%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO364^5 : 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 03:23:18 PM UTC 2025
% Result : Theorem 25.61s 25.68s
% Output : Proof 25.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 41 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 63 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 185 ( 26 ~; 13 |; 0 &; 110 @)
% ( 13 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 16 con; 0-2 aty)
% Number of variables : 37 ( 1 ^; 36 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_j,type,
j: a > a ).
thf(ty_f,type,
f: ( a > a ) > a > a ).
thf(ty_eigen__0,type,
eigen__0: ( a > a ) > $o ).
thf(ty_g,type,
g: ( a > a ) > a > a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_h,type,
h: a > a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
( ( f @ h @ X1 )
!= ( g @ j @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ ( f @ h ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( h = j ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( g @ h @ eigen__2 )
= ( g @ j @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( g @ h @ eigen__2 )
= ( f @ h @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ h @ eigen__2 )
= ( g @ j @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( f @ h )
= ( g @ j ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( f @ h @ X1 )
= ( g @ j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ ( g @ j ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( f @ h @ X1 )
= ( g @ h @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( f @ h @ eigen__2 )
= ( g @ h @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > a,X2: a] :
( ( f @ X1 @ X2 )
= ( g @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cEDEC_pme,conjecture,
( ~ ( ! [X1: a > a,X2: a,X3: a > $o] :
( ( X3 @ ( f @ X1 @ X2 ) )
=> ( X3 @ ( g @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a > $o] :
( ( X2 @ ( h @ X1 ) )
=> ( X2 @ ( j @ X1 ) ) ) )
=> ! [X1: ( a > a ) > $o] :
( ( X1 @ ( f @ h ) )
=> ( X1 @ ( g @ j ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ! [X1: a > a,X2: a,X3: a > $o] :
( ( X3 @ ( f @ X1 @ X2 ) )
=> ( X3 @ ( g @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a > $o] :
( ( X2 @ ( h @ X1 ) )
=> ( X2 @ ( j @ X1 ) ) ) )
=> ! [X1: ( a > a ) > $o] :
( ( X1 @ ( f @ h ) )
=> ( X1 @ ( g @ j ) ) ) ),
inference(assume_negation,[status(cth)],[cEDEC_pme]) ).
thf(h2,assumption,
~ ( ! [X1: a > a,X2: a,X3: a > $o] :
( ( X3 @ ( f @ X1 @ X2 ) )
=> ( X3 @ ( g @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a > $o] :
( ( X2 @ ( h @ X1 ) )
=> ( X2 @ ( j @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( a > a ) > $o] :
( ( X1 @ ( f @ h ) )
=> ( X1 @ ( g @ j ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a > a,X2: a,X3: a > $o] :
( ( X3 @ ( f @ X1 @ X2 ) )
=> ( X3 @ ( g @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a,X2: a > $o] :
( ( X2 @ ( h @ X1 ) )
=> ( X2 @ ( j @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> sP10 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP12
| sP6
| ~ sP5
| ~ sP3 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP5 ),
inference(symeq,[status(thm)],[]) ).
thf(4,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP8
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(8,plain,
( sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP1
| sP10
| ~ sP7 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP13
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h4,h5,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h4,h5,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h4,h5,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,11,h7,h8]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h4,h5,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,12,h6]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,13,h4,h5]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,14,h2,h3]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
( ~ ( ! [X1: a > a,X2: a,X3: a > $o] :
( ( X3 @ ( f @ X1 @ X2 ) )
=> ( X3 @ ( g @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a > $o] :
( ( X2 @ ( h @ X1 ) )
=> ( X2 @ ( j @ X1 ) ) ) )
=> ! [X1: ( a > a ) > $o] :
( ( X1 @ ( f @ h ) )
=> ( X1 @ ( g @ j ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO364^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 01:08:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 25.61/25.68 % SZS status Theorem
% 25.61/25.68 % Mode: cade22grackle2x798d
% 25.61/25.68 % Steps: 134103
% 25.61/25.68 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------