TSTP Solution File: SEU844^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU844^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 17:37:37 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 48
% Syntax : Number of formulae : 55 ( 8 unt; 5 typ; 2 def)
% Number of atoms : 124 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 116 ( 33 ~; 23 |; 0 &; 28 @)
% ( 20 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 24 con; 0-2 aty)
% Number of variables : 14 ( 3 ^; 11 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cS,type,
cS: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_cT,type,
cT: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ( cT @ X1 )
=> ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ( cT @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o,X2: a > $o] : ( X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cT @ eigen__0 )
= ( cS @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cS @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cS @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cT @ eigen__1 )
= ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( cT @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cT @ eigen__1 )
= sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( cT @ X1 )
= ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cT @ eigen__1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cT = cS ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> $false ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cT @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cT
= ( ^ [X1: a] : ~ sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> ~ ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cT @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] : ( cS = X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o] : ( cT = X1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( cT @ X1 )
= ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cGAZING_THM8_pme,conjecture,
( sP1
=> ~ sP15 ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ sP15 ),
inference(assume_negation,[status(cth)],[cGAZING_THM8_pme]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP12
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP18
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP16
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP6
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP19
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(18,plain,
( sP14
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(19,plain,
( ~ sP15
| ~ sP14
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h2,h3]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP15 ),
inference(contra,[status(thm),contra(discharge,[h1])],[21,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU844^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 20:08:26 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: cade22grackle2xfee4
% 0.19/0.41 % Steps: 58
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------