TSTP Solution File: SEU757^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU757^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 Aug 31 17:26:10 EDT 2023
% Result : Theorem 22.01s 22.27s
% Output : Proof 22.01s
% 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__2,type,
eigen__2: $i ).
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( in @ ( binunion @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [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(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [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(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( in @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( binunion @ eigen__1 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X2 @ X1 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) )
=> ( in @ X2 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ ( binunion @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) ) ) ),
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 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X4 @ X2 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> ( in @ ( setminus @ eigen__0 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( in @ ( setminus @ eigen__0 @ eigen__2 ) @ ( powerset @ eigen__0 ) )
=> ( in @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( in @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [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 ) ) ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [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(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP26
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP19
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( in @ ( setminus @ eigen__0 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [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(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 @ ( binintersect @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ eigen__0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( in @ ( binunion @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP1
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP36
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP1
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( in @ ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(def_binintersectT_lem,definition,
( binintersectT_lem
= ( ! [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 ) )
@ ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ) ) ).
thf(def_binunionT_lem,definition,
( binunionT_lem
= ( ! [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 ) )
@ ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ) ) ).
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_setextT,definition,
( setextT
= ( ! [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: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X2 )
@ ( in @ X4 @ X3 ) ) )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X3 )
@ ( in @ X4 @ X2 ) ) )
@ ( X2 = X3 ) ) ) ) ) ) ) ).
thf(def_demorgan2a,definition,
( demorgan2a
= ( ! [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 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
@ ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ).
thf(def_demorgan2b,definition,
( demorgan2b
= ( ! [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 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
@ ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ).
thf(demorgan2,conjecture,
( sP22
=> ( sP32
=> ( sP2
=> ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP22
=> ( sP32
=> ( sP2
=> ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[demorgan2]) ).
thf(h1,assumption,
sP22,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP32
=> ( sP2
=> ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP32,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP2
=> ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP15,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP7,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP39,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( 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 ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP26
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) )
= ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP26,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( setminus @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) )
= ( binintersect @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP1
=> sP29 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP40
| ~ sP36
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP21
| ~ sP33
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP18
| ~ sP30
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP1
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP42
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP37
| ~ sP1
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP41
| ~ sP1
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP23
| ~ sP31
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| ~ sP26
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP17
| ~ sP1
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP20
| ~ sP26
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP14
| ~ sP35
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP28
| ~ sP19
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| ~ sP26
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP27
| ~ sP26
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP24
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP9
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP4
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP4
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP38
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP25
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP34
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP22
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP32
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP15
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP7
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP39
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h1,h3,h5,h7,h9,h11,h15,h18,h19]) ).
thf(36,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])],[h17,35,h18,h19]) ).
thf(37,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)],[h16,36,h17]) ).
thf(38,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])],[h14,37,h15,h16]) ).
thf(39,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)],[h13,38,h14]) ).
thf(40,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)],[h12,39,h13]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,40,h11,h12]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,41,h9,h10]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,42,h7,h8]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,43,h5,h6]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,44,h3,h4]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,45,h1,h2]) ).
thf(0,theorem,
( sP22
=> ( sP32
=> ( sP2
=> ( sP15
=> ( sP7
=> ( sP39
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU757^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n016.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 Aug 23 20:48:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 22.01/22.27 % SZS status Theorem
% 22.01/22.27 % Mode: cade22grackle2x798d
% 22.01/22.27 % Steps: 35674
% 22.01/22.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------