TSTP Solution File: SEU550^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU550^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 17:18:34 EDT 2023
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 80
% Syntax : Number of formulae : 95 ( 25 unt; 6 typ; 3 def)
% Number of atoms : 225 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 250 ( 69 ~; 34 |; 1 &; 65 @)
% ( 31 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 38 con; 0-2 aty)
% Number of variables : 54 ( 5 ^; 48 !; 1 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__4 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__3 )
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__4 = X1 )
=> ( ( eigen__0 @ eigen__4 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ eigen__2 )
=> ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( ( eigen__0 @ eigen__2 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__4 )
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__4 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__4 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP9
=> ( eigen__2 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__1 @ eigen__3 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( sP9
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( eigen__7 = X1 )
=> ( sP17
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP17 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP20 = sP14 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP17
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( eigen__0 @ X1 )
= ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP28
= ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP10
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ).
thf(exu__Cong,conjecture,
! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) )
= ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) )
= ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[exu__Cong]) ).
thf(h2,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( eigen__0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ~ sP16
= ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP27
=> ( ~ sP16 = ~ sP22 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP27,
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP16 != ~ sP22 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h8,assumption,
sP16,
introduced(assumption,[]) ).
thf(h9,assumption,
sP22,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP20
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP20,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP9
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| ~ sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP19
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP27
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(9,plain,
( ~ sP24
| ~ sP20
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| ~ sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP22
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP27
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h4,h11,h12,h7]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,14,h11,h12]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h6,15,h10]) ).
thf(h13,assumption,
~ ( sP30
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP30,
introduced(assumption,[]) ).
thf(h15,assumption,
sP18,
introduced(assumption,[]) ).
thf(17,plain,
( ~ sP23
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP31
| ~ sP10
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP21
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP18
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP27
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP26
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP26
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP8
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(25,plain,
( ~ sP29
| sP28
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP7
| ~ sP28
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP3
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP16
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP27
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h8,h9,h4,h5,h3,h2,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,28,29,h4,h8,h14,h15]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h8,h9,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,30,h14,h15]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h9,31,h13]) ).
thf(33,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,16,32,h6,h7,h8,h9]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,33,h4,h5]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,34,h3]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,35,h2]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) )
= ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[36,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU550^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n020.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 Aug 23 13:10:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % Mode: cade22grackle2xfee4
% 0.20/0.43 % Steps: 216
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------