TSTP Solution File: SEV066^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV066^5 : 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 : n016.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 : Tue Jul 19 18:04:42 EDT 2022
% Result : Theorem 35.33s 35.65s
% Output : Proof 35.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 58
% Syntax : Number of formulae : 69 ( 17 unt; 7 typ; 6 def)
% Number of atoms : 156 ( 6 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 355 ( 74 ~; 27 |; 0 &; 146 @)
% ( 24 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 31 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 90 ( 12 ^ 78 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__46,type,
eigen__46: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__32,type,
eigen__32: $i > $o ).
thf(ty_eigen__27,type,
eigen__27: $i ).
thf(ty_eigen__20,type,
eigen__20: $i > $o ).
thf(ty_eigen__28,type,
eigen__28: $i > $o ).
thf(ty_eigen__50,type,
eigen__50: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__32,definition,
( eigen__32
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( eigen__28 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__28 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__32])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__50,definition,
( eigen__50
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__28 @ X1 )
=> ( eigen__46 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__50])]) ).
thf(eigendef_eigen__20,definition,
( eigen__20
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__20])]) ).
thf(eigendef_eigen__46,definition,
( eigen__46
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] :
( ( eigen__28 @ X2 )
=> ( eigen__32 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eigen__32 @ X2 )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__28 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__46])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__27,definition,
( eigen__27
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__20 @ X1 )
=> ( eigen__20 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__27])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__28 @ eigen__50 )
=> ( eigen__46 @ eigen__50 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i] :
( ~ ( X1 @ X2 @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i] :
( ~ ( X1 @ X2 @ X3 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ~ ( X1 @ X2 @ X4 @ X5 )
=> ( X4 @ X5 ) ) ) )
=> ( !!
@ ( X1
@ ^ [X2: $i] : ~ $false
@ ^ [X2: $i] : $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ! [X1: $i] :
( ( eigen__28 @ X1 )
=> ( eigen__32 @ X1 ) )
=> ~ ! [X1: $i] :
( ( eigen__32 @ X1 )
=> ( eigen__46 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__28 @ X1 )
=> ( eigen__46 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( eigen__28 @ X2 )
=> ( eigen__32 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eigen__32 @ X2 )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__28 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( eigen__28 @ X1 )
=> ( eigen__32 @ X1 ) )
=> ~ ! [X1: $i] :
( ( eigen__32 @ X1 )
=> ( eigen__46 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] : $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__46 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__28 @ eigen__50 )
=> ( eigen__32 @ eigen__50 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( eigen__28 @ X1 )
=> ( eigen__46 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__20 @ X1 )
=> ( eigen__20 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__32 @ X1 )
=> ( eigen__46 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( eigen__28 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__28 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__32 @ eigen__50 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__20 @ eigen__27 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__28 @ X1 )
=> ( eigen__32 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> $false ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X3: $i > $o,X4: $i] :
( ~ ( X2 @ X3 @ X3 @ X4 )
=> ( X1 @ X3 @ X3 @ X4 ) )
=> ~ ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ~ ( ! [X6: $i] :
( ~ ( X2 @ X3 @ X4 @ X6 )
=> ( X1 @ X3 @ X4 @ X6 ) )
=> ~ ! [X6: $i] :
( ~ ( X2 @ X4 @ X5 @ X6 )
=> ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ~ ( X2 @ X3 @ X5 @ X6 )
=> ( X1 @ X3 @ X5 @ X6 ) ) ) )
=> ! [X3: $i] :
( ~ ( X2
@ ^ [X4: $i] : ~ sP18
@ ^ [X4: $i] : sP18
@ X3 )
=> ( X1
@ ^ [X4: $i] : ~ sP18
@ ^ [X4: $i] : sP18
@ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP17
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP15
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__32 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__28 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(cTHM120D_pme,conjecture,
~ sP19 ).
thf(h2,negated_conjecture,
sP19,
inference(assume_negation,[status(cth)],[cTHM120D_pme]) ).
thf(1,plain,
( ~ sP8
| ~ sP23
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| ~ sP22
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP16
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP1
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP1
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP9
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__50]) ).
thf(10,plain,
( sP3
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP4
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__46]) ).
thf(13,plain,
( sP13
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__32]) ).
thf(14,plain,
( sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP21
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP24
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(17,plain,
( sP11
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__27]) ).
thf(18,plain,
( ~ sP20
| ~ sP17
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP10
| sP20
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP17
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20]) ).
thf(21,plain,
~ sP18,
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP19
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(25,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,h2]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[25,h1]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[26,h0]) ).
thf(0,theorem,
~ sP19,
inference(contra,[status(thm),contra(discharge,[h2])],[25,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEV066^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.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 : Tue Jun 28 10:41:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 35.33/35.65 % SZS status Theorem
% 35.33/35.65 % Mode: mode466
% 35.33/35.65 % Inferences: 74104
% 35.33/35.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------