%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU657^2 : 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 : n002.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 02:33:14 PM UTC 2025
% Result : Theorem 0.68s 0.86s
% Output : Proof 0.73s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_kfst,type,
kfst: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_ksnd,type,
ksnd: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
= ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ksnd @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) ) )
= ( ksnd @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) )
= ( setadjoin @ ( kfst @ eigen__0 ) @ ( setadjoin @ ( ksnd @ eigen__0 ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( kfst @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) ) )
= ( kfst @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( setadjoin @ eigen__2 @ emptyset )
= ( setadjoin @ ( ksnd @ eigen__0 ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( kfst @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( setadjoin @ ( setadjoin @ ( kfst @ eigen__0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ eigen__0 ) @ ( setadjoin @ ( ksnd @ eigen__0 ) @ emptyset ) ) @ emptyset ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ksnd @ ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1
= ( kfst @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ eigen__0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ eigen__0 ) @ ( setadjoin @ ( ksnd @ eigen__0 ) @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( setadjoin @ eigen__1 @ emptyset )
= ( setadjoin @ ( kfst @ eigen__0 ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__2
= ( ksnd @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ ( kfst @ eigen__0 ) @ ( setadjoin @ ( ksnd @ eigen__0 ) @ emptyset ) ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_iskpair,definition,
( iskpair
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(def_kpair,definition,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(def_kfstpairEq,definition,
( kfstpairEq
= ( ! [X1: $i,X2: $i] :
( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 ) ) ) ).
thf(def_ksndpairEq,definition,
( ksndpairEq
= ( ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ) ).
thf(kpairsurjEq,conjecture,
( sP8
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ ( ksnd @ X1 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP8
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ ( ksnd @ X1 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ),
inference(assume_negation,[status(cth)],[kpairsurjEq]) ).
thf(h1,assumption,
sP8,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ ( ksnd @ X1 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ ( ksnd @ X1 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ eigen__0 ) )
=> ( eigen__0
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
=> sP12 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ eigen__0 ) )
=> ( eigen__0
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( in @ eigen__1 @ ( setunion @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( eigen__0
!= ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
in @ eigen__1 @ ( setunion @ eigen__0 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( eigen__0
!= ( setadjoin @ ( setadjoin @ eigen__1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( in @ eigen__2 @ ( setunion @ eigen__0 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h12,assumption,
in @ eigen__2 @ ( setunion @ eigen__0 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP14
| sP18
| ~ sP14
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| sP7
| ~ sP1
| sP13 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP15
| ~ sP9
| ~ sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
( sP6
| sP13
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP4
| ~ sP6
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP19
| sP13
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP17
| sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP16
| ~ sP19
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
~ sP13,
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP1
| sP12
| ~ sP16
| sP13 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP11
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP10
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h1,h3,h13,h7]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,17,h12,h13]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,18,h11]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,19,h9,h10]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,20,h8]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,22,h5]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,24,h1,h2]) ).
thf(0,theorem,
( sP8
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ ( ksnd @ X1 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU657^2 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 21:27:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.68/0.86 % SZS status Theorem
% 0.68/0.86 % Mode: cade22grackle2xfee4
% 0.68/0.86 % Steps: 11513
% 0.68/0.86 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------