%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU806^2 : 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 : n007.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 02:39:36 PM UTC 2025
% Result : Theorem 82.95s 83.19s
% Output : Proof 82.95s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ( ( in
@ @+[X2: $i] :
~ ( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) )
@ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ @+[X3: $i] :
~ ( ( in @ X3 @ X1 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ X1 ) ) ) )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) ) ) )
@ ( setadjoin
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ emptyset ) )
=> ~ ! [X1: $i] :
( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3
@ ( setadjoin
@ @+[X4: $i] : ( in @ X4 @ X4 )
@ emptyset ) ) ) ) )
=> ~ ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) ) ) )
@ ( setadjoin
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( @+[X1: $i] :
~ ( ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) ) ) ) )
= ( @+[X1: $i] : ( in @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( in
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP6
=> ~ ( in
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ ( setadjoin
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( @+[X1: $i] : ( in @ X1 @ X1 ) )
= ( @+[X1: $i] :
~ ( ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ ( setadjoin
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP3
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( in
@ @+[X1: $i] : ( in @ X1 @ X1 )
@ @+[X1: $i] : ( in @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3
@ ( setadjoin
@ @+[X4: $i] : ( in @ X4 @ X4 )
@ emptyset ) ) ) ) )
=> ~ ( in @ X1
@ ( setadjoin
@ @+[X2: $i] : ( in @ X2 @ X2 )
@ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> $false ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3
@ ( setadjoin
@ @+[X4: $i] : ( in @ X4 @ X4 )
@ emptyset ) ) ) )
@ ( setadjoin @ X1 @ emptyset ) )
=> ( ( @+[X2: $i] :
~ ( ( in @ X2
@ ( setadjoin
@ @+[X3: $i] : ( in @ X3 @ X3 )
@ emptyset ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3
@ ( setadjoin
@ @+[X4: $i] : ( in @ X4 @ X4 )
@ emptyset ) ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(def_foundationAx,definition,
( foundationAx
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ? [X2: $i] : ( in @ X2 @ X1 )
@ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( (~)
@ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ( in @ X3 @ X1 ) ) ) ) ) ) ) ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP16 ).
thf(def_uniqinunit,definition,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 = X4 )
@ ( ( in @ X3 @ X1 )
<=> ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(notinself,conjecture,
( ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) )
=> ( sP16
=> ( sP9
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) )
=> ( sP16
=> ( sP9
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[notinself]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP16
=> ( sP9
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ~ sP13 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP16,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP9
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ~ sP13 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP4
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP10 ),
inference(symeq,[status(thm)],[]) ).
thf(5,plain,
( ~ sP13
| sP6
| ~ sP10
| sP17 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| ~ sP6
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( sP2
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP2
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP3
| ~ sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
~ sP17,
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP16
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1,h3,h5,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h7,h8])],[h6,16,h7,h8]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h5,h6])],[h4,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) )
=> ( sP16
=> ( sP9
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU806^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n007.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 20:44:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 82.95/83.19 % SZS status Theorem
% 82.95/83.19 % Mode: cade22grackle2x4fb9
% 82.95/83.19 % Steps: 6974
% 82.95/83.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------