%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : MSC025^2 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : 300s
% DateTime : Thu Oct 9 02:02:02 PM UTC 2025
% Result : Theorem 0.47s 0.70s
% Output : Proof 0.47s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_two,type,
two: $i ).
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_b1,type,
b1: $o > $i ).
thf(ty_one,type,
one: $i ).
thf(ty_b2,type,
b2: $o > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ ~ $false )
= two ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o] :
( ( eigen__0 @ X1 )
!= ( eigen__0 @ ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__2 )
= ( eigen__0 @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( b1 @ $false )
= ( b1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__2 )
= ( b2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( two
= ( b2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ ~ sP6 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__0 @ sP10 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( two
= ( eigen__0 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP11
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__0 @ sP10 )
= ( b1 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( one
= ( b2 @ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ sP6 )
= ( eigen__0 @ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( b1 @ ~ sP6 )
= ( b1 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( two
= ( b1 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__0 @ sP13 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__0 @ sP6 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( b2 @ ~ sP6 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__0 @ sP6 )
= ( eigen__0 @ ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( b1 @ ~ sP6 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ sP12
=> ( ( eigen__0 @ sP10 )
= two ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eigen__0 @ sP13 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $o] :
~ ( ( X1
=> ( ( b1 @ X1 )
= one ) )
=> ~ ( ~ X1
=> ( ( b1 @ X1 )
= two ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__0 @ sP10 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( X1 != one )
=> ( X1 = two ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( b2 @ ~ sP6 )
= ( b2 @ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( eigen__0 @ ~ sP6 )
= ( eigen__0 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( b2 @ sP6 )
= ( b2 @ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( b1 @ sP6 )
= two ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( eigen__0 @ sP6 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( one
= ( b1 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ sP27
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( b2 @ sP6 )
= one ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP35
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( ~ sP6 ) = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $o] :
~ ( ( X1
=> ( ( b2 @ X1 )
= two ) )
=> ~ ( ~ X1
=> ( ( b2 @ X1 )
= one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( one
= ( eigen__0 @ ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( eigen__0 @ ~ sP6 )
= ( eigen__0 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( ~ sP6 ) = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( one
= ( eigen__0 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
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,
~ ( sP3
=> ( ( eigen__0 != b1 )
=> ( eigen__0 = b2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP3,
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,
~ sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $o] :
( ( eigen__0 @ X1 )
= ( b2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP12
| ~ sP43
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP35
| sP27
| ~ sP18
| ~ sP35 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP38
| sP17
| sP6
| ~ sP33 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP25
| sP36
| sP6
| ~ sP19 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP11
| sP42
| ~ sP11
| sP6 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP35
| sP45
| ~ sP35
| sP6 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP23
| sP9
| sP6
| ~ sP31 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP34
| sP20
| sP6
| ~ sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP22
| sP14
| sP6
| sP6 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(10,plain,
( sP18
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP2
| sP32
| sP6
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(12,plain,
( sP43
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP29
| sP16
| sP6
| ~ sP20 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(14,plain,
( sP7
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP12
| sP16
| sP6
| ~ sP36 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP12
| sP24
| ~ sP7
| ~ sP42 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP21
| sP8
| sP6
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(18,plain,
( sP1
| ~ sP13
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP27
| sP8
| sP6
| ~ sP17 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP27
| sP24
| ~ sP45
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(22,plain,
( sP44
| sP6
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP31
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP33
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP40
| sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP19
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP5
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
~ sP6,
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP39
| sP35
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP30
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP15
| sP11
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP30
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP26
| sP12
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP30
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP37
| sP27
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP30
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP41
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP41
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP28
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP28
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP3
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP3
| ~ sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(b2,axiom,
sP41 ).
thf(b1,axiom,
sP28 ).
thf(binarity_exhaust,axiom,
sP30 ).
thf(43,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,h2,h7,h9,b2,b1,binarity_exhaust]) ).
thf(44,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)],[h8,43,h9]) ).
thf(45,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h8])],[h5,44,h8]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,45,h7]) ).
thf(47,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h6])],[h4,46,h6]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,47,h4,h5]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,48,h2,h3]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,49,h1]) ).
thf(0,theorem,
! [X1: $o > $i] :
( ! [X2: $o] :
( ( X1 @ X2 )
!= ( X1 @ ~ X2 ) )
=> ( ( X1 != b1 )
=> ( X1 = b2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[50,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : MSC025^2 : TPTP v9.2.0. Released v5.5.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 16:08:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.47/0.70 % SZS status Theorem
% 0.47/0.70 % Mode: cade22grackle2xfee4
% 0.47/0.70 % Steps: 455
% 0.47/0.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------