TSTP Solution File: SEU953^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU953^5 : 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 : n017.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 14:11:00 EDT 2022
% Result : Timeout 293.58s 293.37s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 36
% Syntax : Number of formulae : 41 ( 9 unt; 2 typ; 1 def)
% Number of atoms : 92 ( 35 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 110 ( 20 ~; 16 |; 0 &; 50 @)
% ( 16 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 19 con; 0-2 aty)
% Number of variables : 28 ( 5 ^ 11 !; 0 ?; 28 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_g,type,
g: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
( ( @+[X2: $i] :
( ( g @ X1 )
= ( g @ X2 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( g @ X1 )
= ( g @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ( g @ eigen__8 )
= X1 )
=> ( X1
= ( g @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( g
@ @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) )
= ( g @ eigen__8 ) )
=> ( ( @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) )
= eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( g @ eigen__8 )
= ( g
@ @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) ) )
=> ( ( g
@ @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) )
= ( g @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) )
= eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__8 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( g @ eigen__8 )
!= ( g @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( g @ eigen__8 )
= ( g
@ @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ( g
@ @+[X2: $i] :
( ( g @ eigen__8 )
= ( g @ X2 ) ) )
= ( g @ X1 ) )
=> ( ( @+[X2: $i] :
( ( g @ eigen__8 )
= ( g @ X2 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: $i] :
@+[X2: $i] :
( ( g @ X1 )
= ( g @ X2 ) ) )
= ( ^ [X1: $i] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( g
@ @+[X1: $i] :
( ( g @ eigen__8 )
= ( g @ X1 ) ) )
= ( g @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $i] :
( ( ^ [X2: $i] : ( X1 @ ( g @ X2 ) ) )
!= ( ^ [X2: $i] : X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP1
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( @+[X2: $i] :
( ( g @ X1 )
= ( g @ X2 ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( g @ eigen__8 )
= ( g @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cTHM591_pme,conjecture,
sP14 ).
thf(h1,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[cTHM591_pme]) ).
thf(1,plain,
( ~ sP4
| ~ sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP16
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| ~ sP9
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP9
| sP8 ),
inference(choice_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP15
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(12,plain,
( sP11
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
sP2,
inference(eq_sym,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP14
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h1]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU953^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.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 : 600
% 0.13/0.34 % DateTime : Sun Jun 19 10:59:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 293.58/293.37 % SZS status Theorem
% 293.58/293.37 % Mode: mode469
% 293.58/293.37 % Inferences: 22261
% 293.58/293.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------