%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:56 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_q,type,
q: mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_r,type,
r: mworld > $o ).
thf(ty_eigen__3,type,
eigen__3: mworld ).
thf(sP1,plain,
( sP1
<=> ( r @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( r @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( ( ~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) )
=> sP3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mrel @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ sP6
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) ) )
=> ( ~ sP6
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP6
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( mrel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [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,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP11
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP6
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: mworld] : ( mrel @ eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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,
! [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 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [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 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel5]) ).
thf(h1,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ( sP13
=> ( ~ ! [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(assumption,[]) ).
thf(h2,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP13
=> ( ~ ! [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(assumption,[]) ).
thf(h4,assumption,
sP13,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ! [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(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( mrel @ eigen__0 @ eigen__1 )
=> sP7 ),
introduced(assumption,[]) ).
thf(h9,assumption,
mrel @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP2
=> ( sP16
=> sP3 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP16
=> sP3 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP16,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h17,assumption,
sP11,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP17
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP14
| ~ sP11
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP3
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP10
| sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP15
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| ~ sP15
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| ~ sP2
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(mrel_universal,axiom,
sP12 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h4,h10,h12,h14,h17,h18,mrel_universal]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,12,h17,h18]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,13,h16]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,14,h14,h15]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,15,h12,h13]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h7,16,h11]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,17,h9,h10]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,18,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,19,h6,h7]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,21,h2,h3]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).
thf(0,theorem,
! [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 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 05:43:58 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: cade22grackle2xfee4
% 0.13/0.38 % Steps: 175
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------