TSTP Solution File: SEU651^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU651^2 : 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 : n032.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 17:20:40 EDT 2023
% Result : Theorem 27.63s 28.00s
% Output : Proof 27.63s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
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_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) )
=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6
=> ( eigen__1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( setadjoin @ eigen__3 @ emptyset )
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( setadjoin @ eigen__2 @ emptyset )
= ( setadjoin @ eigen__3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP22
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( setadjoin @ eigen__2 @ emptyset )
= ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> $false ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( in @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(def_uniqinunit,definition,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_secondinupair,definition,
secondinupair = sP9 ).
thf(def_setukpairinjR12,definition,
( setukpairinjR12
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ) ) ).
thf(setukpairinjR1,conjecture,
( sP16
=> ( sP9
=> ( sP33
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP16
=> ( sP9
=> ( sP33
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setukpairinjR1]) ).
thf(h1,assumption,
sP16,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP9
=> ( sP33
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP9,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP33
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP33,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( eigen__1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( eigen__2 = X1 )
=> ( eigen__1 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP23
=> ( sP1
=> sP24 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP23,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> sP24 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(1,plain,
( sP35
| sP30
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP38
| sP22
| ~ sP32
| sP30 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP34
| sP37
| ~ sP36
| sP30 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP25
| sP17
| ~ sP19
| sP30 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP38
| sP26
| ~ sP32
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP6
| ~ sP11
| sP30 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP32
| sP36
| ~ sP20
| ~ sP35 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(8,plain,
( sP19
| sP30
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP29 ),
inference(symeq,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| sP11 ),
inference(symeq,[status(thm)],]) ).
thf(11,plain,
( ~ sP8
| sP7 ),
inference(symeq,[status(thm)],]) ).
thf(12,plain,
( ~ sP28
| ~ sP22
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP13
| ~ sP37
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| ~ sP26
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| ~ sP6
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP5
| ~ sP1
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
~ sP30,
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP10
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP12
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP18
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP21
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP31
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP2
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP27
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP9
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP9
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP33
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP23
| sP20 ),
inference(symeq,[status(thm)],]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h7,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,h11,h13,h14]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,34,h13,h14]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,35,h11,h12]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,36,h10]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,37,h9]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,38,h8]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,39,h7]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,40,h5,h6]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,41,h3,h4]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,42,h1,h2]) ).
thf(0,theorem,
( sP16
=> ( sP9
=> ( sP33
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[43,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU651^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.35 % Computer : n032.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Wed Aug 23 19:49:26 EDT 2023
% 0.11/0.35 % CPUTime :
% 27.63/28.00 % SZS status Theorem
% 27.63/28.00 % Mode: cade22grackle2x798d
% 27.63/28.00 % Steps: 4410
% 27.63/28.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------