TSTP Solution File: SEU897^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU897^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : 300s
% DateTime : Thu Aug 31 17:37:48 EDT 2023
% Result : Theorem 20.27s 20.53s
% Output : Proof 20.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 60
% Syntax : Number of formulae : 70 ( 13 unt; 8 typ; 5 def)
% Number of atoms : 164 ( 29 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 221 ( 70 ~; 31 |; 0 &; 59 @)
% ( 24 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 31 con; 0-2 aty)
% Number of variables : 35 ( 5 ^; 30 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cS,type,
cS: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__1,type,
eigen__1: a > a ).
thf(ty_cR,type,
cR: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a] :
( ( cR @ X2 )
=> ( X1
!= ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( cS @ X2 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( a > a ) > $o,X2: a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a > a] :
~ ! [X2: a] :
( ~ ! [X3: a] :
( ( cR @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( cS @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ( ( cR @ X1 )
=> ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ( eigen__0 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ( ( cR @ X1 )
=> ( eigen__3
!= ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__3
= ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cR @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( cR @ X1 )
=> ( eigen__0 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__8 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ( cS @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cS @ eigen__4 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ~ ! [X2: a] :
( ( cR @ X2 )
=> ( X1
!= ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( cS @ X2 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( cS @ X1 )
=> ( eigen__0 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cR @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ! [X1: a] :
( ( cR @ X1 )
=> ( eigen__3
!= ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: a] :
( ( cS @ X1 )
=> ( eigen__3
!= ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( cR @ X1 )
=> ( eigen__3
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cS @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP10
=> ( cS @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP16
= ( ! [X1: a > a,X2: a] :
( ~ ! [X3: a] :
( ( cR @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( cS @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cS @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP3
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cS @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP13
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a] :
( ( cS @ X1 )
=> ( eigen__3
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ~ ! [X2: a] :
( ( cR @ X2 )
=> ( X1 != X2 ) )
=> ~ ! [X2: a] :
( ( cS @ X2 )
=> ( X1 != X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > a,X2: a] :
( ~ ! [X3: a] :
( ( cR @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( cS @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(cTHM30_pme,conjecture,
sP17 ).
thf(h2,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[cTHM30_pme]) ).
thf(1,plain,
( ~ sP13
| sP20
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP4 ),
inference(symeq,[status(thm)],]) ).
thf(3,plain,
( sP21
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP21
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| ~ sP10
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP18
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP9
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(8,plain,
( ~ sP3
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP16
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP22
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP19
| sP3
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP23
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP15
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP12
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( ~ sP24
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( sP11
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP11
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP8
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(20,plain,
( sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP5
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP24
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(23,plain,
( sP16
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(24,plain,
( sP17
| ~ sP16
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP17
| sP16
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,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,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h2])],[26,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU897^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.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 : 300
% 0.12/0.33 % DateTime : Wed Aug 23 13:53:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.27/20.53 % SZS status Theorem
% 20.27/20.53 % Mode: cade22grackle2x798d
% 20.27/20.53 % Steps: 1002
% 20.27/20.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------