%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP075^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 01:44:58 PM UTC 2025
% Result : Theorem 20.54s 20.76s
% Output : Proof 20.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 48
% Syntax : Number of formulae : 54 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 136 ( 9 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 179 ( 55 ~; 30 |; 0 &; 57 @)
% ( 21 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 27 con; 0-2 aty)
% Number of variables : 29 ( 12 ^; 17 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
hF_Mirabelle_hf: $tType ).
thf(ty_hF_Mirabelle_hmem,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(ty_eigen__2,type,
eigen__2: hF_Mirabelle_hf ).
thf(ty_a,type,
a: hF_Mirabelle_hf ).
thf(ty_eigen__0,type,
eigen__0: hF_Mirabelle_hf ).
thf(ty_p,type,
p: $o ).
thf(ty_hF_Mirabelle_HBex,type,
hF_Mirabelle_HBex: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > $o ).
thf(h0,assumption,
! [X1: hF_Mirabelle_hf > $o,X2: hF_Mirabelle_hf] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: hF_Mirabelle_hf] :
~ ~ ( hF_Mirabelle_hmem @ X1 @ a ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ X1 @ a )
=> ~ p ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ X1 @ X2 )
=> ~ ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
=> ~ ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ a )
=> ~ p ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ a @ X1 )
=> ~ ! [X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X2 @ a )
=> ~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: hF_Mirabelle_hf] : p )
= ( ^ [X1: hF_Mirabelle_hf] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( hF_Mirabelle_HBex @ a
@ ^ [X1: hF_Mirabelle_hf] : $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ a ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( hF_Mirabelle_HBex @ a
@ ^ [X1: hF_Mirabelle_hf] : p )
=> ~ ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ a )
=> ~ p ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ a )
=> ~ p ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( hF_Mirabelle_HBex @ a
@ ^ [X1: hF_Mirabelle_hf] : p )
= ( ~ sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> p ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( hF_Mirabelle_hmem @ eigen__2 @ a )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( hF_Mirabelle_hmem @ eigen__0 @ a ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( hF_Mirabelle_HBex @ a
@ ^ [X1: hF_Mirabelle_hf] : sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP13 = ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( hF_Mirabelle_HBex
= ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf > $o] :
~ ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP12
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( hF_Mirabelle_HBex @ a )
= ( ^ [X1: hF_Mirabelle_hf > $o] :
~ ! [X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X2 @ a )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBex @ X1 )
= ( ^ [X2: hF_Mirabelle_hf > $o] :
~ ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( hF_Mirabelle_hmem @ eigen__2 @ a ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ a @ X1 )
= ( ~ ! [X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X2 @ a )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> $false ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(conj_0,conjecture,
sP14 ).
thf(h1,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP6
| ~ sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP16
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP4
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP11
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP13
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| sP5
| ~ sP4
| sP21 ),
inference(mating_rule,[status(thm)],[]) ).
thf(8,plain,
( sP8
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(9,plain,
~ sP21,
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP20
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP7
| ~ sP13
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP6
| sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(13,plain,
( ~ sP17
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP3
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP2
| sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP2
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP18
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( sP14
| ~ sP13
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP14
| sP13
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP15
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_5_HBex__def,axiom,
sP15 ).
thf(fact_2_hbexE,axiom,
sP1 ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h1,fact_5_HBex__def,fact_2_hbexE]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP075^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n002.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 18:35:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.54/20.76 % SZS status Theorem
% 20.54/20.76 % Mode: cade22sinegrackle2xfaf3
% 20.54/20.76 % Steps: 4647
% 20.54/20.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------