TSTP Solution File: SEU924^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU924^5 : 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 : Tue Jul 19 14:10:52 EDT 2022
% Result : Theorem 1.99s 2.23s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 29
% Syntax : Number of formulae : 38 ( 14 unt; 4 typ; 4 def)
% Number of atoms : 70 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 129 ( 30 ~; 12 |; 0 &; 45 @)
% ( 11 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 16 con; 0-2 aty)
% Number of variables : 43 ( 16 ^ 27 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $i ).
thf(h0,assumption,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i > $i] :
~ ( ( ( X1 @ eigen__2 )
= eigen__0 )
=> ( eigen__0 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $i] :
~ ( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i] : eigen__0 )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : eigen__0 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
= eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i] :
~ ! [X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i] : X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : X1 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( X2 @ X3 )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__1 @ X1 )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i] : eigen__0 )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : eigen__0 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( eigen__3 @ eigen__2 )
= eigen__0 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 @ eigen__2 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ~ ! [X1: $i > $i] :
( ( ( X1 @ eigen__2 )
= eigen__0 )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i] : eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : eigen__0 ) ) )
=> ( X1 @ eigen__1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i] :
( ( ( X1 @ eigen__2 )
= eigen__0 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i] : X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : X1 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( X2 @ X3 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP6
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i] : eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : eigen__0 ) ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cTHM134_pme,conjecture,
sP9 ).
thf(h2,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cTHM134_pme]) ).
thf(1,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(3,plain,
sP3,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| ~ sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP6
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP2
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(8,plain,
( sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP7
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP1
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(11,plain,
( sP9
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
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(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[12,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU924^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 18:37:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.23 % SZS status Theorem
% 1.99/2.23 % Mode: mode506
% 1.99/2.23 % Inferences: 58282
% 1.99/2.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------