%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN364^5 : 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 : n016.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 03:16:38 PM UTC 2025
% Result : Theorem 20.22s 20.88s
% Output : Proof 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 52
% Syntax : Number of formulae : 62 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 154 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 361 ( 95 ~; 26 |; 0 &; 177 @)
% ( 23 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 28 con; 0-2 aty)
% Number of variables : 24 ( 2 ^; 22 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_g,type,
g: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_f,type,
f: $i > $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cM,type,
cM: $i > $o ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_eigen__12,type,
eigen__12: $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] :
~ ~ ( ~ ( cP @ ( g @ eigen__0 ) @ X1 )
=> ~ ( ( cM @ ( g @ eigen__0 ) )
=> ~ ( cQ @ ( f @ ( g @ eigen__0 ) @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ~ ( cP @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ X1 )
=> ~ ( ( cM @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) )
=> ~ ( cQ @ ( f @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( cP @ ( g @ eigen__0 ) @ eigen__1 )
=> ~ ( ( cM @ ( g @ eigen__0 ) )
=> ~ ( cQ @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cM @ ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ ( g @ eigen__0 ) @ ( g @ eigen__0 ) )
=> ~ ( cP @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( ~ ( cP @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ X1 )
=> ~ ( ( cM @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) )
=> ~ ( cQ @ ( f @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ( cP @ ( g @ eigen__0 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cM @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cQ @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( cP @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ eigen__12 )
=> ~ ( sP6
=> ~ ( cQ @ ( f @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ eigen__12 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
~ ( cP @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP6
=> ~ ( cQ @ ( f @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP @ ( g @ eigen__0 ) @ ( g @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ( ~ ( cP @ ( g @ eigen__0 ) @ X1 )
=> ~ ( ( cM @ ( g @ eigen__0 ) )
=> ~ ( cQ @ ( f @ ( g @ eigen__0 ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP5
=> ! [X1: $i] : ( cP @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cM @ ( g @ eigen__0 ) )
=> ~ ( cQ @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ~ ( cP @ X1 @ X2 )
=> ~ ( ( cM @ X1 )
=> ~ ( cQ @ ( f @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cP @ ( g @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] : ( cP @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( cP @ ( g @ eigen__0 ) @ X1 )
=> ~ ( cP @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cP @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP9
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cQ @ ( f @ ( g @ eigen__0 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( cP @ X1 @ X2 )
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP @ ( g @ eigen__0 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(cX2115,conjecture,
( ~ ( ~ ( sP22
=> ~ sP15 )
=> ~ sP2 )
=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ ( g @ X1 ) @ X2 )
=> ~ ( cP @ X1 @ X1 ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( sP22
=> ~ sP15 )
=> ~ sP2 )
=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ ( g @ X1 ) @ X2 )
=> ~ ( cP @ X1 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cX2115]) ).
thf(h2,assumption,
~ ( ~ ( sP22
=> ~ sP15 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ ( g @ X1 ) @ X2 )
=> ~ ( cP @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP22
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
sP22,
introduced(assumption,[]) ).
thf(h7,assumption,
sP15,
introduced(assumption,[]) ).
thf(h8,assumption,
sP18,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( sP10
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP8
| sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP4
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(5,plain,
( ~ sP20
| sP9
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP15
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP22
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| ~ sP21
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP5
| ~ sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( sP14
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP17
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP1
| sP23
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| sP5
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP12
| sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(17,plain,
( ~ sP3
| ~ sP11
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP22
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP15
| ~ sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,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,h6,h7,h5,h8]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h3,21,h8]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,22,h6,h7]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,23,h4,h5]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,24,h2,h3]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[25,h0]) ).
thf(0,theorem,
( ~ ( ~ ( sP22
=> ~ sP15 )
=> ~ sP2 )
=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ ( g @ X1 ) @ X2 )
=> ~ ( cP @ X1 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[25,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN364^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n016.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 15:16:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.22/20.88 % SZS status Theorem
% 20.22/20.88 % Mode: cade22grackle2x798d
% 20.22/20.88 % Steps: 11914
% 20.22/20.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------