%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU683^2 : 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 02:33:43 PM UTC 2025
% Result : Theorem 20.23s 20.73s
% Output : Proof 20.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__3 @ ( setadjoin @ eigen__2 @ emptyset ) )
=> ( eigen__3 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ( eigen__1 @ eigen__3 )
=> ( in @ eigen__3 @ ( dsetconstr @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__4 @ ( setadjoin @ eigen__2 @ emptyset ) )
=> ( eigen__4 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__4 @ ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__4 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ( sP1
=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( dsetconstr @ eigen__0 @ eigen__1 )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ eigen__3 @ ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ eigen__4 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__2 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( eigen__1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( in @ eigen__3 @ ( dsetconstr @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( in @ eigen__3 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP16
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP1
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__3 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> $false ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(def_dsetconstrI,definition,
( dsetconstrI
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).
thf(def_uniqinunit,definition,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_ex1,definition,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ).
thf(ex1E2,conjecture,
( sP13
=> ( sP20
=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP13
=> ( sP20
=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ex1E2]) ).
thf(h1,assumption,
sP13,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP20
=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP20,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
=> ( ( dsetconstr @ eigen__0 @ X1 )
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__1 ) )
=> ( ( dsetconstr @ eigen__0 @ eigen__1 )
!= ( setadjoin @ X1 @ emptyset ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( eigen__1 @ X1 )
=> ( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__1 ) )
=> ( ( dsetconstr @ eigen__0 @ eigen__1 )
!= ( setadjoin @ X1 @ emptyset ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( eigen__1 @ X1 )
=> ( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( in @ eigen__2 @ ( dsetconstr @ eigen__0 @ eigen__1 ) )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h10,assumption,
in @ eigen__2 @ ( dsetconstr @ eigen__0 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP10,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( sP16
=> ( ( eigen__1 @ X1 )
=> ( eigen__3 = X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP8,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( sP16
=> ( ( eigen__1 @ X1 )
=> ( eigen__3 = X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP27
=> ( sP16
=> ( sP1
=> sP17 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP27,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP16
=> ( sP1
=> sP17 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP16,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP1
=> sP17 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP1,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP23
| sP6
| ~ sP10
| sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP19
| sP11
| ~ sP10
| sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP25
| sP3
| ~ sP14
| sP26 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP24
| ~ sP1
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP22
| ~ sP16
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
~ sP26,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| ~ sP27
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| ~ sP8
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP14 ),
inference(symeq,[status(thm)],[]) ).
thf(10,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP18
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP5
| ~ sP6
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| ~ sP11
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP15
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP21
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP20
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP20
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP3
| sP17 ),
inference(symeq,[status(thm)],[]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h1,h3,h11,h13,h16,h18,h20,h21]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,21,h20,h21]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,22,h18,h19]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,23,h16,h17]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,24,h15]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,25,h13,h14]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h8,26,h12]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,27,h10,h11]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,28,h9]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,29,h7,h8]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,30,h6]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,31,h5]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,32,h3,h4]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,33,h1,h2]) ).
thf(0,theorem,
( sP13
=> ( sP20
=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU683^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 : 300
% 0.13/0.34 % DateTime : Wed Oct 8 21:04:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 20.23/20.73 % SZS status Theorem
% 20.23/20.73 % Mode: cade22grackle2x798d
% 20.23/20.73 % Steps: 2301
% 20.23/20.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------