TSTP Solution File: SYO101^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO101^5 : 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 04:45:12 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 44
% Syntax : Number of formulae : 53 ( 10 unt; 7 typ; 4 def)
% Number of atoms : 116 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 179 ( 52 ~; 18 |; 0 &; 64 @)
% ( 17 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 24 con; 0-2 aty)
% Number of variables : 22 ( 4 ^; 18 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cR,type,
cR: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_cW,type,
cW: $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__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( cP @ eigen__0 )
=> ! [X2: $i] :
~ ( ( cR @ eigen__0 @ X1 )
=> ~ ( cP @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( cP @ cW )
=> ! [X2: $i] :
~ ( ( cR @ cW @ X1 )
=> ~ ( cP @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cP @ X1 )
=> ( cR @ cW @ cW ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cP @ X1 )
=> ( cR @ cW @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( cP @ X1 )
=> ! [X3: $i] :
~ ( ( cR @ X1 @ X2 )
=> ~ ( cP @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cP @ eigen__4 )
=> ( cR @ cW @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( ( cR @ cW @ eigen__1 )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ cW @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__0 )
=> ( cR @ cW @ cW ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ eigen__0 )
=> ! [X1: $i] :
~ ( ( cR @ eigen__0 @ eigen__3 )
=> ~ ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
~ ( sP7
=> ! [X2: $i] :
~ ( ( cR @ eigen__0 @ X1 )
=> ~ ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ cW ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cR @ cW @ eigen__1 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
~ ( sP9
=> ! [X2: $i] :
~ ( ( cR @ cW @ X1 )
=> ~ ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ( ( cR @ eigen__0 @ eigen__3 )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X2 )
=> ( cR @ cW @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cR @ cW @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ cW @ cW ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cR @ eigen__0 @ eigen__3 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM83,conjecture,
( sP1
=> ~ sP13 ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ sP13 ),
inference(assume_negation,[status(cth)],[cTHM83]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(3,plain,
( ~ sP13
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP17
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| ~ sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP7
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(8,plain,
( ~ sP1
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP11
| sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(13,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP16
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(15,plain,
( ~ sP13
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2,h3]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP13 ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO101^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 07:34:03 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 47
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------