%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU730^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 Oct 9 02:34:57 PM UTC 2025
% Result : Theorem 20.24s 20.52s
% Output : Proof 20.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setminus,type,
setminus: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) )
=> ( in @ X1 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) )
=> ( in @ X2 @ X1 ) ) )
=> ( subset @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) @ ( powerset @ eigen__0 ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( subset @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> ( in @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP1
=> ( sP5
=> sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ eigen__1 ) ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP5
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(def_complementT_lem,definition,
( complementT_lem
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ).
thf(def_subsetTI,definition,
( subsetTI
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( powerset @ X1 ) )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X2 )
@ ( in @ X4 @ X3 ) ) )
@ ( subset @ X2 @ X3 ) ) ) ) ) ) ).
thf(def_doubleComplementE1,definition,
( doubleComplementE1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
@ ( in @ X3 @ X2 ) ) ) ) ) ) ).
thf(doubleComplementSub2,conjecture,
( sP4
=> ( sP18
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP4
=> ( sP18
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[doubleComplementSub2]) ).
thf(h1,assumption,
sP4,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP18
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP18,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( subset @ ( setminus @ eigen__0 @ ( setminus @ eigen__0 @ X1 ) ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP17
| ~ sP5
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP13
| ~ sP1
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP15
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP12
| ~ sP7
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP2
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP8
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1,h3,h5,h9,h10]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,15,h9,h10]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,16,h8]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,17,h7]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,18,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,19,h3,h4]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).
thf(0,theorem,
( sP4
=> ( sP18
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU730^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 20:39:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 20.24/20.52 % SZS status Theorem
% 20.24/20.52 % Mode: cade22grackle2x798d
% 20.24/20.52 % Steps: 873
% 20.24/20.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------