%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU754^2 : 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 : n023.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 02:36:03 PM UTC 2025
% Result : Theorem 185.71s 181.79s
% Output : Proof 185.71s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_setminus,type,
setminus: $i > $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__3 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ X4 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__2 )
=> ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> ~ ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ sP6
=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ X4 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ~ ( in @ X2 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ ( in @ eigen__3 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ~ ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( in @ eigen__3 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ~ ( in @ X2 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP6
=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP22
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP8
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP25
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP35
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP37
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(def_binintersectI,definition,
( binintersectI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ).
thf(def_setminusI,definition,
( setminusI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( (~) @ ( in @ X3 @ X2 ) )
@ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ).
thf(def_setminusER,definition,
( setminusER
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
@ ( (~) @ ( in @ X3 @ X2 ) ) ) ) ) ).
thf(def_binunionTILcontra,definition,
( binunionTILcontra
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( powerset @ X1 ) )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( (~) @ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
@ ( (~) @ ( in @ X4 @ X2 ) ) ) ) ) ) ) ) ).
thf(def_binunionTIRcontra,definition,
( binunionTIRcontra
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( powerset @ X1 ) )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( (~) @ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
@ ( (~) @ ( in @ X4 @ X3 ) ) ) ) ) ) ) ) ).
thf(demorgan2a,conjecture,
( sP5
=> ( sP19
=> ( sP30
=> ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ( sP19
=> ( sP30
=> ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[demorgan2a]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP19
=> ( sP30
=> ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP19,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP30
=> ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP30,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ ( setminus @ eigen__0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP8,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP37
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP37,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP25
=> ( sP1
=> sP27 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP25,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP1
=> sP27 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP1,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP17
| ~ sP25
| sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP40
| sP41
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| ~ sP25
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP21
| sP41
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP20
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP42
| ~ sP35
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP43
| ~ sP37
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP33
| ~ sP37
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP2
| ~ sP11
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP31
| sP6
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP14
| ~ sP25
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP32
| sP22
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP39
| ~ sP25
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP29
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP4
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP28
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP7
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP36
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP10
| ~ sP1
| ~ sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP16
| ~ sP8
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP38
| ~ sP8
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP26
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP23
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP23
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP24
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP34
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP5
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP19
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP30
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP3
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP15
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h17,h15,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h1,h3,h5,h7,h9,h13,h16,h19,h21,h22]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,35,h21,h22]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,36,h19,h20]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h17,37,h18]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,38,h16,h17]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h14,39,h15]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,40,h13,h14]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,41,h12]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h10,42,h11]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,43,h9,h10]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,44,h7,h8]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,45,h5,h6]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,46,h3,h4]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,47,h1,h2]) ).
thf(0,theorem,
( sP5
=> ( sP19
=> ( sP30
=> ( sP3
=> ( sP15
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[48,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU754^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 21:32:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 185.71/181.79 % SZS status Theorem
% 185.71/181.79 % Mode: cade22grackle2x2d0b
% 185.71/181.79 % Steps: 11042
% 185.71/181.79 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------