%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 12:26:58 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( r @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( r @ eigen__2 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( r @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( r @ eigen__0 @ X2 ) )
=> ( r @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( r @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] : ( r @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_cartesian_product,definition,
( cartesian_product
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X1 @ X3 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_pair_rel,definition,
( pair_rel
= ( ^ [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = X1 )
| ( X4 = X2 ) ) ) ) ).
thf(def_id_rel,definition,
( id_rel
= ( ^ [X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ X2 )
& ( X2 = X3 ) ) ) ) ).
thf(def_sub_rel,definition,
( sub_rel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_is_rel_on,definition,
( is_rel_on
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
! [X4: $i,X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X5 )
@ ( ( X2 @ X4 )
& ( X3 @ X5 ) ) ) ) ) ).
thf(def_restrict_rel_domain,definition,
( restrict_rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 )
& ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_diagonal,definition,
( rel_diagonal
= ( ^ [X1: $i,X2: $i] : ( X1 = X2 ) ) ) ).
thf(def_rel_composition,definition,
( rel_composition
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i,X4: $i] :
? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X2 @ X5 @ X4 ) ) ) ) ).
thf(def_reflexive,definition,
( reflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irreflexive,definition,
( irreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 @ X2 ) ) ) ) ).
thf(def_symmetric,definition,
( symmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_transitive,definition,
( transitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_equiv_rel,definition,
( equiv_rel
= ( ^ [X1: $i > $i > $o] :
( ( reflexive @ X1 )
& ( symmetric @ X1 )
& ( transitive @ X1 ) ) ) ) ).
thf(def_rel_codomain,definition,
( rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_rel_domain,definition,
( rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_rel_inverse,definition,
( rel_inverse
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_equiv_classes,definition,
( equiv_classes
= ( ^ [X1: $i > $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ! [X4: $i] :
( ( X2 @ X4 )
<=> ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(def_restrict_rel_codomain,definition,
( restrict_rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X2 @ X4 )
& ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_field,definition,
( rel_field
= ( ^ [X1: $i > $i > $o,X2: $i] :
( ( rel_domain @ X1 @ X2 )
| ( rel_codomain @ X1 @ X2 ) ) ) ) ).
thf(def_well_founded,definition,
( well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X5 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(def_upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X4 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(thm,conjecture,
sP1 = sP8 ).
thf(h0,negated_conjecture,
sP1 != sP8,
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP8,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h1,h2,h0])],[1,2,h1,h5]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,3,h5]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP7
| ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h6,h3,h4,h0])],[5,6,7,h8,h9,h4]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h3,h4,h0]),tab_negimp(discharge,[h8,h9])],[h7,8,h8,h9]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h3,h4,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,9,h7]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,10,h6]) ).
thf(12,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,4,11,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1 = sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.08/0.35 % Computer : n028.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 07:40:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: cade22grackle2xfee4
% 0.13/0.38 % Steps: 22
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------