%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:02:55 PM UTC 2026
% Result : Theorem 1.03s 1.40s
% Output : Proof 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 58
% Syntax : Number of formulae : 65 ( 18 unt; 0 typ; 11 def)
% Number of atoms : 227 ( 12 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 400 ( 49 ~; 27 |; 0 &; 200 @)
% ( 24 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 39 con; 0-2 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 22 ^; 58 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_q,type,
q: mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_r,type,
r: mworld > $o ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( q @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ eigen__0 @ eigen__4 )
=> ( p @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mrel @ eigen__0 @ eigen__1 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( q @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( mrel @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( !! @ ( mrel @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( mrel @ eigen__0 @ eigen__1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( !! @ ( mrel @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( mrel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( mrel @ mactual @ eigen__0 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( q @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP13
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP10
=> ( p @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( p @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(pel5,conjecture,
sP19 ).
thf(h1,negated_conjecture,
~ sP19,
inference(assume_negation,[status(cth)],[pel5]) ).
thf(1,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP6
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP17
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP22
| ~ sP10
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP2
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| ~ sP16
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP4
| ~ sP6
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP8
| sP17
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP20
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( sP21
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP21
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP5
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP15
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(18,plain,
( sP3
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP3
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP18
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP19
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(mrel_universal,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,mrel_universal,h1]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
sP19,
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 05:45:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.03/1.40 % SZS status Theorem
% 1.03/1.40 % Mode: mode506
% 1.03/1.40 % Inferences: 39017
% 1.03/1.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------