TSTP Solution File: NUM705^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM705^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 11:40:37 EDT 2023
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 65
% Syntax : Number of formulae : 71 ( 12 unt; 7 typ; 2 def)
% Number of atoms : 191 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 297 ( 72 ~; 31 |; 0 &; 104 @)
% ( 28 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 32 con; 0-2 aty)
% Number of variables : 37 ( 5 ^; 32 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_p,type,
p: nat > $o ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_some,type,
some: ( nat > $o ) > $o ).
thf(ty_lessis,type,
lessis: nat > nat > $o ).
thf(h0,assumption,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: nat] :
~ ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ eigen__0 @ X2 ) )
=> ~ ( p @ eigen__0 ) )
=> ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( eigen__0 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: nat] :
~ ! [X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ( ~ ( more @ X2 @ X1 )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( some @ p )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__0 @ X1 ) )
=> ~ ( p @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( lessis @ eigen__0 @ X1 )
=> ~ ( more @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( more @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( p @ eigen__1 )
=> ( lessis @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( lessis @ eigen__1 @ eigen__0 )
=> ( ~ sP7
=> ( eigen__0 = eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( lessis @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( p @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP4
=> ( ~ ( ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__1 @ X1 ) )
=> ~ sP12 )
=> ( eigen__0 = eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__1 @ X1 ) )
=> ~ sP12 )
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( lessis @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( some @ p ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP13
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: nat] :
( ~ sP4
=> ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP14
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP18
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: nat > $o] :
( ( some @ X1 )
=> ( some
@ ^ [X2: nat] :
~ ( ! [X3: nat] :
( ( X1 @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: nat] :
( ( lessis @ eigen__1 @ X1 )
=> ( ~ ( more @ X1 @ eigen__1 )
=> ( X1 = eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(satz27a,conjecture,
~ sP6 ).
thf(h1,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[satz27a]) ).
thf(1,plain,
( ~ sP10
| sP7
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP28
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| ~ sP12
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| ~ sP13
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP23
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP24
| ~ sP14
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP18
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| ~ sP20
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP27
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP26
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP26
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP16
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP16
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP4
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP15
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP22
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(23,plain,
( sP11
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(24,plain,
( ~ sP6
| ~ sP11
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(satz27,axiom,
sP27 ).
thf(satz10d,axiom,
sP19 ).
thf(satz14,axiom,
sP1 ).
thf(s,axiom,
sP20 ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h1,satz27,satz10d,satz14,s]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[25,h0]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h1])],[25,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM705^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 12:04:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: cade22grackle2xfee4
% 0.20/0.41 % Steps: 91
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------