%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO113^5 : 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 : n031.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 03:22:46 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 77
% Syntax : Number of formulae : 89 ( 19 unt; 0 typ; 1 def)
% Number of atoms : 233 ( 6 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 357 ( 128 ~; 39 |; 0 &; 96 @)
% ( 34 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 39 con; 0-2 aty)
% Number of variables : 12 ( 1 ^; 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cODD,type,
cODD: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_c0,type,
c0: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cEVEN,type,
cEVEN: $i > $o ).
thf(ty_cNUMBER,type,
cNUMBER: $i > $o ).
thf(ty_cS,type,
cS: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( cNUMBER @ X1 )
= ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cEVEN @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cNUMBER @ ( cS @ c0 ) )
= ( ~ ( cEVEN @ ( cS @ c0 ) )
=> ( cODD @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) )
=> ( cODD @ ( cS @ ( cS @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cNUMBER @ c0 )
=> ~ ( cNUMBER @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) )
= sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP2
=> ( cODD @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( cEVEN @ ( cS @ c0 ) )
=> ( cODD @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cNUMBER @ c0 )
= sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cODD @ ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cNUMBER @ eigen__1 )
= ( ~ ( cEVEN @ eigen__1 )
=> ( cODD @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( cEVEN @ eigen__1 )
=> ( cODD @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cEVEN @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cNUMBER @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cNUMBER @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cEVEN @ eigen__1 )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cNUMBER @ ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ~ ( ( cNUMBER @ X1 )
=> ~ ( cNUMBER @ ( cS @ X1 ) ) )
=> ~ ( ( cNUMBER @ ( cS @ X1 ) )
=> ~ ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cODD @ ( cS @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( cNUMBER @ ( cS @ eigen__1 ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ~ sP5
=> ~ sP20 )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( cNUMBER @ eigen__0 )
=> ~ ( cNUMBER @ ( cS @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cNUMBER @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cEVEN @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP5
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cNUMBER @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cODD @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP15
=> ~ ( cNUMBER @ ( cS @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP30
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( cODD @ X1 )
=> ( cODD @ ( cS @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP29
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cNUMBER @ ( cS @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(cTHM350,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 )
=> ~ sP23 )
=> ~ sP1 )
=> ! [X1: $i] : ( cNUMBER @ X1 ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 )
=> ~ sP23 )
=> ~ sP1 )
=> ! [X1: $i] : ( cNUMBER @ X1 ) ),
inference(assume_negation,[status(cth)],[cTHM350]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 )
=> ~ sP23 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] : ( cNUMBER @ X1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 )
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP23,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP32,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP2
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP10,
introduced(assumption,[]) ).
thf(h12,assumption,
sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
sP13,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP4
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP8
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP3
| sP18
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP12
| sP26
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP11
| ~ sP15
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP33
| ~ sP29
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP17
| ~ sP26
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP32
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP9
| sP28
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( sP24
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP19
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP22
| ~ sP34
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP30
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP30
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP31
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP31
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP20
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(26,plain,
( ~ sP5
| ~ sP28
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP27
| sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP23
| sP27
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h12,h13,h10,h11,h8,h9,h6,h7,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,h12,h13,h11,h9,h7,h5,h14]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__0)],[h3,29,h14]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,30,h12,h13]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,31,h10,h11]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,32,h8,h9]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,33,h6,h7]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,34,h4,h5]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,35,h2,h3]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( sP2
=> ~ sP13 )
=> ~ sP10 )
=> ~ sP32 )
=> ~ sP23 )
=> ~ sP1 )
=> ! [X1: $i] : ( cNUMBER @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[36,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO113^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 00:49:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 246
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------