TSTP Solution File: SEV176^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV176^5 : 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 : n024.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 : Thu Aug 31 19:32:51 EDT 2023
% Result : Theorem 0.37s 0.60s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 28
% Syntax : Number of formulae : 34 ( 9 unt; 3 typ; 1 def)
% Number of atoms : 83 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 135 ( 32 ~; 15 |; 0 &; 64 @)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 18 ( 1 ^; 17 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cR,type,
cR: $i > $i > $o ).
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] :
~ ( ( cR @ eigen__0 @ X1 )
=> ~ ( cR @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( ( cR @ eigen__0 @ eigen__0 )
= ( ! [X1: $i] :
( ( cR @ eigen__0 @ X1 )
=> ~ ( cR @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cR @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cR @ eigen__0 @ eigen__0 )
=> ~ ( cR @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ~ ( cR @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cR @ eigen__1 @ eigen__0 )
= ( ! [X1: $i] :
( ( cR @ eigen__1 @ X1 )
=> ~ ( cR @ X1 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cR @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( cR @ X1 @ eigen__0 )
= ( ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cR @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( cR @ eigen__1 @ X1 )
=> ~ ( cR @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP8
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( cR @ eigen__0 @ X1 )
=> ~ ( cR @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cTHM25,conjecture,
! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X2 @ X1 )
= ( ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ~ ( cR @ X3 @ X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X2 @ X1 )
= ( ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ~ ( cR @ X3 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM25]) ).
thf(h2,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP6
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(9,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP6
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,12,h2]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X2 @ X1 )
= ( ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ~ ( cR @ X3 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV176^5 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : Thu Aug 24 02:27:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.37/0.60 % SZS status Theorem
% 0.37/0.60 % Mode: cade22grackle2xfee4
% 0.37/0.60 % Steps: 2080
% 0.37/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------