TSTP Solution File: SEV293^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV293^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 18:05:45 EDT 2022
% Result : Theorem 143.56s 143.89s
% Output : Proof 143.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 127
% Syntax : Number of formulae : 137 ( 22 unt; 8 typ; 7 def)
% Number of atoms : 400 ( 94 equ; 7 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 446 ( 159 ~; 68 |; 0 &; 110 @)
% ( 56 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 66 usr; 64 con; 0-2 aty)
% Number of variables : 76 ( 25 ^ 51 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_cONE,type,
cONE: ( $i > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cSUCC,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(ty_cZERO,type,
cZERO: ( $i > $o ) > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0
!= ( (=) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
!= ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $o] :
( ( cONE @ X1 )
!= ( ~ ! [X2: $i] :
( X1
!= ( (=) @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ~ ( cZERO
@ ^ [X2: $i] :
~ ( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( X1 != eigen__3 )
=> ~ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( cZERO
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( eigen__0
!= ( (=) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o] :
( ( X1 @ ( cONE @ eigen__0 ) )
=> ! [X2: $o] :
( ( ( cONE @ eigen__0 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__2 )
=> ~ ( cZERO
@ ^ [X1: $i] :
~ ( ( X1 != eigen__2 )
=> ~ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__7 != eigen__3 )
=> ~ ( eigen__0 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cZERO
@ ^ [X1: $i] :
~ ( ( X1 != eigen__3 )
=> ~ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o] :
( ( ( cONE @ eigen__0 )
= X1 )
=> ( X1
!= ( ~ sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0
= ( (=) @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ( cONE @ eigen__0 )
= ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ( cZERO
@ ^ [X2: $i] :
~ ( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) ) )
=> ( ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ( cZERO
@ ^ [X2: $i] :
~ ( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) )
!= ( ~ sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0
= ( (=) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cZERO
@ ^ [X1: $i] :
~ ( ( X1 != eigen__2 )
=> ~ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: ( $i > $o ) > $o] :
( ( cSUCC @ X1 )
= ( ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__6 = eigen__2 )
=> ( eigen__2 = eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( X1 != eigen__2 )
=> ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( eigen__6 = X1 )
=> ( X1 = eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__3 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ! [X1: $i > $o] :
( ( cONE @ X1 )
= ( cSUCC @ cZERO @ X1 ) )
=> ! [X1: ( $i > $o ) > $o] :
( ( ( cSUCC @ cZERO )
= X1 )
=> ! [X2: $i > $o] :
( ( cONE @ X2 )
= ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( X1 @ ( cSUCC @ cZERO ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ( cSUCC @ cZERO )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i > $o] :
( ( cZERO @ X1 )
= ( ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__7 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: ( $i > $o ) > $o,X2: ( ( $i > $o ) > $o ) > $o] :
( ( X2 @ X1 )
=> ! [X3: ( $i > $o ) > $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( cSUCC @ cZERO )
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( cZERO
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cONE @ eigen__0 )
= ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ( cZERO
@ ^ [X2: $i] :
~ ( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__6 != eigen__2 )
=> ~ ( eigen__0 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__6 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP18
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( X1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i > $o] :
( ( cONE @ X1 )
= ( ~ ! [X2: $i] :
( X1
!= ( (=) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eigen__0 @ eigen__7 )
= sP18 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP26
=> ! [X1: $i > $o] :
( ( cONE @ X1 )
= ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( cZERO
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( ( cONE @ eigen__0 )
!= ( ~ sP2 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cONE
= ( cSUCC @ cZERO ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP7
= ( ! [X1: $i] :
( ( X1 != eigen__3 )
=> ~ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP34
= ( eigen__2 = eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( cONE
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( X1
!= ( (=) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP12 = sP16 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP28
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ( cZERO
@ ^ [X2: $i] :
~ ( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( cONE @ eigen__0 )
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( ~ sP45 )
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i > $o] :
( ( cONE @ X1 )
= ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( cZERO
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ( X1 != eigen__3 )
=> ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__0 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP28 = sP25 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__2 = eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i > $o] :
( ( cONE @ X1 )
= ( cSUCC @ cZERO @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: ( $i > $o ) > $o] :
( ( ( cSUCC @ cZERO )
= X1 )
=> ! [X2: $i > $o] :
( ( cONE @ X2 )
= ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_cONE,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(cX6101_pme,conjecture,
sP42 ).
thf(h2,negated_conjecture,
~ sP42,
inference(assume_negation,[status(cth)],[cX6101_pme]) ).
thf(1,plain,
( ~ sP32
| ~ sP18
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP33
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP36
| ~ sP50
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP40
| sP7
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP49
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(9,plain,
( ~ sP22
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP54
| sP34
| ~ sP52 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| ~ sP31
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP27
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP41
| ~ sP34
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP41
| sP34
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP30
| sP31
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP19
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(19,plain,
( sP11
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP44
| ~ sP28
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP51
| sP28
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
sP25,
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
sP27,
inference(eq_sym,[status(thm)],]) ).
thf(25,plain,
( ~ sP45
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP15
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP9
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP2
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( sP2
| sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(30,plain,
( ~ sP43
| ~ sP12
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP5
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP22
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP10
| ~ sP29
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP48
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( sP45
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(38,plain,
( sP47
| sP45
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP47
| ~ sP45
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP37
| ~ sP26
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP56
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP20
| ~ sP55
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP21
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP13
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP24
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
sP24,
inference(eq_ind,[status(thm)],]) ).
thf(47,plain,
( ~ sP53
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP38
| sP46
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP4
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP39
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
sP3,
inference(eq_ind,[status(thm)],]) ).
thf(53,plain,
( ~ sP1
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP35
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(55,plain,
( sP42
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(cSUCC_def,axiom,
sP53 ).
thf(cONE,axiom,
sP39 ).
thf(cZERO,axiom,
sP1 ).
thf(56,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,cSUCC_def,cONE,cZERO,h2]) ).
thf(57,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[56,h1]) ).
thf(58,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[57,h0]) ).
thf(0,theorem,
sP42,
inference(contra,[status(thm),contra(discharge,[h2])],[56,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV293^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 28 00:55:31 EDT 2022
% 0.12/0.32 % CPUTime :
% 143.56/143.89 % SZS status Theorem
% 143.56/143.89 % Mode: mode389
% 143.56/143.89 % Inferences: 20696
% 143.56/143.89 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------