TSTP Solution File: NUM636^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM636^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 13:54:23 EDT 2022
% Result : Theorem 144.93s 144.79s
% Output : Proof 144.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 90
% Syntax : Number of formulae : 95 ( 15 unt; 8 typ; 1 def)
% Number of atoms : 221 ( 54 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 307 ( 82 ~; 46 |; 0 &; 110 @)
% ( 40 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 45 con; 0-2 aty)
% Number of variables : 46 ( 21 ^ 25 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set,type,
set: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_eigen__2,type,
eigen__2: nat ).
thf(ty_esti,type,
esti: nat > set > $o ).
thf(ty_setof,type,
setof: ( nat > $o ) > set ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_n_1,type,
n_1: nat ).
thf(ty_x,type,
x: nat ).
thf(h0,assumption,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: nat] :
~ ( ( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) )
=> ( esti @ ( suc @ X1 )
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( x
= ( suc @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( suc @ eigen__2 )
!= x )
=> ( esti @ ( suc @ eigen__2 )
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( suc @ x )
= x )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( suc @ eigen__2 )
= x )
=> ( x
= ( suc @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( esti @ ( suc @ x )
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( n_1 = x ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( x
= ( suc @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( suc @ X1 )
!= n_1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> ( esti @ n_1
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
=> ( ( suc @ x )
!= x ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( x = eigen__2 )
=> ( eigen__2 = x ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( esti @ n_1
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) )
=> ( ! [X1: nat] :
( ( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) )
=> ( esti @ ( suc @ X1 )
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) )
=> ! [X1: nat] :
( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( suc @ x )
= n_1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__2 = x ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( x = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ( suc @ X1 )
!= ( suc @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: nat] :
( ( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) )
=> ( esti @ ( suc @ X1 )
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( n_1 = n_1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( suc @ x )
= ( suc @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: nat] :
( ( x != X1 )
=> ( ( suc @ x )
!= ( suc @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: nat] :
( ( X1 != x )
=> ( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: nat] :
( ( ( suc @ x )
= X1 )
=> ( X1
= ( suc @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: nat] :
( ( x = X1 )
=> ( X1 = x ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( esti @ eigen__2
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( esti @ n_1
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: set] :
( ( esti @ n_1 @ X1 )
=> ( ! [X2: nat] :
( ( esti @ X2 @ X1 )
=> ( esti @ ( suc @ X2 ) @ X1 ) )
=> ! [X2: nat] : ( esti @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP18
=> ! [X1: nat] :
( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( esti @ ( suc @ eigen__2 )
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: nat] :
( ( ( suc @ eigen__2 )
= X1 )
=> ( X1
= ( suc @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( suc @ x )
= x ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: nat,X2: nat] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: nat] :
( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( suc @ x )
= ( suc @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( esti @ eigen__2
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) )
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP16
=> ~ sP34 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( suc @ eigen__2 )
= x ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: nat] :
( ( esti @ X1
@ ( setof
@ ^ [X2: nat] : ( X2 != x ) ) )
=> ( X1 != x ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( esti @ eigen__2
@ ( setof
@ ^ [X1: nat] : ( X1 != x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(satz2,conjecture,
~ sP31 ).
thf(h1,negated_conjecture,
sP31,
inference(assume_negation,[status(cth)],[satz2]) ).
thf(1,plain,
( ~ sP31
| sP34
| ~ sP20
| ~ sP8 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP37
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP30
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP32
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| ~ sP16
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP24
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP36
| sP16
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
sP19,
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP14
| ~ sP2
| ~ sP19 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(11,plain,
sP20,
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP38
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP25
| ~ sP40
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP22
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP3
| sP37
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP35
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP35
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP18
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(21,plain,
( ~ sP22
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP10
| sP7
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP13
| ~ sP26
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP28
| ~ sP18
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP33
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP38
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP11
| ~ sP6
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP39
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP1
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP32
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP4
| ~ sP31
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP23
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP32
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
sP32,
inference(eq_sym,[status(thm)],]) ).
thf(satz1,axiom,
sP17 ).
thf(ax3,axiom,
sP9 ).
thf(estii,axiom,
sP39 ).
thf(ax5,axiom,
sP27 ).
thf(estie,axiom,
sP1 ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,satz1,ax3,estii,ax5,estie,h1]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0]) ).
thf(0,theorem,
~ sP31,
inference(contra,[status(thm),contra(discharge,[h1])],[36,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM636^1 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n018.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 : 600
% 0.12/0.33 % DateTime : Thu Jul 7 03:23:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 144.93/144.79 % SZS status Theorem
% 144.93/144.79 % Mode: mode483
% 144.93/144.79 % Inferences: 1367
% 144.93/144.79 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------