%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO223^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Oct 9 03:23:03 PM UTC 2025
% Result : Theorem 0.47s 0.67s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 65
% Syntax : Number of formulae : 74 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 182 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 205 ( 74 ~; 46 |; 0 &; 36 @)
% ( 30 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 38 con; 0-2 aty)
% Number of variables : 15 ( 3 ^; 12 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cLIKE,type,
cLIKE: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_cP,type,
cP: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_cUNIQUE,type,
cUNIQUE: $i > $o ).
thf(ty_cJ,type,
cJ: $i ).
thf(ty_cS,type,
cS: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] : ( X1 != cP ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] : ( cP != X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( cUNIQUE @ cS ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cUNIQUE @ cP )
= ( cLIKE @ cP @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cLIKE @ cJ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ! [X1: $i] : ( cS = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cS = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cUNIQUE @ cP ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cLIKE @ cP @ cS ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 = cS ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__11 = cP ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] : ( cP = X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cS = eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP2
=> ( ( cUNIQUE @ cJ )
!= ( ~ ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cS = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cP = cJ ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] : ( cS = X1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cUNIQUE @ cJ )
= ( ~ ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cUNIQUE @ eigen__0 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ! [X2: $i] : ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o] :
( ( ( X1 @ cP )
= sP8 )
=> ( ( X1 @ cJ )
!= ( ~ sP20 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cS = cP ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cS = cJ ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cUNIQUE @ cJ ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cLIKE @ cJ @ cJ ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP8
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP25
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cJ = cP ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] : ( X1 = cP ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(cLING2,conjecture,
( ~ ( sP19
=> ~ sP1 )
=> ~ sP21 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP19
=> ~ sP1 )
=> ~ sP21 ),
inference(assume_negation,[status(cth)],[cLING2]) ).
thf(h2,assumption,
~ ( sP19
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP21,
introduced(assumption,[]) ).
thf(h4,assumption,
sP19,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP22
| sP10
| ~ sP12
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP30
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(4,plain,
( ~ sP30
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP22
| sP23
| ~ sP22
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP16
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP11
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(8,plain,
( ~ sP27
| sP8
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP21
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP22
| sP9
| ~ sP6
| sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP16
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| sP8
| ~ sP9
| ~ sP29 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP8
| sP26
| ~ sP24
| ~ sP15 ),
inference(mating_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP28
| ~ sP25
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP18
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP20
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( sP20
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(19,plain,
( sP17
| ~ sP25
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP2
| ~ sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP13
| ~ sP2
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP21
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP1
| sP25
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP16
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP16
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP5
| ~ sP1
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP1
| sP7
| ~ sP22 ),
inference(mating_rule,[status(thm)],[]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h4,h5,h3]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,30,h4,h5]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,31,h2,h3]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[32,h0]) ).
thf(0,theorem,
( ~ ( sP19
=> ~ sP1 )
=> ~ sP21 ),
inference(contra,[status(thm),contra(discharge,[h1])],[32,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO223^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : Thu Oct 9 01:29:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.47/0.67 % SZS status Theorem
% 0.47/0.67 % Mode: cade22grackle2xfee4
% 0.47/0.67 % Steps: 6741
% 0.47/0.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------