TSTP Solution File: SET576^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 Aug 31 15:17:33 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_member,type,
member: mu > mu > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: mu ).
thf(ty_eigen__1,type,
eigen__1: mu ).
thf(ty_intersect,type,
intersect: mu > mu > $i > $o ).
thf(ty_disjoint,type,
disjoint: mu > mu > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( ( intersect @ eigen__1 @ eigen__2 @ eigen__0 )
=> ~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X1 @ eigen__2 @ eigen__0 ) ) ) )
=> ~ ( ~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X1 @ eigen__2 @ eigen__0 ) ) )
=> ( intersect @ eigen__1 @ eigen__2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( exists_in_world @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( exists_in_world @ eigen__1 @ eigen__0 )
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( disjoint @ eigen__1 @ X1 @ eigen__0 )
=> ~ ( intersect @ eigen__1 @ X1 @ eigen__0 ) )
=> ~ ( ~ ( intersect @ eigen__1 @ X1 @ eigen__0 )
=> ( disjoint @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ~ ( ( ( intersect @ X2 @ X3 @ X1 )
=> ~ ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ~ ( member @ X4 @ X3 @ X1 ) ) ) )
=> ~ ( ~ ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ~ ( member @ X4 @ X3 @ X1 ) ) )
=> ( intersect @ X2 @ X3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( disjoint @ eigen__1 @ X1 @ eigen__0 )
=> ~ ( intersect @ eigen__1 @ X1 @ eigen__0 ) )
=> ~ ( ~ ( intersect @ eigen__1 @ X1 @ eigen__0 )
=> ( disjoint @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ~ ( ( ( intersect @ X1 @ X2 @ eigen__0 )
=> ~ ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ( member @ X3 @ X1 @ eigen__0 )
=> ~ ( member @ X3 @ X2 @ eigen__0 ) ) ) )
=> ~ ( ~ ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ( member @ X3 @ X1 @ eigen__0 )
=> ~ ( member @ X3 @ X2 @ eigen__0 ) ) )
=> ( intersect @ X1 @ X2 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( intersect @ eigen__1 @ eigen__2 @ eigen__0 )
=> ( disjoint @ eigen__1 @ eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( intersect @ eigen__1 @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ~ ( ( ( disjoint @ X1 @ X2 @ eigen__0 )
=> ~ ( intersect @ X1 @ X2 @ eigen__0 ) )
=> ~ ( ~ ( intersect @ X1 @ X2 @ eigen__0 )
=> ( disjoint @ X1 @ X2 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ~ ( ( ( disjoint @ X2 @ X3 @ X1 )
=> ~ ( intersect @ X2 @ X3 @ X1 ) )
=> ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
=> ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X1 @ eigen__2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( exists_in_world @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ( disjoint @ eigen__1 @ eigen__2 @ eigen__0 )
=> ~ sP8 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( intersect @ eigen__1 @ X1 @ eigen__0 )
=> ~ ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( intersect @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( disjoint @ eigen__1 @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( intersect @ eigen__1 @ X1 @ eigen__0 )
=> ~ ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( intersect @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP2
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP8
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [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_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X3 )
@ ? [X5: $i] :
( ( X1 @ X2 @ X5 )
& ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( ( X1 @ X3 @ X4 )
| ( X3 = X4 )
| ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
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_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
| ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s4,definition,
( mdia_s4
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).
thf(prove_th17,conjecture,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ~ ( member @ X4 @ X3 @ X1 ) ) )
=> ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ~ ( member @ X4 @ X3 @ X1 ) ) )
=> ( disjoint @ X2 @ X3 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[prove_th17]) ).
thf(h1,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ( member @ X3 @ X1 @ eigen__0 )
=> ~ ( member @ X3 @ X2 @ eigen__0 ) ) )
=> ( disjoint @ X1 @ X2 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP12
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( disjoint @ eigen__1 @ X1 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP12,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ~ ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( disjoint @ eigen__1 @ X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP2
=> ( sP11
=> sP15 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP11
=> sP15 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP18
| ~ sP8
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP1
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP17
| ~ sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP16
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| ~ sP12
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP8
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP19
| ~ sP2
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(disjoint_defn,axiom,
sP10 ).
thf(intersect_defn,axiom,
sP4 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h6,h8,h9,disjoint_defn,intersect_defn]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,15,h8,h9]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,17,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,20,h1]) ).
thf(0,theorem,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ~ ( member @ X4 @ X3 @ X1 ) ) )
=> ( disjoint @ X2 @ X3 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 12:47:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % Mode: cade22grackle2xfee4
% 0.19/0.42 % Steps: 135
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------