## TSTP Solution File: SEV391^5 by Satallax---3.5

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV391^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n002.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
% DateTime : Tue Mar 30 22:05:25 EDT 2021

% Result   : Theorem 0.20s
% Output   : Proof 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   30 (   7 unt;   5 typ;   1 def)
%            Number of atoms       :   57 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  120 (  26   ~;  10   |;   0   &;  63   @)
%                                         (   9 <=>;  12  =>;   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     :   17 (  15 usr;  13 con; 0-3 aty)
%            Number of variables   :   10 (   1   ^   9   !;   0   ?;  10   :)

% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: \$i ).

thf(ty_h,type,
h: \$i > \$i ).

thf(ty_eigen__2,type,
eigen__2: \$i ).

thf(ty_cP,type,
cP: \$i > \$i > \$i > \$o ).

thf(ty_k,type,
k: \$i > \$i ).

thf(h0,assumption,
! [X1: \$i > \$o,X2: \$i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: \$i] :
~ ~ ! [X2: \$i] :
~ ( ( ~ ( cP @ a @ ( h @ X1 ) @ X1 )
=> ( cP @ a @ ( k @ X1 ) @ X1 ) )
=> ( cP @ a @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
( sP1
<=> ( ~ ( cP @ a @ ( h @ eigen__2 ) @ eigen__2 )
=> ( cP @ a @ ( k @ eigen__2 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
( sP2
<=> ( sP1
=> ( cP @ a @ a @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
( sP3
<=> ! [X1: \$i] :
~ ! [X2: \$i] :
~ ( ( ~ ( cP @ a @ ( h @ X1 ) @ X1 )
=> ( cP @ a @ ( k @ X1 ) @ X1 ) )
=> ( cP @ a @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
( sP4
<=> ( sP1
=> ( cP @ a @ ( k @ eigen__2 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
( sP5
<=> ! [X1: \$i] :
~ ! [X2: \$i] :
~ ! [X3: \$i] :
~ ( ( ~ ( cP @ a @ ( h @ X2 ) @ X2 )
=> ( cP @ X1 @ ( k @ X2 ) @ X2 ) )
=> ( cP @ X1 @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
( sP6
<=> ( cP @ a @ ( k @ eigen__2 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
( sP7
<=> ( cP @ a @ ( h @ eigen__2 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
( sP8
<=> ( sP1
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
( sP9
<=> ! [X1: \$i] :
~ ( sP1
=> ( cP @ a @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(cTHM87_pme,conjecture,
~ sP5 ).

thf(h1,negated_conjecture,
sP5,
inference(assume_negation,[status(cth)],[cTHM87_pme]) ).

thf(1,plain,
( sP4
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
( ~ sP9
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).

thf(3,plain,
( sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
( ~ sP9
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).

thf(5,plain,
( ~ sP1
| sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
( sP2
| sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
( ~ sP9
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).

thf(8,plain,
( sP3
| sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(9,plain,
( ~ sP5
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).

thf(10,plain,
\$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,h1]) ).

thf(11,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).

thf(0,theorem,
~ sP5,
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEV391^5 : TPTP v7.5.0. Released v4.0.0.
% 0.08/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Mar 26 15:14:44 EDT 2021
% 0.13/0.35  % CPUTime  :
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  % Mode: mode213
% 0.20/0.43  % Inferences: 952
% 0.20/0.43  % SZS output start Proof
% See solution above
% 0.20/0.43  % SZS output end Proof
%------------------------------------------------------------------------------
```