TSTP Solution File: SYO270^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO270^5 : 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 : n029.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 04:46:06 EDT 2023
% Result : Theorem 20.22s 20.45s
% Output : Proof 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 34 ( 8 unt; 6 typ; 2 def)
% Number of atoms : 71 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 188 ( 37 ~; 10 |; 0 &; 111 @)
% ( 10 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 24 ( 2 ^; 22 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_g,type,
g: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_h,type,
h: $i > $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__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ! [X2: $i] : ( cP @ X2 @ ( g @ ( h @ eigen__2 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__2 ) ) @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ! [X2: $i] : ( cP @ X2 @ ( h @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
( ~ ( ! [X3: $i] : ( cP @ X3 @ ( X1 @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__2 @ ( g @ ( h @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ! [X2: $i] : ( cP @ X2 @ ( g @ ( h @ eigen__2 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__2 ) ) @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ! [X1: $i] : ( cP @ X1 @ ( h @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ eigen__2 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
( ~ ( ! [X3: $i] : ( cP @ X3 @ ( X1 @ ( g @ ( h @ eigen__2 ) ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__2 ) ) @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: $i] : ( cP @ X1 @ ( g @ ( h @ eigen__2 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__2 ) ) @ eigen__15 ) )
=> ( cP @ eigen__15 @ ( g @ ( h @ eigen__15 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] : ( cP @ X1 @ ( g @ ( h @ eigen__2 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__2 ) ) @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] : ( cP @ X1 @ ( g @ ( h @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ~ ( ! [X4: $i] : ( cP @ X4 @ ( X2 @ X1 ) )
=> ~ ( cP @ X1 @ X3 ) )
=> ( cP @ X3 @ ( g @ ( h @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ~ ( ! [X2: $i] : ( cP @ X2 @ ( h @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cTHM85,conjecture,
~ sP9 ).
thf(h1,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[cTHM85]) ).
thf(1,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(5,plain,
( ~ sP5
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(9,plain,
( ~ sP1
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,h1]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO270^5 : 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 : n029.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 04:00:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 20.22/20.45 % SZS status Theorem
% 20.22/20.45 % Mode: cade22grackle2x798d
% 20.22/20.45 % Steps: 510
% 20.22/20.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------