TSTP Solution File: SEU752^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU752^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : 600s
% DateTime : Tue Jul 19 14:01:18 EDT 2022
% Result : Theorem 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setminus,type,
setminus: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__2 )
=> ~ ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__3 @ ( binunion @ ( 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 @ X2 )
=> ~ ( in @ X4 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( ~ ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ( ~ ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( in @ eigen__3 @ eigen__2 )
=> ~ ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
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
<=> ( sP2
=> ( ~ ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( in @ eigen__3 @ eigen__0 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> ~ ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ~ ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ~ ( in @ X2 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
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 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( in @ eigen__3 @ eigen__1 )
=> ~ ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ~ ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP24
=> ( ~ ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP24
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP9
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( in @ eigen__3 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP32
=> ~ ( in @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__2 ) )
=> ~ ( in @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [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 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ~ ( in @ X2 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP30
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP4
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(def_binunionE,definition,
binunionE = sP5 ).
thf(def_setminusI,definition,
setminusI = sP19 ).
thf(def_setminusER,definition,
setminusER = sP27 ).
thf(def_binintersectTELcontra,definition,
binintersectTELcontra = sP3 ).
thf(def_binintersectTERcontra,definition,
binintersectTERcontra = sP14 ).
thf(demorgan1b,conjecture,
( sP5
=> ( sP19
=> ( sP27
=> ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ( sP19
=> ( sP27
=> ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[demorgan1b]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP19
=> ( sP27
=> ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP19,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP27
=> ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP27,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP14,
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 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ 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 @ ( binunion @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ eigen__0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) )
=> ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP9,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ X1 ) ) )
=> ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP36
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP36,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binunion @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP24
=> ( sP2
=> sP25 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP24,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP2
=> sP25 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP2,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP38
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP34
| ~ sP32
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP38
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP35
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP42
| ~ sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP27
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| ~ sP2
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP15
| sP32
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP31
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP33
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP26
| ~ sP24
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP41
| sP30
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP19
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP28
| ~ sP24
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP21
| sP39
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP40
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP13
| ~ sP36
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP3
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP37
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP17
| ~ sP9
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP11
| ~ sP24
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP8
| sP16
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP20
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP23
| ~ sP36
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP29
| ~ sP9
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,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,h1,h3,h5,h7,h9,h13,h16,h19,h21,h22]) ).
thf(35,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])],[h20,34,h21,h22]) ).
thf(36,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])],[h18,35,h19,h20]) ).
thf(37,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)],[h17,36,h18]) ).
thf(38,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])],[h15,37,h16,h17]) ).
thf(39,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)],[h14,38,h15]) ).
thf(40,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])],[h12,39,h13,h14]) ).
thf(41,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)],[h11,40,h12]) ).
thf(42,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)],[h10,41,h11]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,42,h9,h10]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,43,h7,h8]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,44,h5,h6]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,45,h3,h4]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,46,h1,h2]) ).
thf(0,theorem,
( sP5
=> ( sP19
=> ( sP27
=> ( sP3
=> ( sP14
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[47,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU752^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n029.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 : 600
% 0.12/0.34 % DateTime : Sun Jun 19 06:09:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.58 % SZS status Theorem
% 0.19/0.58 % Mode: mode213
% 0.19/0.58 % Inferences: 192
% 0.19/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------