TSTP Solution File: SEV221^5 by Satallax---3.5

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```%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV221^5 : 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 : n014.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 22:05:09 EDT 2021

% Result   : Theorem 25.98s
% Output   : Proof 25.98s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   72 (  13 unt;   7 typ;   4 def)
%            Number of atoms       :  194 (  21 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  306 ( 112   ~;  35   |;   0   &;  85   @)
%                                         (  25 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   35 (  33 usr;  29 con; 0-2 aty)
%            Number of variables   :   41 (  18   ^  23   !;   0   ?;  41   :)

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

thf(ty_eigen__2,type,
eigen__2: a > \$o ).

thf(ty_eigen__1,type,
eigen__1: a > \$o ).

thf(ty_eigen__0,type,
eigen__0: a ).

thf(ty_cZ,type,
cZ: a > \$o ).

thf(ty_eigen__3,type,
eigen__3: a > \$o ).

thf(ty_cW,type,
cW: ( a > \$o ) > \$o ).

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

thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ~ ! [X2: a > \$o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(h1,assumption,
! [X1: a > \$o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a] :
( ( ~ ( ~ ! [X2: a > \$o] :
( ( cW @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( cZ @ X1 ) ) )
!= ( ~ ! [X2: a > \$o] :
( ~ ! [X3: a > \$o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ( ( cZ @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
( sP1
<=> ( ( ~ ( ~ ! [X1: a > \$o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ( cZ @ eigen__0 ) ) )
= ( ~ ! [X1: a > \$o] :
( ~ ! [X2: a > \$o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
( sP2
<=> ( cW @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
( sP3
<=> ( ( cZ @ eigen__0 )
=> ~ ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
( sP4
<=> ! [X1: a > \$o] :
( ~ ! [X2: a > \$o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
( sP5
<=> ( ( cZ @ eigen__0 )
=> ~ ( eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( ~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
( sP7
<=> ! [X1: a > \$o] :
( ( cW @ X1 )
=> ( ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( eigen__2 @ X2 ) ) )
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
( sP8
<=> ( ( eigen__1 @ eigen__0 )
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
( sP9
<=> ( ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__2 @ X1 ) ) )
= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
( sP10
<=> ( cW @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
( sP11
<=> ( sP2
=> ( eigen__1
!= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
( sP12
<=> ( ~ ! [X1: a > \$o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) )
=> ~ ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
( sP13
<=> ( ~ ! [X1: a > \$o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ( cZ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
( sP14
<=> ! [X1: a > \$o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
( sP15
<=> ( eigen__1
= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( ~ ( ~ ! [X2: a > \$o] :
( ( cW @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( cZ @ X1 ) ) )
= ( ~ ! [X2: a > \$o] :
( ~ ! [X3: a > \$o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ( ( cZ @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
( sP18
<=> ( cZ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
( sP19
<=> ( sP2
=> ~ ( eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
( sP20
<=> ! [X1: a > \$o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
( sP21
<=> ( sP10
=> ~ ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
( sP22
<=> ( eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
( sP23
<=> ( sP10
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
( sP24
<=> ( ~ sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
( sP25
<=> ( eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(cTHM61_pme,conjecture,
sP17 ).

thf(h2,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[cTHM61_pme]) ).

thf(1,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
( ~ sP7
| sP23 ),
inference(all_rule,[status(thm)],]) ).

thf(3,plain,
( ~ sP23
| ~ sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
( ~ sP3
| ~ sP18
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
( ~ sP24
| sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
( ~ sP4
| sP24 ),
inference(all_rule,[status(thm)],]) ).

thf(7,plain,
( sP5
| sP22 ),
inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
( sP5
| sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
( ~ sP8
| ~ sP16
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).

thf(11,plain,
( ~ sP14
| sP19 ),
inference(all_rule,[status(thm)],]) ).

thf(12,plain,
( ~ sP19
| ~ sP2
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
( ~ sP15
| sP6 ),
inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
( sP11
| sP15 ),
inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
( sP11
| sP2 ),
inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
( sP20
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(17,plain,
( sP21
| sP25 ),
inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
( sP21
| sP10 ),
inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
( sP12
| sP16 ),
inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
( sP12
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
( sP14
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(22,plain,
( ~ sP13
| sP14
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
( sP4
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(24,plain,
( sP13
| sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
( sP13
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
( sP1
| sP13
| sP4 ),
inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
( sP1
| ~ sP13
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
( sP17
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(29,plain,
\$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h2]) ).

thf(30,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[29,h1]) ).

thf(31,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[30,h0]) ).

thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h2])],[29,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV221^5 : TPTP v7.5.0. 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 : n014.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 : Fri Mar 26 14:33:37 EDT 2021
% 0.13/0.34  % CPUTime  :
% 25.98/26.31  % SZS status Theorem
% 25.98/26.31  % Mode: mode454
% 25.98/26.31  % Inferences: 423
% 25.98/26.31  % SZS output start Proof
% See solution above
% 25.98/26.31  % SZS output end Proof
%------------------------------------------------------------------------------
```