TSTP Solution File: SYO105^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO105^5 : 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 : n029.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 : Fri Sep 1 04:45:13 EDT 2023
% Result : Theorem 13.38s 13.61s
% Output : Proof 13.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 85
% Syntax : Number of formulae : 102 ( 27 unt; 14 typ; 8 def)
% Number of atoms : 220 ( 11 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 375 ( 129 ~; 35 |; 0 &; 135 @)
% ( 31 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 44 con; 0-3 aty)
% Number of variables : 44 ( 8 ^; 36 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_y,type,
y: $i ).
thf(ty_eigen__81,type,
eigen__81: $i ).
thf(ty_eigen__6809,type,
eigen__6809: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__6804,type,
eigen__6804: $i ).
thf(ty_eigen__6807,type,
eigen__6807: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__6895,type,
eigen__6895: $i ).
thf(ty_cP,type,
cP: $i > $i > $i > $o ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__6808,type,
eigen__6808: $i ).
thf(ty_eigen__6810,type,
eigen__6810: $i ).
thf(ty_cQ,type,
cQ: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6804,definition,
( eigen__6804
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( cQ @ eigen__0 @ y )
=> ~ ( ( cP @ eigen__81 @ y @ eigen__6 )
=> ~ ( cR @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6804])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
~ ! [X3: $i] :
~ ( ( cQ @ eigen__0 @ y )
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__81,definition,
( eigen__81
= ( eps__0
@ ^ [X1: $i] :
~ ( cP @ X1 @ y @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__81])]) ).
thf(eigendef_eigen__6809,definition,
( eigen__6809
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6809])]) ).
thf(eigendef_eigen__6895,definition,
( eigen__6895
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
~ ( ( cQ @ eigen__6807 @ y )
=> ~ ( ( cP @ X1 @ y @ eigen__6808 )
=> ~ ( cR @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6895])]) ).
thf(eigendef_eigen__6808,definition,
( eigen__6808
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] : ( cP @ X2 @ y @ X1 )
=> ! [X2: $i] :
~ ( cR @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6808])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( cQ @ eigen__0 @ y )
=> ~ ( ( cP @ eigen__0 @ y @ eigen__6 )
=> ~ ( cR @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__6810,definition,
( eigen__6810
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
~ ( ( cQ @ eigen__6807 @ y )
=> ~ ( ( cP @ X1 @ y @ eigen__81 )
=> ~ ( cR @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6810])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ y @ X1 )
=> ! [X2: $i] :
~ ( cR @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( cR @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cR @ eigen__6809 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] : ( cP @ X1 @ y @ eigen__6808 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cP @ eigen__81 @ y @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( cQ @ eigen__6807 @ y )
=> ~ ( ( cP @ X1 @ y @ eigen__81 )
=> ~ ( cR @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( cQ @ eigen__6807 @ y )
=> ~ ( ( cP @ X1 @ y @ eigen__6808 )
=> ~ ( cR @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
~ ( cQ @ X1 @ y ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cP @ eigen__0 @ y @ eigen__6 )
=> ~ ( cR @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cQ @ eigen__6807 @ y ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] : ( cP @ X1 @ y @ eigen__6 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] : ( cP @ X1 @ y @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ~ ( cR @ eigen__6804 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( cQ @ eigen__0 @ y )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP10
=> ~ ( ( cP @ eigen__6895 @ y @ eigen__6808 )
=> ~ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP8
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( cQ @ eigen__0 @ y )
=> ~ ( ( cP @ X1 @ y @ eigen__6 )
=> ~ ( cR @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cP @ eigen__6895 @ y @ eigen__6808 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cR @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ! [X3: $i] :
~ ( ( cQ @ eigen__0 @ y )
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cQ @ eigen__0 @ y ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
~ ( sP10
=> ~ ( sP19
=> ~ ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ! [X3: $i] :
~ ! [X4: $i] :
~ ( ( cQ @ X1 @ y )
=> ~ ( ( cP @ X3 @ y @ X2 )
=> ~ ( cR @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
~ ( sP22
=> ~ ( sP5
=> ~ ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ! [X3: $i] :
~ ( sP10
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
~ ( sP10
=> ~ ( ( cP @ eigen__6810 @ y @ eigen__81 )
=> ~ ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP10
=> ~ ( ( cP @ eigen__6810 @ y @ eigen__81 )
=> ~ ( cR @ eigen__81 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
~ ( sP22
=> ~ ( ( cP @ eigen__0 @ y @ eigen__6 )
=> ~ ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP22
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP19
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(cX2201TEST,conjecture,
( ~ sP17 = ~ sP24 ) ).
thf(h1,negated_conjecture,
( ~ sP17 != ~ sP24 ),
inference(assume_negation,[status(cth)],[cX2201TEST]) ).
thf(h2,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h4,assumption,
sP17,
introduced(assumption,[]) ).
thf(h5,assumption,
sP24,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP22,
introduced(assumption,[]) ).
thf(1,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP30
| ~ sP22
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP25
| sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6804]) ).
thf(4,plain,
( ~ sP18
| ~ sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP12
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__81]) ).
thf(6,plain,
( ~ sP11
| ~ sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP9
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP15
| ~ sP22
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP29
| sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(12,plain,
( ~ sP18
| ~ sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP21
| sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(14,plain,
( ~ sP24
| ~ sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h8,h7,h3]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h6,15,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h2,16,h6,h7]) ).
thf(h9,assumption,
sP26,
introduced(assumption,[]) ).
thf(18,plain,
( ~ sP4
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP31
| ~ sP19
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP16
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP23
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP7
| sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6895]) ).
thf(23,plain,
( ~ sP26
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP8
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( sP28
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP27
| ~ sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( sP6
| sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6810]) ).
thf(28,plain,
( sP2
| sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6809]) ).
thf(29,plain,
( sP14
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP14
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP1
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6808]) ).
thf(32,plain,
( ~ sP17
| sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP26
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h4,h5,h1,h0])],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h4,h9]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__6807)],[h5,34,h9]) ).
thf(36,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,17,35,h2,h3,h4,h5]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0]) ).
thf(0,theorem,
( ~ sP17 = ~ sP24 ),
inference(contra,[status(thm),contra(discharge,[h1])],[36,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYO105^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 00:31:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 13.38/13.61 % SZS status Theorem
% 13.38/13.61 % Mode: cade22grackle2xfee4
% 13.38/13.61 % Steps: 658730
% 13.38/13.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------