%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR132^2 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 01:22:47 PM UTC 2025
% Result : Theorem 0.56s 0.77s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 96 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 300 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 390 ( 128 ~; 63 |; 0 &; 126 @)
% ( 42 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 56 usr; 53 con; 0-2 aty)
% Number of variables : 60 ( 36 ^; 24 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_likes_THFTYPE_IiioI,type,
likes_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lBill_THFTYPE_i,type,
lBill_THFTYPE_i: $i ).
thf(ty_n2009_THFTYPE_i,type,
n2009_THFTYPE_i: $i ).
thf(ty_lBen_THFTYPE_i,type,
lBen_THFTYPE_i: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_lAnna_THFTYPE_i,type,
lAnna_THFTYPE_i: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_lSue_THFTYPE_i,type,
lSue_THFTYPE_i: $i ).
thf(ty_lYearFn_THFTYPE_IiiI,type,
lYearFn_THFTYPE_IiiI: $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_holdsDuring_THFTYPE_IiooI,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
thf(ty_parent_THFTYPE_IiioI,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
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] :
~ ( parent_THFTYPE_IiioI @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] : ( parent_THFTYPE_IiioI @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] : ( likes_THFTYPE_IiioI @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( likes_THFTYPE_IiioI @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 )
= ( ^ [X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
= ( ~ ( ~ ( ~ ( ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( likes_THFTYPE_IiioI @ eigen__0 )
= ( ^ [X1: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ! [X1: $i,X2: $i] : ( parent_THFTYPE_IiioI @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] : ( likes_THFTYPE_IiioI @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
= ( ~ ( ~ ( ~ ( ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] : ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ( ~ ( ~ ( ( likes_THFTYPE_IiioI @ X1 @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ lAnna_THFTYPE_i ) )
=> ( likes_THFTYPE_IiioI
= ( ^ [X2: $i,X3: $i] : ~ $false ) ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X2: $i,X3: $i] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] : ( likes_THFTYPE_IiioI @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ eigen__1 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ( ~ ( ~ ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ) )
=> ( likes_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) )
=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( parent_THFTYPE_IiioI @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ~ ( ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) )
=> sP13 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( likes_THFTYPE_IiioI @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ~ sP10 ) = ( ~ sP17 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] : ( parent_THFTYPE_IiioI @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ sP16 )
=> ( likes_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ( ~ ( ~ ( ( X2 @ X3 @ lBill_THFTYPE_i )
=> ~ ( X1 @ X3 @ lAnna_THFTYPE_i ) )
=> ( X2
= ( ^ [X4: $i,X5: $i] : ~ $false ) ) )
=> ( X1
= ( ^ [X4: $i,X5: $i] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( likes_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP18 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( likes_THFTYPE_IiioI @ eigen__0 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP16 = ( ~ sP17 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> $false ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( parent_THFTYPE_IiioI @ eigen__1 )
= ( ^ [X1: $i] : ~ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ sP16 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( likes_THFTYPE_IiioI @ X1 )
= ( ^ [X2: $i] : ~ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i,X2: $i] : ( parent_THFTYPE_IiioI @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( ~ sP36 ) = ( ~ sP17 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i > $i > $o,X2: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ( ~ ( ~ ( ( X1 @ X2 @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ lAnna_THFTYPE_i ) )
=> ( X1
= ( ^ [X3: $i,X4: $i] : ~ sP31 ) ) )
=> sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ~ ( ~ ( ~ ( ( parent_THFTYPE_IiioI @ X1 @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ lAnna_THFTYPE_i ) )
=> sP13 )
=> sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(con,conjecture,
~ sP23 ).
thf(h1,negated_conjecture,
sP23,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP15
| sP14
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP32
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP27
| sP18
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP28
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP35
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP34
| ~ sP40
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP33
| sP34
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP21
| sP33
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP38
| ~ sP42
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP24
| sP12
| ~ sP38
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP25
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP3
| sP40
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP29
| sP16
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP37
| sP36
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP37
| ~ sP36
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP19
| ~ sP10
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP7
| ~ sP42
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP7
| sP42
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP1
| sP22
| ~ sP3
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP26
| sP22
| ~ sP29
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP5
| sP22
| ~ sP37
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP30
| sP22
| ~ sP19
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP24
| sP22
| ~ sP7
| sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP8
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP36
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
~ sP31,
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP20
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(32,plain,
( sP6
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(33,plain,
( sP36
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(34,plain,
( sP10
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(35,plain,
( ~ sP9
| ~ sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP39
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP41
| ~ sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP39
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP23
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax_080,axiom,
sP24 ).
thf(ax_053,axiom,
sP30 ).
thf(ax_028,axiom,
sP5 ).
thf(ax_008,axiom,
sP26 ).
thf(ax_003,axiom,
sP1 ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h1,ax_080,ax_053,ax_028,ax_008,ax_003]) ).
thf(41,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[40,h0]) ).
thf(0,theorem,
~ sP23,
inference(contra,[status(thm),contra(discharge,[h1])],[40,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : CSR132^2 : TPTP v9.2.0. Released v4.1.0.
% 0.10/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 8 17:11:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.56/0.77 % SZS status Theorem
% 0.56/0.77 % Mode: cade22sinegrackle2x6978
% 0.56/0.77 % Steps: 5981
% 0.56/0.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------