TSTP Solution File: LCL733^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL733^5 : 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 : n006.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 08:04:46 EDT 2023
% Result : Theorem 0.15s 0.42s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 24
% Syntax : Number of formulae : 32 ( 13 unt; 4 typ; 2 def)
% Number of atoms : 51 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 40 ~; 8 |; 0 &; 25 @)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 13 con; 0-2 aty)
% Number of variables : 22 ( 2 ^; 20 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__0,type,
eigen__0: b > $o ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b] :
~ ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: b > $o] :
~ ~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: b > $o] :
~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP2
=> ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: b > $o] :
~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b] :
~ ( ~ sP2
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cX5310_SUB4,conjecture,
( sP1
=> ~ sP7 ) ).
thf(h2,negated_conjecture,
~ ( sP1
=> ~ sP7 ),
inference(assume_negation,[status(cth)],[cX5310_SUB4]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(4,plain,
( sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(7,plain,
( ~ sP1
| ~ sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,h3,h4]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[9,h1]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[10,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP7 ),
inference(contra,[status(thm),contra(discharge,[h2])],[9,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL733^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 02:49:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 % Mode: cade22grackle2xfee4
% 0.15/0.42 % Steps: 18
% 0.15/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------