TSTP Solution File: NUM808^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM808^5 : 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 : n005.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 13:56:49 EDT 2022
% Result : Theorem 27.15s 27.01s
% Output : Proof 27.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 50 ( 8 unt; 4 typ; 2 def)
% Number of atoms : 109 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 193 ( 55 ~; 24 |; 0 &; 70 @)
% ( 19 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 25 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 22 ( 1 ^ 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
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] :
~ ( ~ ! [X2: $i] :
~ ( r @ X1 @ X2 )
=> ~ ! [X2: $i] :
~ ( r @ ( cS @ X1 ) @ 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 ) )
=> ~ ( r @ c0 @ c0 ) )
=> ~ ! [X1: $i] :
( ( r @ X1 @ X1 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( r @ c0 @ c0 )
=> ~ ! [X1: $i] :
( ( r @ X1 @ X1 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( r @ X1 @ X1 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( r @ ( cS @ eigen__1 ) @ ( cS @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ! [X1: $i] :
~ ( r @ eigen__1 @ X1 )
=> ~ ! [X1: $i] :
~ ( r @ ( cS @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( r @ eigen__1 @ eigen__1 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
~ ( r @ c0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] : ( r @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP3
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
~ ( r @ ( cS @ eigen__1 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( r @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP1
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( r @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( r @ c0 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( r @ X1 @ X2 )
=> ~ ! [X2: $i] :
~ ( r @ ( cS @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ~ sP8
=> ~ sP16 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP8
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_cIND,definition,
cIND = sP2 ).
thf(cTHM130A,conjecture,
sP13 ).
thf(h1,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[cTHM130A]) ).
thf(1,plain,
( ~ sP11
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP14
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP16
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP2
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP18
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| sP8
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| ~ sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP19
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP19
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP13
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP13
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM808^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jul 5 16:04:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 27.15/27.01 % SZS status Theorem
% 27.15/27.01 % Mode: mode454
% 27.15/27.01 % Inferences: 5101
% 27.15/27.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------