TSTP Solution File: SEV101^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV101^5 : 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 : n032.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 18:04:51 EDT 2022
% Result : Theorem 45.16s 45.41s
% Output : Proof 45.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 74
% Syntax : Number of formulae : 85 ( 15 unt; 8 typ; 6 def)
% Number of atoms : 267 ( 40 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 402 ( 125 ~; 39 |; 0 &; 128 @)
% ( 31 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 38 con; 0-2 aty)
% Number of variables : 75 ( 12 ^ 63 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: $o ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__7,type,
eigen__7: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__11,type,
eigen__11: $i > $o ).
thf(ty_eigen__10,type,
eigen__10: $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__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] :
( ( ( eigen__7 @ X2 )
!= $false )
=> ( eigen__10 @ X2 ) )
=> ~ ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( ( eigen__7 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( ( eigen__7 @ X3 )
!= $false )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( ( eigen__7 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: $i] :
~ ( ( ( eigen__7 @ X1 )
!= $false )
=> ( eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( ( X1 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: $i] :
~ ( ( ( eigen__8 @ X1 )
!= $false )
=> ( eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ! [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 ) ) ) )
=> ! [X2: $i] :
( ~ ( X1
@ ^ [X3: $i] :
( ~ p
=> ~ p )
@ ^ [X3: $i] :
~ ( p
=> p )
@ X2 )
=> ~ ( p
=> p ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__8 @ eigen__9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( ( eigen__7 @ X2 )
!= sP3 )
=> ( eigen__10 @ X2 ) )
=> ~ ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= sP3 )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( ( eigen__7 @ X2 )
!= sP3 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__8 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( p
=> p ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] :
( ( ( eigen__7 @ X1 )
!= sP3 )
=> ( eigen__10 @ X1 ) )
=> ~ ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= sP3 )
=> ( eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP7
=> ! [X1: $i] :
( ( ( eigen__7 @ X1 )
!= sP3 )
=> ( eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( ~ p
=> ~ p )
!= sP3 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__10 @ eigen__12 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( ( eigen__7 @ X3 )
!= sP3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
!= sP3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( ( eigen__7 @ X3 )
!= sP3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= sP3 )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( ( X1 @ X4 )
!= sP3 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
!= sP3 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( ( X1 @ X4 )
!= sP3 )
=> ( X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__7 @ eigen__12 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP14
=> ( eigen__10 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__10 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP2
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] : sP9 ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( ( eigen__7 @ X1 )
!= sP3 )
=> ( eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP14
=> ( eigen__11 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [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] :
( ~ p
=> ~ p )
@ ^ [X4: $i] : ~ sP6
@ X3 )
=> ( X1
@ ^ [X4: $i] :
( ~ p
=> ~ p )
@ ^ [X4: $i] : ~ sP6
@ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP10
=> ( eigen__11 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( ( eigen__7 @ X1 )
!= sP3 )
=> ( eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> p ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= sP3 )
=> ( eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ~ sP24
=> ~ sP24 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__11 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( ( eigen__8 @ X1 )
!= sP3 )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP24
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP25
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(cTHM120E_pme,conjecture,
~ sP21 ).
thf(h2,negated_conjecture,
sP21,
inference(assume_negation,[status(cth)],[cTHM120E_pme]) ).
thf(1,plain,
( ~ sP15
| sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP16
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP22
| sP10
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP30
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP30
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP27
| ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP27
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP26
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP20
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP20
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP7
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP7
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP19
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(15,plain,
( sP8
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(18,plain,
( sP11
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(19,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP2
| sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP17
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP17
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP29
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(24,plain,
( sP12
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(25,plain,
( sP13
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(26,plain,
( ~ sP25
| ~ sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP31
| sP25
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP6
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP6
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP1
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP21
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(33,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,h2]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[33,h1]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[34,h0]) ).
thf(0,theorem,
~ sP21,
inference(contra,[status(thm),contra(discharge,[h2])],[33,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SEV101^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.08 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Tue Jun 28 16:14:27 EDT 2022
% 0.07/0.27 % CPUTime :
% 45.16/45.41 % SZS status Theorem
% 45.16/45.41 % Mode: mode456
% 45.16/45.41 % Inferences: 158
% 45.16/45.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------