TSTP Solution File: SEU652^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU652^2 : 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 : n013.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 17:20:43 EDT 2023
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% 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__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
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( setadjoin @ eigen__2 @ emptyset )
= ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP12
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( in @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] : ( in @ eigen__2 @ ( setadjoin @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] : ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP6
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP7 ).
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 = sP23 ).
thf(upairequniteq,conjecture,
( sP7
=> ( sP31
=> ( sP23
=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ( sP31
=> ( sP23
=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[upairequniteq]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP31
=> ( sP23
=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP31,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP23
=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP23,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ X1 @ emptyset ) )
=> sP25 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP1
=> sP25 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP12
| ~ sP1
| sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP33
| ~ sP8
| ~ sP24 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP29
| sP3
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| sP3
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP20
| sP3
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP28
| sP6
| ~ sP1
| sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP26
| ~ sP29
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| ~ sP20
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP15
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP15
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP21
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP18
| ~ sP12
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP32
| ~ sP6
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP31
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP7
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP30
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP19
| ~ sP33
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP31
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP7
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP27
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP23
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP31
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,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,h1,h3,h5,h10,h11]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,30,h10,h11]) ).
thf(32,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)],[h8,31,h9]) ).
thf(33,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)],[h7,32,h8]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,33,h7]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,34,h5,h6]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,35,h3,h4]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,36,h1,h2]) ).
thf(0,theorem,
( sP7
=> ( sP31
=> ( sP23
=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[37,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU652^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Wed Aug 23 17:02:32 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % Mode: cade22grackle2xfee4
% 0.20/0.47 % Steps: 501
% 0.20/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------