TSTP Solution File: MSC025^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : MSC025^2 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 : Sun Jul 17 22:57:36 EDT 2022
% Result : Theorem 0.44s 0.60s
% Output : Proof 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $i ).
thf(ty_b2,type,
b2: $o > $i ).
thf(ty_b1,type,
b1: $o > $i ).
thf(ty_two,type,
two: $i ).
thf(ty_one,type,
one: $i ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__1 )
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ $false )
= ( eigen__0 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( b1 @ eigen__1 )
!= one )
=> ( ( b1 @ eigen__1 )
= two ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ $false
=> ( ( b2 @ ~ $false )
= two ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( ( b2 @ ~ $false )
= X1 )
=> ( X1
= ( b2 @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ ~ $false )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( X1 != one )
=> ( X1 = two ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( b2 @ eigen__2 )
!= one )
=> ( ( b2 @ eigen__2 )
= two ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( b2 @ $false )
= one ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ $false )
= two ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( b2 @ ~ $false )
= ( b2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( one
= ( eigen__0 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ ~ $false )
= one ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( ( b1 @ $false )
= X1 )
=> ( X1
= ( b1 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( b1 @ $false )
= ( eigen__0 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP10
=> ( two
= ( eigen__0 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] :
~ ( ( X1
=> ( ( b1 @ X1 )
= one ) )
=> ~ ( ~ X1
=> ( ( b1 @ X1 )
= two ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ $false )
= one ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ $false
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( $false
=> ( ( b2 @ $false )
= two ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP11
=> ( ( b2 @ eigen__2 )
= ( b2 @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__0 @ ~ $false )
= ( eigen__0 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__0 @ $false )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ~ $false )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( b2 @ eigen__2 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( two
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eigen__0 @ $false )
= ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP18
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( b1 @ ~ $false )
= one ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( ( b1 @ eigen__1 )
= two )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP4
=> ~ ( $false
=> ( ( b2 @ ~ $false )
= one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( b2 @ ~ $false )
= ( eigen__0 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( b2 @ $false )
= ( b2 @ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( b1 @ $false )
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( $false
=> ( ( b1 @ $false )
= one ) )
=> ~ ( ~ $false
=> ( ( b1 @ $false )
= two ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP35
=> ( ( b1 @ eigen__1 )
= ( b1 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( b1 @ eigen__1 )
= ( b1 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( ( b1 @ eigen__1 )
= X1 )
=> ( X1
= ( b1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( two = two ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( b2 @ ~ $false )
= two ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( one
= ( b2 @ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( $false = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( b1 @ eigen__1 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( eigen__0 @ ~ $false )
= ( eigen__0 @ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( b2 @ sP31 )
= ( b2 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( eigen__0 @ ~ $false )
= two ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP13
=> sP48 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( $false = sP31 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ $false
=> ( ( b1 @ $false )
= two ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP18
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] :
( ( ( eigen__0 @ ~ $false )
= X1 )
=> ( X1
= ( eigen__0 @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( one
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $o] :
( ( eigen__0 @ X1 )
!= ( eigen__0 @ ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( b1 @ ~ $false )
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( b1 @ $false )
= two ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ( ( eigen__0 @ $false )
= X1 )
=> ( X1
= ( eigen__0 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( two
= ( b2 @ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ( eigen__0 @ sP31 )
= ( b2 @ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( one = one ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( b2 @ sP31 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( ~ $false
=> sP29 )
=> ~ ( $false
=> ( ( b1 @ ~ $false )
= two ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( two
= ( eigen__0 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( one
= ( eigen__0 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i] :
( ( ( b2 @ sP31 )
= X1 )
=> ( X1
= ( b2 @ sP31 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> $false ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ~ sP67
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ( ~ sP67 )
= sP31 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP13
=> sP65 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $o] :
~ ( ( X1
=> ( ( b2 @ X1 )
= two ) )
=> ~ ( ~ X1
=> ( ( b2 @ X1 )
= one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( b1 @ sP72 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP62
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(goal,conjecture,
! [X1: $o > $i] :
( ! [X2: $o] :
( ( X1 @ X2 )
!= ( X1 @ ~ X2 ) )
=> ( ( X1 != b1 )
=> ( X1 = b2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $o > $i] :
( ! [X2: $o] :
( ( X1 @ X2 )
!= ( X1 @ ~ X2 ) )
=> ( ( X1 != b1 )
=> ( X1 = b2 ) ) ),
inference(assume_negation,[status(cth)],[goal]) ).
thf(h1,assumption,
~ ( sP55
=> ( ( eigen__0 != b1 )
=> ( eigen__0 = b2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP55,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( eigen__0 != b1 )
=> ( eigen__0 = b2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
eigen__0 != b1,
introduced(assumption,[]) ).
thf(h5,assumption,
eigen__0 != b2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $o] :
( ( eigen__0 @ X1 )
= ( b1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $o] :
( ( eigen__0 @ X1 )
= ( b2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP60,
introduced(assumption,[]) ).
thf(1,plain,
( sP43
| sP67
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP44
| sP15
| ~ sP38
| ~ sP65 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( sP24
| sP67
| ~ sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP50
| sP67
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP42
| ~ sP61
| ~ sP34 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP29
| sP54
| ~ sP61
| ~ sP56 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( sP69
| sP67
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP41
| sP64
| ~ sP40
| ~ sP33 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP25
| sP33
| ~ sP47
| ~ sP12 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(10,plain,
( sP45
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP27
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP23
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
sP61,
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
sP40,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP35
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP37
| ~ sP35
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP14
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP56
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP34
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP11
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP21
| ~ sP11
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP5
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP48
| sP60
| ~ sP45
| ~ sP59 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP48
| sP2
| ~ sP64
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP13
| sP1
| ~ sP6
| ~ sP54 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP13
| sP2
| ~ sP12
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP10
| sP1
| ~ sP23
| ~ sP26 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP18
| sP60
| ~ sP27
| ~ sP42 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP57
| sP2
| ~ sP64
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP74
| ~ sP62
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP66
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP8
| sP25
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP30
| ~ sP73
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP39
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP3
| sP44
| sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP70
| ~ sP13
| sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP53
| sP70 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP49
| sP13
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP16
| ~ sP10
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP58
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP52
| ~ sP18
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP58
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP28
| sP18
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP7
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP7
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP46
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP51
| sP67
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP36
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP68
| sP67
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP63
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP17
| ~ sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP17
| ~ sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP19
| sP67
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP20
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP46
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
~ sP67,
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP4
| sP67
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( sP32
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP71
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP71
| ~ sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP46
| sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP46
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP55
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP46
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP46
| sP66 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
sP46,
inference(eq_sym,[status(thm)],]) ).
thf(binarity_exhaust,axiom,
sP7 ).
thf(b1,axiom,
sP17 ).
thf(b2,axiom,
sP71 ).
thf(71,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,binarity_exhaust,b1,b2,h2,h7,h9]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,71,h9]) ).
thf(73,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h8])],[h5,72,h8]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,73,h7]) ).
thf(75,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h6])],[h4,74,h6]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,75,h4,h5]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,76,h2,h3]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,77,h1]) ).
thf(0,theorem,
! [X1: $o > $i] :
( ! [X2: $o] :
( ( X1 @ X2 )
!= ( X1 @ ~ X2 ) )
=> ( ( X1 != b1 )
=> ( X1 = b2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[78,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MSC025^2 : TPTP v8.1.0. Released v5.5.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n011.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 : Fri Jul 1 15:46:49 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.44/0.60 % SZS status Theorem
% 0.44/0.60 % Mode: mode213
% 0.44/0.60 % Inferences: 1531
% 0.44/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------