%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET096^1 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 02:23:42 PM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__2 )
=> ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( eigen__3 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__3 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : sP5 ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 = X1 )
| ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
( (~)
@ ? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X3 = X2 ) )
=> ( ( X1
!= ( ^ [X3: $i] : sP5 ) )
=> ( X1
= ( ^ [X3: $i] : ( X3 = X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X3 = X2 ) )
=> ( ( X1
!= ( ^ [X3: $i] : sP5 ) )
=> ( X1
= ( ^ [X3: $i] : ( X3 = X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X2 = X1 ) )
=> ( ( eigen__0
!= ( ^ [X2: $i] : sP5 ) )
=> ( eigen__0
= ( ^ [X2: $i] : ( X2 = X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ( ( eigen__0
!= ( ^ [X1: $i] : sP5 ) )
=> ( eigen__0
= ( ^ [X1: $i] : ( X1 = eigen__1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( eigen__0
!= ( ^ [X1: $i] : sP5 ) )
=> ( eigen__0
= ( ^ [X1: $i] : ( X1 = eigen__1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( eigen__0
!= ( ^ [X1: $i] : sP5 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( eigen__0
!= ( ^ [X1: $i] : ( X1 = eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
= sP5 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( X1 = eigen__1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1 != sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,h3,h11,h12]) ).
thf(4,plain,
( ~ sP9
| sP3
| ~ sP9
| sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
~ sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP6
| ~ sP3
| sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP7
| sP1
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| ~ sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h10,h9,h8,h7,h5,h6,h3,h4,h2,h1,h0])],[4,5,6,7,8,9,h3,h8,h13,h14]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h10,h9,h8,h7,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h11,h12]),tab_be(discharge,[h13,h14])],[h10,3,10,h11,h12,h13,h14]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,11,h10]) ).
thf(13,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h2,h1,h0]),tab_fe(discharge,[h9])],[h6,12,h9]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,13,h8]) ).
thf(15,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_fe(discharge,[h7])],[h5,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,17,h2]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,18,h1]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X3 = X2 ) )
=> ( ( X1
!= ( ^ [X3: $i] : sP5 ) )
=> ( X1
= ( ^ [X3: $i] : ( X3 = X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET096^1 : TPTP v9.2.0. Released v3.6.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 14:39:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % Mode: cade22grackle2xfee4
% 0.20/0.43 % Steps: 34
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------