TSTP Solution File: SYO111^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO111^5 : 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 : n008.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 : Fri Sep 1 04:45:14 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 39 ( 14 unt; 5 typ; 1 def)
% Number of atoms : 93 ( 1 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 182 ( 94 ~; 7 |; 0 &; 30 @)
% ( 8 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 25 ( 1 ^; 24 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cN,type,
cN: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cM,type,
cM: $i > $o ).
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
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] :
~ ~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ~ ( cM @ X1 )
=> ~ ! [X2: $i] :
~ ( cN @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cN @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( cM @ eigen__0 )
=> ~ ! [X1: $i] :
~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ~ ! [X1: $i] : ( cG @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] : ( cG @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cN @ X1 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ( cN @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cM @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM80,conjecture,
( ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP7 ) )
=> ~ ( ~ sP7
=> ~ sP5 ) )
=> ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ) ) ).
thf(h1,negated_conjecture,
~ ( ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP7 ) )
=> ~ ( ~ sP7
=> ~ sP5 ) )
=> ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ) ),
inference(assume_negation,[status(cth)],[cTHM80]) ).
thf(h2,assumption,
( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP7 ) )
=> ~ ( ~ sP7
=> ~ sP5 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] : ( cM @ X1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP2
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,h10,h9,h7,h5]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h8,6,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,7,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,8,h6,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,9,h4,h5]) ).
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] : ( cM @ X1 )
=> ~ sP5 )
=> ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP7 ) )
=> ~ ( ~ sP7
=> ~ sP5 ) )
=> ( ~ ( ~ ( ~ ! [X1: $i] : ( cM @ X1 )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO111^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 01:06:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: cade22grackle2xfee4
% 0.21/0.41 % Steps: 42
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------