TSTP Solution File: SYO238^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO238^5 : 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 : n002.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 04:46:00 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 37 ( 12 unt; 5 typ; 1 def)
% Number of atoms : 65 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 14 ~; 9 |; 0 &; 23 @)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 7 ( 3 ^; 4 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_x,type,
x: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_cB,type,
cB: $o ).
thf(ty_f,type,
f: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
( ( f @ ( f @ X1 ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( f @ ( f @ eigen__0 ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( f @ ( f @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ ( f @ eigen__0 ) )
= ( f @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ eigen__0 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> cB ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> cB ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( f @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cADDHYP5,conjecture,
( sP9
=> ( sP7
=> ( ( cP @ x )
=> sP8 ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP9
=> ( sP7
=> ( ( cP @ x )
=> sP8 ) ) ),
inference(assume_negation,[status(cth)],[cADDHYP5]) ).
thf(h2,assumption,
sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP7
=> ( ( cP @ x )
=> sP8 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( cP @ x )
=> sP8 ),
introduced(assumption,[]) ).
thf(h6,assumption,
cP @ x,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP2
| sP1
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(6,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| ~ sP3
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h4,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,8,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,
( sP9
=> ( sP7
=> ( ( cP @ x )
=> sP8 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO238^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n002.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 04:32:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % Mode: cade22grackle2xfee4
% 0.19/0.42 % Steps: 78
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------