TSTP Solution File: NUM812^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM812^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 : 600s
% DateTime : Mon Jul 18 13:56:50 EDT 2022
% Result : Theorem 26.70s 26.13s
% Output : Proof 26.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 35 ( 10 unt; 3 typ; 2 def)
% Number of atoms : 84 ( 33 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 151 ( 62 ~; 12 |; 0 &; 36 @)
% ( 12 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 18 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 24 ( 1 ^ 23 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_c0,type,
c0: $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] :
~ ( ( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) )
=> ( ( ( cS @ X1 )
!= c0 )
=> ~ ! [X2: $i] :
( ( cS @ X1 )
!= ( cS @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cS @ eigen__1 )
!= ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( ( c0 != c0 )
=> ~ ! [X1: $i] :
( c0
!= ( cS @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) )
=> ( ( ( cS @ X1 )
!= c0 )
=> ~ ! [X2: $i] :
( ( cS @ X1 )
!= ( cS @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cS @ eigen__1 )
= ( cS @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( c0 != c0 )
=> ~ ! [X1: $i] :
( c0
!= ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( c0 = c0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ~ ! [X1: $i] :
( ( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) )
=> ( ( ( cS @ X1 )
!= c0 )
=> ~ ! [X2: $i] :
( ( cS @ X1 )
!= ( cS @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( eigen__1 != c0 )
=> ~ ! [X1: $i] :
( eigen__1
!= ( cS @ X1 ) ) )
=> ( ( ( cS @ eigen__1 )
!= c0 )
=> ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( ( X1 != c0 )
=> ~ ! [X2: $i] :
( X1
!= ( cS @ X2 ) ) )
=> ( ( ( cS @ X1 )
!= c0 )
=> ~ ! [X2: $i] :
( ( cS @ X1 )
!= ( cS @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( cS @ eigen__1 )
!= c0 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_cIND,definition,
cIND = sP1 ).
thf(cTHM578,conjecture,
sP10 ).
thf(h1,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[cTHM578]) ).
thf(1,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP9
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| ~ sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP10
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM812^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 01:28:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.49/9.88 slave returned with unknown status
% 26.70/26.13 % SZS status Theorem
% 26.70/26.13 % Mode: mode454
% 26.70/26.13 % Inferences: 118
% 26.70/26.13 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------