TSTP Solution File: SYO094^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO094^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Thu Jul 21 19:30:16 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 26
% Syntax : Number of formulae : 35 ( 11 unt; 4 typ; 2 def)
% Number of atoms : 64 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 83 ( 22 ~; 8 |; 0 &; 31 @)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 13 con; 0-2 aty)
% Number of variables : 9 ( 2 ^ 7 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $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 @ eigen__0 )
=> ( cR @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cR @ eigen__0 @ eigen__0 )
=> ( cR @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cR @ eigen__0 @ eigen__0 )
=> ( cR @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cR @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cR @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X1 @ X1 )
=> ( cR @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( sP5
=> ( cR @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM55A,conjecture,
( ( ~ sP1
=> sP2 )
=> ~ sP6 ) ).
thf(h1,negated_conjecture,
~ ( ( ~ sP1
=> sP2 )
=> ~ sP6 ),
inference(assume_negation,[status(cth)],[cTHM55A]) ).
thf(h2,assumption,
( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(3,plain,
( ~ sP6
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,h4,h3]) ).
thf(6,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP8
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(9,plain,
( ~ sP6
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h2,h3,h1,h0])],[6,7,8,9,h5,h3]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,5,10,h4,h5]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
( ( ~ sP1
=> sP2 )
=> ~ sP6 ),
inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO094^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 02:49:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % Mode: mode213
% 0.14/0.38 % Inferences: 16
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------