TSTP Solution File: SEU550^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 13:53:11 EDT 2022
% Result : Theorem 26.04s 26.60s
% Output : Proof 26.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 101
% Syntax : Number of formulae : 112 ( 19 unt; 6 typ; 7 def)
% Number of atoms : 310 ( 72 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 344 ( 86 ~; 56 |; 0 &; 90 @)
% ( 45 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 54 usr; 53 con; 0-2 aty)
% Number of variables : 65 ( 7 ^ 58 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( eigen__0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( X2 = X3 ) ) ) )
= ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) )
= ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( eigen__0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( X2 = X3 ) ) ) )
= ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( ( eigen__0 @ eigen__2 )
= ( eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__2 )
= ( eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( ( eigen__0 @ eigen__2 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__11 = eigen__11 )
=> ( ( eigen__0 @ eigen__11 )
= ( eigen__1 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ) )
= ( ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__9 = X1 )
=> ( ( eigen__0 @ eigen__9 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP8
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP12
=> ( eigen__2 = eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( sP8
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__0 @ eigen__11 )
=> ( eigen__3 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP10
=> ( eigen__3 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__0 @ eigen__11 )
= sP10 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__0 @ eigen__9 )
= sP12 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__1 @ eigen__2 )
=> ~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( eigen__0 @ X1 )
= ( eigen__1 @ X2 ) ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__3 = eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__11 = eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) )
= ( ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP8
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__2 = eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( eigen__9 = eigen__9 )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( eigen__0 @ eigen__9 )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( eigen__11 = X1 )
=> ( ( eigen__0 @ eigen__11 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eigen__1 @ eigen__3 )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP25
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__0 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__9 = eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( eigen__0 @ X1 )
= ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__0 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ).
thf(exu__Cong,conjecture,
sP29 ).
thf(h2,negated_conjecture,
~ sP29,
inference(assume_negation,[status(cth)],[exu__Cong]) ).
thf(1,plain,
( ~ sP22
| ~ sP40
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP28,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| sP43
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
sP41,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
sP2,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| ~ sP28
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP33
| ~ sP41
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP37
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP42
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP21
| ~ sP10
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP19
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP19
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP36
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(17,plain,
( ~ sP42
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP17
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP34
| ~ sP43
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP15
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP15
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP44
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(23,plain,
( ~ sP13
| sP8
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| ~ sP8
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP4
| ~ sP25
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP24
| ~ sP30
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP16
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP14
| ~ sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP42
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP35
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP3
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP42
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP20
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( sP38
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP38
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP39
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP39
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP20
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(40,plain,
( sP35
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(41,plain,
( sP7
| sP35
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP7
| ~ sP35
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP26
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP26
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP1
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(46,plain,
( sP29
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(47,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,h2]) ).
thf(48,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[47,h1]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[48,h0]) ).
thf(0,theorem,
sP29,
inference(contra,[status(thm),contra(discharge,[h2])],[47,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 23:13:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 26.04/26.60 % SZS status Theorem
% 26.04/26.60 % Mode: mode454
% 26.04/26.60 % Inferences: 1513
% 26.04/26.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------