TSTP Solution File: SEV087^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV087^5 : 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 : n020.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 18:04:47 EDT 2022
% Result : Theorem 9.77s 10.04s
% Output : Proof 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 81
% Syntax : Number of formulae : 94 ( 17 unt; 8 typ; 8 def)
% Number of atoms : 296 ( 78 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 283 ( 108 ~; 46 |; 0 &; 50 @)
% ( 34 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 39 con; 0-2 aty)
% Number of variables : 56 ( 16 ^ 40 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i > $o ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( X1 = eigen__0 )
=> ( eigen__0 != X1 ) )
=> ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( eigen__5 = eigen__4 )
=> ( X1 != eigen__5 ) )
=> ( X1 = eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i > $o] : ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__8 @ X1 )
!= ( eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__6 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( X1 = eigen__4 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ( ( ^ [X1: $i] : $false )
!= ( ^ [X1: $i] : ~ $false ) )
=> ~ ! [X1: $i > $o] : ( X1 = X1 ) )
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) )
=> ~ ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X1 = eigen__4 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 = eigen__0 )
=> ( eigen__0 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ( ^ [X1: $i] : sP5 )
!= ( ^ [X1: $i] : ~ sP5 ) )
=> ~ ! [X1: $i > $o] : ( X1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ~ ( ( eigen__5 = eigen__4 )
=> ( X1 != eigen__5 ) )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ( eigen__5 = eigen__4 )
=> ( eigen__6 != eigen__5 ) )
=> ( eigen__6 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__6 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( sP5
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP6
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__6 @ eigen__7 )
= ( eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] : ( X1 = X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__5 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__8 @ eigen__9 )
= ( eigen__8 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP4
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__5 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ^ [X1: $i] : sP5 )
= ( ^ [X1: $i] : ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( eigen__8 @ X1 )
= ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( ~ ( ~ ( X1
@ ^ [X2: $i] : ~ sP5
@ ^ [X2: $i] : sP5 )
=> ~ ! [X2: $i > $o] : ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eigen__6 @ eigen__7 )
= ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i > $o] :
( ~ ( ( X1 = eigen__0 )
=> ( eigen__0 != X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__8 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP24
= ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP20
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(cTHM120H_pme,conjecture,
~ sP23 ).
thf(h2,negated_conjecture,
sP23,
inference(assume_negation,[status(cth)],[cTHM120H_pme]) ).
thf(1,plain,
( ~ sP15
| ~ sP5
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| sP5
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP21
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
sP17,
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP22
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(7,plain,
( sP29
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP13
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(9,plain,
( ~ sP6
| sP21
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| ~ sP31
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP31
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP30
| ~ sP24
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP30
| sP24
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP26
| ~ sP31
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP26
| sP31
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP28
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(19,plain,
( ~ sP20
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP9
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP33
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP33
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP34
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP8
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP8
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP7
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(27,plain,
( sP3
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(28,plain,
( sP25
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(29,plain,
( ~ sP11
| sP6
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP4
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP18
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP18
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP27
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(34,plain,
( sP2
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(35,plain,
( ~ sP1
| sP11
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP23
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,h2]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[37,h1]) ).
thf(39,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[38,h0]) ).
thf(0,theorem,
~ sP23,
inference(contra,[status(thm),contra(discharge,[h2])],[37,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV087^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.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 15:05:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.77/10.04 % SZS status Theorem
% 9.77/10.04 % Mode: mode495
% 9.77/10.04 % Inferences: 170
% 9.77/10.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------