TSTP Solution File: SET044^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET044^5 : 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 : n004.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 15:15:29 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 24
% Syntax : Number of formulae : 31 ( 9 unt; 3 typ; 1 def)
% Number of atoms : 75 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 110 ( 34 ~; 12 |; 0 &; 52 @)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 19 ( 1 ^; 18 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cF,type,
cF: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( ~ ( cF @ X2 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( cF @ X1 @ eigen__0 )
= ( cF @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cF @ X1 @ eigen__1 )
= ( ~ ( cF @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cF @ eigen__1 @ eigen__0 )
= ( cF @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cF @ eigen__1 @ eigen__1 )
= ( ~ ( cF @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( ~ ( cF @ X2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ! [X3: $i] :
( ( cF @ X3 @ X2 )
= ( ~ ( cF @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cF @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cF @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cPELL40,conjecture,
( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( cF @ X2 @ X2 ) )
=> ~ sP6 ) ).
thf(h1,negated_conjecture,
~ ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( cF @ X2 @ X2 ) )
=> ~ sP6 ),
inference(assume_negation,[status(cth)],[cPELL40]) ).
thf(h2,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( cF @ X2 @ X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP6
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h4,h3]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h2,9,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,10,h2,h3]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cF @ X2 @ X1 )
= ( cF @ X2 @ X2 ) )
=> ~ sP6 ),
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET044^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 16:08:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 % SZS status Theorem
% 0.19/0.59 % Mode: cade22grackle2xfee4
% 0.19/0.59 % Steps: 1283
% 0.19/0.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------