%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET924^1 : TPTP v9.2.0. Released v8.1.0.
% 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 Oct 9 02:24:54 PM UTC 2025
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_singleton,type,
singleton: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_empty,type,
empty: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_in,type,
in: $i > $i > mworld > $o ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_set_difference,type,
set_difference: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ ( singleton @ eigen__0 ) @ mactual )
= ( ~ ( in @ eigen__0 @ X1 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__0 @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ eigen__1 ) @ ( singleton @ eigen__0 ) @ mactual )
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ eigen__1 ) @ ( singleton @ eigen__0 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
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(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(t67_zfmisc_1,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[t67_zfmisc_1]) ).
thf(h1,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( empty @ eigen__2 @ mactual ),
introduced(assumption,[]) ).
thf(h8,assumption,
empty @ eigen__3 @ mactual,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(l34_zfmisc_1,axiom,
sP4 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0])],[1,2,3,l34_zfmisc_1,h3,h4]) ).
thf(rc1_xboole_0,axiom,
~ ! [X1: $i] :
~ ( empty @ X1 @ mactual ) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[rc1_xboole_0,4,h8]) ).
thf(rc2_xboole_0,axiom,
~ ! [X1: $i] : ( empty @ X1 @ mactual ) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[rc2_xboole_0,5,h7]) ).
thf(h9,assumption,
~ ( empty @ eigen__4 @ mactual ),
introduced(assumption,[]) ).
thf(h10,assumption,
empty @ eigen__5 @ mactual,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP3
| sP5
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,h5,h6,h2,h1,h0])],[7,8,9,l34_zfmisc_1,h5,h6]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h5,h6,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[rc1_xboole_0,10,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[rc2_xboole_0,11,h9]) ).
thf(13,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,6,12,h3,h4,h5,h6]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET924^1 : TPTP v9.2.0. Released v8.1.0.
% 0.07/0.13 % 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 : Wed Oct 8 14:38:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % Mode: cade22grackle2xfee4
% 0.20/0.49 % Steps: 1414
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------