TSTP Solution File: SYO113^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO113^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : Thu Jul 21 19:30:22 EDT 2022
% Result : Theorem 33.69s 33.61s
% Output : Proof 33.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 91
% Syntax : Number of formulae : 97 ( 8 unt; 7 typ; 2 def)
% Number of atoms : 261 ( 8 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 432 ( 118 ~; 52 |; 0 &; 158 @)
% ( 41 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 47 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 18 ( 2 ^ 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i > $i ).
thf(ty_cEVEN,type,
cEVEN: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cNUMBER,type,
cNUMBER: $i > $o ).
thf(ty_c0,type,
c0: $i ).
thf(ty_cODD,type,
cODD: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( cNUMBER @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ~ ( ~ ( ( cEVEN @ c0 )
=> ~ ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) )
=> ~ ( cODD @ ( cS @ c0 ) ) )
=> ~ ! [X1: $i] :
( ( cODD @ X1 )
=> ( cODD @ ( cS @ ( cS @ X1 ) ) ) ) )
=> ~ ( ~ ( ~ ( ( cNUMBER @ c0 )
=> ~ ( cNUMBER @ ( cS @ c0 ) ) )
=> ~ ! [X1: $i] :
( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) )
=> ! [X1: $i] :
~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( cNUMBER @ X1 )
= ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cEVEN @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cEVEN @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cODD @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( sP2
=> ~ ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) )
=> ~ ( cODD @ ( cS @ c0 ) ) )
=> ~ ! [X1: $i] :
( ( cODD @ X1 )
=> ( cODD @ ( cS @ ( cS @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP5
=> ~ ( ~ ( ~ ( ( cNUMBER @ c0 )
=> ~ ( cNUMBER @ ( cS @ c0 ) ) )
=> ~ ! [X1: $i] :
( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) )
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) )
= ( ~ ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cNUMBER @ eigen__1 )
=> ~ ( cNUMBER @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cODD @ eigen__1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cNUMBER @ X1 )
= ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cNUMBER @ ( cS @ c0 ) )
= ( ~ ( cEVEN @ ( cS @ c0 ) )
=> ( cODD @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( cODD @ X1 )
=> ( cODD @ ( cS @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cODD @ ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP10
=> ~ ( ( cNUMBER @ ( cS @ eigen__1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( cNUMBER @ c0 )
=> ~ ( cNUMBER @ ( cS @ c0 ) ) )
=> ~ ! [X1: $i] :
( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( cNUMBER @ c0 )
=> ~ ( cNUMBER @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cNUMBER @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP3
=> ( cODD @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( sP2
=> ~ sP23 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cNUMBER @ ( cS @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( !! @ cNUMBER ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP2
=> ( cODD @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP25
=> ~ ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP1
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ( cEVEN @ ( cS @ c0 ) )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP18
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( cNUMBER @ eigen__0 )
=> ~ ( cNUMBER @ ( cS @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cODD @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( cNUMBER @ ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( cNUMBER @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( cNUMBER @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP36 = sP27 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP20 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP2
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(cTHM350,conjecture,
sP29 ).
thf(h1,negated_conjecture,
~ sP29,
inference(assume_negation,[status(cth)],[cTHM350]) ).
thf(1,plain,
( sP33
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP30
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP35
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP3
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| ~ sP34
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| sP3
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP39
| ~ sP20
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP27
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP38
| sP36
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP12
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP12
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP40
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP15
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP23
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP10
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP28
| ~ sP25
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP17
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP17
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP41
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP41
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP24
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP24
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP5
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP19
| ~ sP36
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP32
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(33,plain,
( ~ sP18
| sP19
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP31
| sP18
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP7
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP1
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP26
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(40,plain,
( sP29
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP29
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,h1]) ).
thf(43,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[42,h0]) ).
thf(0,theorem,
sP29,
inference(contra,[status(thm),contra(discharge,[h1])],[42,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO113^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.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 : Sat Jul 9 09:29:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 33.69/33.61 % SZS status Theorem
% 33.69/33.61 % Mode: mode448
% 33.69/33.61 % Inferences: 2197
% 33.69/33.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------