%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN365^5 : 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 : n011.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 20.27s 20.48s
% Output : Proof 20.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 47 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 116 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 218 ( 60 ~; 17 |; 0 &; 90 @)
% ( 16 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 16 ( 1 ^; 15 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cR,type,
cR: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_h,type,
h: $i > $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_g,type,
g: $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] :
~ ~ ( ( cP @ eigen__0 )
=> ~ ( ( cR @ eigen__0 @ ( g @ ( h @ X1 ) ) )
=> ~ ( cP @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( sP1
=> ~ ( ( cR @ eigen__0 @ ( g @ ( h @ X1 ) ) )
=> ~ ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cR @ eigen__0 @ ( g @ ( h @ eigen__1 ) ) )
=> ~ ( cP @ ( g @ ( h @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ~ ( ( cR @ eigen__0 @ ( g @ ( h @ eigen__1 ) ) )
=> ~ ( cP @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__1 )
=> ~ ( ( cP @ ( g @ eigen__1 ) )
=> ~ ( cP @ ( h @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ ( g @ eigen__1 ) )
=> ~ ( cP @ ( h @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ ( g @ ( h @ eigen__1 ) ) )
=> ~ ( cP @ ( h @ ( h @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cP @ ( h @ eigen__1 ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cR @ eigen__0 @ ( g @ ( h @ eigen__1 ) ) )
=> ~ ( cP @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( ( cP @ ( g @ X1 ) )
=> ~ ( cP @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP @ ( h @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( cR @ eigen__0 @ X1 )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cR @ eigen__0 @ ( g @ ( h @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( cP @ X1 )
=> ~ ( ( cR @ X1 @ ( g @ ( h @ X2 ) ) )
=> ~ ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cP @ ( g @ ( h @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cX2116,conjecture,
( ~ ( sP15
=> ~ sP10 )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ~ ( cP @ X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP15
=> ~ sP10 )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ~ ( cP @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cX2116]) ).
thf(h2,assumption,
~ ( sP15
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ~ ( cP @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP15,
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP12,
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| ~ sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP6
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| ~ sP13
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP3
| ~ sP14
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP9
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP9
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP4
| ~ sP1
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP2
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(13,plain,
( ~ sP15
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h4,h5,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,15,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,16,h4,h5]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
( ~ ( sP15
=> ~ sP10 )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ~ ( cP @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN365^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.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 15:11:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.27/20.48 % SZS status Theorem
% 20.27/20.48 % Mode: cade22grackle2x798d
% 20.27/20.48 % Steps: 376
% 20.27/20.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------