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__0 ) )
=> ( in @ X1 @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_powersetI,definition,
powersetI = sP7 ).
thf(def_setminusEL,definition,
setminusEL = sP5 ).
thf(complementT_lem,conjecture,
( sP7
=> ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[complementT_lem]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ X1 ) @ ( powerset @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> sP6 ),
introduced(assumption,[]) ).
thf(h7,assumption,
in @ eigen__1 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,h1,h3,h8]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,7,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,8,h5]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( sP7
=> ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU714^2 : 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
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 08:05:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 8
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------