%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU688^2 : 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 : n015.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 02:33:52 PM UTC 2025
% Result : Theorem 42.01s 40.85s
% Output : Proof 42.01s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__76,type,
eigen__76: $i ).
thf(ty_eigen__79,type,
eigen__79: $i ).
thf(ty_eigen__77,type,
eigen__77: $i ).
thf(ty_eigen__83,type,
eigen__83: $i ).
thf(ty_eigen__81,type,
eigen__81: $i ).
thf(ty_eigen__75,type,
eigen__75: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__74,type,
eigen__74: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(ty_func,type,
func: $i > $i > $i > $o ).
thf(ty_eigen__82,type,
eigen__82: $i ).
thf(ty_eigen__84,type,
eigen__84: $i ).
thf(ty_eigen__78,type,
eigen__78: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__80,type,
eigen__80: $i ).
thf(ty_eigen__85,type,
eigen__85: $i ).
thf(ty_funcSet,type,
funcSet: $i > $i > $i ).
thf(ty_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(ty_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(ty_eigen__86,type,
eigen__86: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ eigen__0 @ X1 ) )
=> ( func @ eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> infuncsetfunc ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__4 @ eigen__1 )
=> ( sP2
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__2 @ ( funcSet @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ ( funcSet @ eigen__0 @ eigen__1 ) )
=> ( func @ eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ X1 )
= X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> funcGraphProp2 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( func @ eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ( func @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ( func @ eigen__0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ eigen__0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( func @ X1 @ X2 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( func @ eigen__0 @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( ( ap @ eigen__0 @ eigen__1 @ X1 @ X2 )
= X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
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(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_func,definition,
( func
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( breln @ X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ex1 @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ).
thf(def_infuncsetfunc,definition,
( infuncsetfunc
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
@ ( func @ X1 @ X2 @ X3 ) ) ) ) ).
thf(def_funcGraphProp2,definition,
( funcGraphProp2
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( func @ X1 @ X2 @ X3 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X2 )
@ ( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ ( kpair @ X4 @ X5 ) @ X3 )
@ ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ) ).
thf(funcGraphProp4,conjecture,
( sP3
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcGraphProp4]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP9,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ eigen__0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ eigen__0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( funcSet @ eigen__0 @ eigen__1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( ( ap @ eigen__0 @ eigen__1 @ X1 @ X2 )
= X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP6
=> sP8 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
sP21,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h14,assumption,
sP16,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h18,assumption,
sP13,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h21,assumption,
sP19,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP2
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP16
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP18
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| ~ sP21
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP11
| ~ sP10
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| ~ sP6
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP14
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP19
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP13
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h21,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h18,h21,h8,h11,h14,h16,h17]) ).
thf(h24,assumption,
~ ! [X1: $i,X2: $i] :
( ( func @ eigen__74 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__74 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ eigen__74 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: $i] :
( ( func @ eigen__74 @ eigen__75 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__74 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__75 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( ( ap @ eigen__74 @ eigen__75 @ X1 @ X2 )
= X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ( func @ eigen__74 @ eigen__75 @ eigen__76 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__74 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__75 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ X1 )
= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
func @ eigen__74 @ eigen__75 @ eigen__76,
introduced(assumption,[]) ).
thf(h28,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__74 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__75 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ X1 )
= X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ( in @ eigen__77 @ eigen__74 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__75 )
=> ( ( in @ ( kpair @ eigen__77 @ X1 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ eigen__77 )
= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
in @ eigen__77 @ eigen__74,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__75 )
=> ( ( in @ ( kpair @ eigen__77 @ X1 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ eigen__77 )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( ( in @ eigen__78 @ eigen__75 )
=> ( ( in @ ( kpair @ eigen__77 @ eigen__78 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ eigen__77 )
= eigen__78 ) ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
in @ eigen__78 @ eigen__75,
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ( in @ ( kpair @ eigen__77 @ eigen__78 ) @ eigen__76 )
=> ( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ eigen__77 )
= eigen__78 ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
in @ ( kpair @ eigen__77 @ eigen__78 ) @ eigen__76,
introduced(assumption,[]) ).
thf(h36,assumption,
( ( ap @ eigen__74 @ eigen__75 @ eigen__76 @ eigen__77 )
!= eigen__78 ),
introduced(assumption,[]) ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h35,h36,h33,h34,h32,h30,h31,h29,h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[h3,h22]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h32,h30,h31,h29,h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h34,15,h35,h36]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h30,h31,h29,h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h33,h34])],[h32,16,h33,h34]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h30,h31,h29,h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__78)],[h31,17,h32]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h30,h31])],[h29,18,h30,h31]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h28,h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__77)],[h28,19,h29]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,20,h27,h28]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__76)],[h25,21,h26]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__75)],[h24,22,h25]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__74)],[h23,23,h24]) ).
thf(funcGraphProp2,axiom,
sP9 = sP19 ).
thf(25,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h1,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_bq(discharge,[h3,h21]),tab_bq(discharge,[h22,h23])],[funcGraphProp2,14,24,h3,h21,h22,h23]) ).
thf(h37,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ eigen__79 @ X1 ) )
=> ( func @ eigen__79 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( funcSet @ eigen__79 @ eigen__80 ) )
=> ( func @ eigen__79 @ eigen__80 @ X1 ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ( in @ eigen__81 @ ( funcSet @ eigen__79 @ eigen__80 ) )
=> ( func @ eigen__79 @ eigen__80 @ eigen__81 ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
in @ eigen__81 @ ( funcSet @ eigen__79 @ eigen__80 ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( func @ eigen__79 @ eigen__80 @ eigen__81 ),
introduced(assumption,[]) ).
thf(26,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h21,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[h1,h19]) ).
thf(h42,assumption,
~ ! [X1: $i,X2: $i] :
( ( func @ eigen__82 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__82 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ eigen__82 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
~ ! [X1: $i] :
( ( func @ eigen__82 @ eigen__83 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__82 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__83 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( ( ap @ eigen__82 @ eigen__83 @ X1 @ X2 )
= X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( ( func @ eigen__82 @ eigen__83 @ eigen__84 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__82 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__83 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ X1 )
= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
func @ eigen__82 @ eigen__83 @ eigen__84,
introduced(assumption,[]) ).
thf(h46,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__82 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__83 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ X1 )
= X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ( in @ eigen__85 @ eigen__82 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__83 )
=> ( ( in @ ( kpair @ eigen__85 @ X1 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ eigen__85 )
= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
in @ eigen__85 @ eigen__82,
introduced(assumption,[]) ).
thf(h49,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__83 )
=> ( ( in @ ( kpair @ eigen__85 @ X1 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ eigen__85 )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h50,assumption,
~ ( ( in @ eigen__86 @ eigen__83 )
=> ( ( in @ ( kpair @ eigen__85 @ eigen__86 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ eigen__85 )
= eigen__86 ) ) ),
introduced(assumption,[]) ).
thf(h51,assumption,
in @ eigen__86 @ eigen__83,
introduced(assumption,[]) ).
thf(h52,assumption,
~ ( ( in @ ( kpair @ eigen__85 @ eigen__86 ) @ eigen__84 )
=> ( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ eigen__85 )
= eigen__86 ) ),
introduced(assumption,[]) ).
thf(h53,assumption,
in @ ( kpair @ eigen__85 @ eigen__86 ) @ eigen__84,
introduced(assumption,[]) ).
thf(h54,assumption,
( ( ap @ eigen__82 @ eigen__83 @ eigen__84 @ eigen__85 )
!= eigen__86 ),
introduced(assumption,[]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h53,h54,h51,h52,h50,h48,h49,h47,h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[h3,h22]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h50,h48,h49,h47,h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h53,h54])],[h52,27,h53,h54]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h50,h48,h49,h47,h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h51,h52])],[h50,28,h51,h52]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h48,h49,h47,h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h50]),tab_negall(eigenvar,eigen__86)],[h49,29,h50]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h49])],[h47,30,h48,h49]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h45,h46,h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h47]),tab_negall(eigenvar,eigen__85)],[h46,31,h47]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h44,h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h45,h46])],[h44,32,h45,h46]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h43,h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__84)],[h43,33,h44]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h42,h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h43]),tab_negall(eigenvar,eigen__83)],[h42,34,h43]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__82)],[h23,35,h42]) ).
thf(37,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h40,h41,h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_bq(discharge,[h3,h21]),tab_bq(discharge,[h22,h23])],[funcGraphProp2,26,36,h3,h21,h22,h23]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h40,h41])],[h39,37,h40,h41]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h39]),tab_negall(eigenvar,eigen__81)],[h38,38,h39]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h37,h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__80)],[h37,39,h38]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h37]),tab_negall(eigenvar,eigen__79)],[h20,40,h37]) ).
thf(infuncsetfunc,axiom,
sP3 = sP13 ).
thf(42,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_bq(discharge,[h1,h18]),tab_bq(discharge,[h19,h20])],[infuncsetfunc,25,41,h1,h18,h19,h20]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,42,h16,h17]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,43,h14,h15]) ).
thf(45,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,44,h13]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,45,h11,h12]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,46,h10]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,47,h8,h9]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,48,h7]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,49,h6]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,50,h5]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,51,h3,h4]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,52,h1,h2]) ).
thf(0,theorem,
( sP3
=> ( sP9
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[53,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU688^2 : TPTP v9.2.0. Released v3.7.0.
% 0.04/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 21:42:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 42.01/40.85 % SZS status Theorem
% 42.01/40.85 % Mode: cade22grackle2x6987
% 42.01/40.85 % Steps: 6813
% 42.01/40.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------