%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU751^2 : 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 : n003.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 186.04s 182.23s
% Output : Proof 186.04s
% 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__1,type,
eigen__1: $i ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ~ ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( in @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( in @ eigen__3 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ~ ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( in @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__3 @ eigen__0 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( sP13
=> ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [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,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( in @ ( setminus @ eigen__0 @ eigen__2 ) @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( in @ eigen__3 @ eigen__0 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( in @ eigen__3 @ eigen__0 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP9
=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( in @ eigen__3 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP31
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP9
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( in @ ( setminus @ eigen__0 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [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,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP29
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP37
=> sP42 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP13
=> ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ X1 @ eigen__2 )
=> ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [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,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) )
=> ~ ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
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_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_complementT_lem,definition,
( complementT_lem
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ).
thf(def_complementTE1,definition,
( complementTE1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [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(demorgan1a,conjecture,
( sP25
=> ( sP7
=> ( sP23
=> ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP25
=> ( sP7
=> ( sP23
=> ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[demorgan1a]) ).
thf(h1,assumption,
sP25,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP7
=> ( sP23
=> ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP23
=> ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP23,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP36,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP18,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,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 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP9,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP47
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP47,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP29
=> ( sP1
=> sP31 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP29,
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( sP1
=> sP31 ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP1,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP31,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP29
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP30
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP21
| ~ sP37
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP15
| ~ sP38
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| sP31
| ~ sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP34
| sP31
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP40
| ~ sP29
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP42
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP10
| sP33
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP26
| ~ sP29
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP11
| sP51
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP22
| ~ sP29
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP43
| ~ sP37
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP44
| ~ sP13
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP16
| ~ sP17
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP6
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP28
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP24
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP48
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP3
| ~ sP1
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP41
| ~ sP47
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP35
| ~ sP9
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP5
| ~ sP38
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP19
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP50
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP46
| ~ sP47
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP27
| ~ sP9
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP32
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP32
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP2
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP2
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP49
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP39
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP25
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP20
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP7
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP23
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP36
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP4
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP18
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h20,h18,h19,h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,h1,h3,h5,h7,h9,h11,h15,h18,h21,h23,h24]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h22,42,h23,h24]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,43,h21,h22]) ).
thf(45,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__3)],[h19,44,h20]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,45,h18,h19]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__2)],[h16,46,h17]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,47,h15,h16]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h13,48,h14]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__0)],[h12,49,h13]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,50,h11,h12]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,51,h9,h10]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,52,h7,h8]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,53,h5,h6]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,54,h3,h4]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,55,h1,h2]) ).
thf(0,theorem,
( sP25
=> ( sP7
=> ( sP23
=> ( sP36
=> ( sP4
=> ( sP18
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[56,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU751^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.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 21:26:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 186.04/182.23 % SZS status Theorem
% 186.04/182.23 % Mode: cade22grackle2x2d0b
% 186.04/182.23 % Steps: 17146
% 186.04/182.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------