%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU684^2 : 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 : n024.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 02:33:46 PM UTC 2025
% Result : Theorem 20.29s 20.59s
% Output : Proof 20.29s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) )
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) )
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) )
=> ( in
@ ( kpair @ eigen__3
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) )
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in
@ ( kpair @ eigen__3
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] : ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 ) ) ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_dsetconstrER,definition,
( dsetconstrER
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( X2 @ X3 ) ) ) ) ).
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_theprop,definition,
( theprop
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( singleton @ X1 )
@ ( in @ ( setunion @ X1 ) @ X1 ) ) ) ) ).
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_funcImageSingleton,definition,
( funcImageSingleton
= ( ! [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 )
@ ( singleton
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ) ).
thf(def_ap,definition,
( ap
= ( ^ [X1: $i,X2: $i,X3: $i,X4: $i] :
( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ).
thf(funcGraphProp1,conjecture,
( sP3
=> ( sP8
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ( sP8
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcGraphProp1]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP8
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in
@ ( kpair @ X3
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
@ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ~ ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in
@ ( kpair @ X2
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) )
@ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ sP11 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in
@ ( kpair @ X1
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 ) ) ) )
@ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in
@ ( kpair @ X1
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 ) ) ) )
@ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP12 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| ~ sP9
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP6
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| ~ sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,h1,h3,h13,h15,h16]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,9,h15,h16]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h11,10,h14]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,11,h12,h13]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,13,h9]) ).
thf(15,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)],[h7,14,h8]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,15,h7]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,17,h3,h4]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,18,h1,h2]) ).
thf(0,theorem,
( sP3
=> ( sP8
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( kpair @ X4
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
@ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU684^2 : TPTP v9.2.0. Released v3.7.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 20:35:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 20.29/20.59 % SZS status Theorem
% 20.29/20.59 % Mode: cade22grackle2x798d
% 20.29/20.59 % Steps: 1225
% 20.29/20.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------