TSTP Solution File: SYO257^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO257^5 : 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 : n012.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 04:46:03 EDT 2023
% Result : Theorem 22.63s 22.84s
% Output : Proof 22.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 32 ( 8 unt; 6 typ; 2 def)
% Number of atoms : 65 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 171 ( 34 ~; 9 |; 0 &; 101 @)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 25 ( 2 ^; 23 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_g,type,
g: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_h,type,
h: $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
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] :
~ ( ! [X2: $i > $i,X3: $i] :
~ ( ( cP @ X3 @ ( X2 @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i > $i,X3: $i] :
~ ( ( cP @ X3 @ ( X2 @ ( g @ ( h @ eigen__1 ) ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ! [X2: $i > $i,X3: $i] :
~ ( ( cP @ X3 @ ( X2 @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__1 @ ( g @ ( h @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ! [X2: $i > $i,X3: $i] :
~ ( ( cP @ X3 @ ( X2 @ ( g @ ( h @ eigen__1 ) ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ( ( cP @ X1 @ ( g @ ( h @ eigen__1 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i > $i,X2: $i] :
~ ( ( cP @ X2 @ ( X1 @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ eigen__1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ! [X3: $i > $i,X4: $i] :
~ ( ( cP @ X4 @ ( X3 @ X1 ) )
=> ~ ( cP @ X1 @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i > $i,X2: $i] :
~ ( ( cP @ X2 @ ( X1 @ ( g @ ( h @ eigen__1 ) ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ eigen__4 ) )
=> ( cP @ eigen__4 @ ( g @ ( h @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $i,X2: $i] :
~ ( ( cP @ X2 @ ( X1 @ ( g @ ( h @ eigen__1 ) ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM84,conjecture,
~ sP7 ).
thf(h1,negated_conjecture,
sP7,
inference(assume_negation,[status(cth)],[cTHM84]) ).
thf(1,plain,
( sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(6,plain,
( ~ sP7
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP1
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(9,plain,
( ~ sP7
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,h1]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).
thf(0,theorem,
~ sP7,
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO257^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 23:44:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 22.63/22.84 % SZS status Theorem
% 22.63/22.84 % Mode: cade22grackle2x798d
% 22.63/22.84 % Steps: 313
% 22.63/22.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------