TSTP Solution File: SYO546^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO546^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 : Thu Jul 21 19:33:21 EDT 2022
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 110
% Syntax : Number of formulae : 120 ( 16 unt; 7 typ; 5 def)
% Number of atoms : 474 ( 136 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 508 ( 237 ~; 74 |; 0 &; 34 @)
% ( 48 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 56 con; 0-2 aty)
% Number of variables : 77 ( 62 ^ 15 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(ty_f,type,
f: $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $o] :
( ( f @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__0 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__0 != eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $o] :
( ( f @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> ~ ( ( f
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( f
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( f @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( f @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP10
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( f @ eigen__4 )
= ( ~ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> $false ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o] :
( ( f @ X1 )
= sP14 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( f
= ( ^ [X1: $o] : sP14 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o] :
( ( eigen__4 = X1 )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP9 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__4 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP8 = sP14 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP16
=> ( eigen__0 != eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( f
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP22
=> ~ ( sP10
=> ( eigen__0 != eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP6
=> ~ ( ( f
= ( ^ [X1: $o] : ~ sP14 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP16
=> ( X1 != eigen__0 ) )
=> ~ ( sP10
=> ( X1 != eigen__0 ) ) )
=> ~ ( sP23
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ sP14 ) )
=> ( X1 != eigen__0 ) ) ) )
!= eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ sP24
=> ~ ( sP23
=> ( eigen__0 != eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $o] :
( ( f @ X1 )
= ( ~ sP14 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__3 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( f @ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__4 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP16
=> ( X1 != eigen__0 ) )
=> ~ ( sP10
=> ( X1 != eigen__0 ) ) )
=> ~ ( sP23
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ sP14 ) )
=> ( X1 != eigen__0 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( f
= ( ^ [X1: $o] : ~ sP14 ) )
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP16
=> ( X1 != eigen__0 ) )
=> ~ ( sP10
=> ( X1 != eigen__0 ) ) )
=> ~ ( sP23
=> ( X1 != eigen__0 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ sP14 ) )
=> ( X1 != eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( f
= ( ^ [X1: $o] : ~ sP14 ) )
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( f
= ( ^ [X1: $o] : ~ sP14 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP23
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP30
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP33 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP37 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP2 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP10
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP29
= ( ~ sP14 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( f @ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP10
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(def_case,definition,
( case
= ( ^ [X1: $o > $o,X2: $i,X3: $i,X4: $i,X5: $i] :
( eps
@ ^ [X6: $i] :
( ~ ( ~ ( ( ( X1
= ( ^ [X7: $o] : sP14 ) )
=> ( X6 != X2 ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ X7 ) )
=> ( X6 != X3 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : X7 ) )
=> ( X6 != X4 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ sP14 ) )
=> ( X6 != X5 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i] :
( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP16
=> ( X2 != X1 ) )
=> ~ ( sP10
=> ( X2 != X1 ) ) )
=> ~ ( sP23
=> ( X2 != X1 ) ) )
=> ~ ( sP38
=> ( X2 != X1 ) ) ) )
= X1 ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP16
=> ( X2 != X1 ) )
=> ~ ( sP10
=> ( X2 != X1 ) ) )
=> ~ ( sP23
=> ( X2 != X1 ) ) )
=> ~ ( sP38
=> ( X2 != X1 ) ) ) )
= X1 ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(1,plain,
( sP41
| ~ sP33
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP20
| ~ sP33
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP30
| sP33
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP40
| ~ sP30
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP45
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP42
| ~ sP37
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP28
| ~ sP37
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP43
| sP2
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP47
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP47
| sP29
| ~ sP41 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP47
| sP9
| ~ sP20 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP29
| ~ sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP8
| sP9
| ~ sP28 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP9
| sP29
| ~ sP43 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
~ sP14,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| ~ sP47
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP12
| sP47
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP1
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(20,plain,
( sP21
| sP8
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP15
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(22,plain,
( sP19
| ~ sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP19
| sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP5
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(25,plain,
( sP46
| ~ sP29
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
sP45,
inference(eq_sym,[status(thm)],]) ).
thf(27,plain,
( sP27
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(28,plain,
( sP44
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP11
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP7
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP3
| ~ sP11
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP34
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP6
| sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP25
| sP6
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP16
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP23
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP48
| ~ sP10
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP22
| ~ sP16
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
sP31,
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP38
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP39
| ~ sP23
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP24
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP24
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP36
| ~ sP38
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP26
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP26
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP4
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP4
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP35
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(51,plain,
( sP25
| sP35 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,h2]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,52,h2]) ).
thf(54,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[53,h0]) ).
thf(0,theorem,
! [X1: $i] :
( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP16
=> ( X2 != X1 ) )
=> ~ ( sP10
=> ( X2 != X1 ) ) )
=> ~ ( sP23
=> ( X2 != X1 ) ) )
=> ~ ( sP38
=> ( X2 != X1 ) ) ) )
= X1 ),
inference(contra,[status(thm),contra(discharge,[h1])],[53,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO546^1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.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 : Fri Jul 8 19:26:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % Mode: mode213
% 0.18/0.36 % Inferences: 153
% 0.18/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------