%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU672^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 02:33:32 PM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_ex1,definition,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_func,definition,
( func
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( breln @ X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ex1 @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ).
thf(funcImageSingleton,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcImageSingleton]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ~ ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ sP3 )
=> sP3 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h7,h9,h10]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,3,h9,h10]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,4,h8]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,5,h6,h7]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,6,h4,h5]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,7,h3]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU672^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.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 22:00:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % Mode: cade22grackle2xfee4
% 0.19/0.42 % Steps: 21
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------