%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU630^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 : Wed Feb 25 09:35:46 AM UTC 2026
% Result : Theorem 0.30s 1.35s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 90 ( 43 unt; 0 typ; 4 def)
% Number of atoms : 933 ( 152 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 1616 ( 36 ~; 57 |; 45 &;1338 @)
% ( 4 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 15 con; 0-2 aty)
% ( 47 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 225 ( 117 ^; 90 !; 18 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_29,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f76,f86,f92,f99,f109]) ).
thf(f109,plain,
( ~ spl4_1
| spl4_3
| spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl4_1
| spl4_3
| spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f107,f80]) ).
thf(f80,plain,
( ( $false
!= ( in @ sK3 @ sK2 ) )
| spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f79,definition,
( spl4_3
<=> ( $false
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f107,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_1
| spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f102,f84]) ).
thf(f84,plain,
( ( $false
!= ( in @ sK0 @ sK1 ) )
| spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl4_4
<=> ( $false
= ( in @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f102,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ( $false = $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f46,f72]) ).
thf(f72,plain,
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl4_1
<=> ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
@ X4 ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 )
@ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f24,f23]) ).
thf(f23,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',kpair) ).
thf(f24,plain,
ubforcartprodlem3 = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK0 @ sK3 ) @ ( cartprod @ sK1 @ sK2 ) ) )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X0 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ) ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ X3 ) @ ( cartprod @ sK1 @ sK2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ X3 ) @ ( cartprod @ sK1 @ sK2 ) ) ) )
=> ( ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK0 @ sK3 ) @ ( cartprod @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X0 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ) ) )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X0 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ) ) )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( dsetconstrI = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X0 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X0 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',cartprodpairin) ).
thf(f30,plain,
( ubforcartprodlem3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ubforcartprodlem3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) )
= ubforcartprodlem3 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X4: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X4 ) ) ) ) ) )
= ubforcartprodlem3 ),
file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',ubforcartprodlem3) ).
thf(f99,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $false = $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f28,f85]) ).
thf(f85,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f28,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f92,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f81,f27]) ).
thf(f27,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f81,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f86,plain,
( spl4_3
| spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f77,f74,f83,f79]) ).
thf(f74,definition,
( spl4_2
<=> ! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f77,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_2 ),
inference(equality_resolution,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ sK2 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f76,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f68,f74,f70]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ sK2 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ sK2 ) )
| ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ sK2 ) )
= $false )
| ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ sK2 ) )
@ X2 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ sK2 ) ) )
& ( in @ X1 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ sK2 ) ) )
& ( in @ Y0 @ sK1 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ sK2 ) ) )
& ( in @ Y0 @ sK1 ) ) ) )
| ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK2 ) ) )
& ( in @ Y1 @ sK1 ) ) )
@ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
| ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $false
= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) ) ) )
| ( $true != $true )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK2 ) ) )
& ( in @ Y1 @ sK1 ) ) )
@ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(superposition,[status(thm)],[f47,f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( X1 @ X2 )
= $false )
| ( $false
= ( in @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X2 @ X3 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f31,f25]) ).
thf(f25,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f31,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',dsetconstrI) ).
thf(f47,plain,
( $true
!= ( in @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK2 ) ) )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK2 ) ) )
& ( in @ Y1 @ sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
!= ( in
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK3 )
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f23,f32]) ).
thf(f32,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f29,f23]) ).
thf(f29,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ( in @ X3 @ X0 )
& ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( kpair @ X3 @ X4 )
= X2 ) ) ) ) )
= cartprod ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X4 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ( in @ X3 @ X0 )
& ? [X5: $i] :
( ( in @ X5 @ X4 )
& ( ( kpair @ X3 @ X5 )
= X2 ) ) ) ) )
= cartprod ),
file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',cartprod) ).
thf(f26,plain,
( $true
!= ( in @ ( kpair @ sK0 @ sK3 ) @ ( cartprod @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU630^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:29:00 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU630^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Ordered Pairs - Cartesian Products
% 0.28/0.46 % Version : Especial > Reduced > Especial.
% 0.28/0.46 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B -> in (kpair x y)
% 0.28/0.46 % (cartprod A B)))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC132l [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 15 ( 4 unt; 10 typ; 4 def)
% 0.28/0.46 % Number of atoms : 19 ( 5 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 5 ( 3 avg)
% 0.28/0.46 % Number of connectives : 62 ( 0 ~; 0 |; 2 &; 52 @)
% 0.28/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 13 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 11 ( 10 usr; 3 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 19 ( 6 ^; 11 !; 2 ?; 19 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=187
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binunion_type,type,
% 0.28/0.46 binunion: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(kpair_type,type,
% 0.28/0.46 kpair: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(kpair,definition,
% 0.28/0.46 ( kpair
% 0.28/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(cartprod_type,type,
% 0.28/0.46 cartprod: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(cartprod,definition,
% 0.28/0.46 ( cartprod
% 0.28/0.46 = ( ^ [A: $i,B: $i] :
% 0.28/0.46 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.28/0.46 @ ^ [Xx: $i] :
% 0.28/0.46 ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ? [Xz: $i] :
% 0.28/0.46 ( ( in @ Xz @ B )
% 0.28/0.46 & ( Xx
% 0.28/0.46 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ubforcartprodlem3_type,type,
% 0.28/0.46 ubforcartprodlem3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(ubforcartprodlem3,definition,
% 0.28/0.46 ( ubforcartprodlem3
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ B )
% 0.28/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(cartprodpairin,conjecture,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 => ( ubforcartprodlem3
% 0.28/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ B )
% 0.28/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 0.30/1.30 ---- Embedded in THF ---
% 0.30/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.30 %%% Generated on Tue Feb 24 12:29:01 EST 2026
% 0.30/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.30 %%% Logic specification used:
% 0.30/1.30 %%% thf(spec, logic, $$dhol).
% 0.30/1.30
% 0.30/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2DTF32199.p
% See solution above
% 0.30/1.30 ------------------------
% 0.30/1.31 ---- Cleaned THF ---
% 0.30/1.31 thf(in_type,type,
% 0.30/1.31 in: $i > $i > $o ).
% 0.30/1.31
% 0.30/1.31 thf(emptyset_type,type,
% 0.30/1.31 emptyset: $i ).
% 0.30/1.31
% 0.30/1.31 thf(setadjoin_type,type,
% 0.30/1.31 setadjoin: $i > $i > $i ).
% 0.30/1.31
% 0.30/1.31 thf(powerset_type,type,
% 0.30/1.31 powerset: $i > $i ).
% 0.30/1.31
% 0.30/1.31 thf(dsetconstr_type,type,
% 0.30/1.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/1.31
% 0.30/1.31 thf(dsetconstrI_type,type,
% 0.30/1.31 dsetconstrI: $o ).
% 0.30/1.31
% 0.30/1.31 thf(dsetconstrI,definition,
% 0.30/1.31 ( dsetconstrI
% 0.30/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.31 ( ( in @ Xx @ A )
% 0.30/1.31 => ( ( Xphi @ Xx )
% 0.30/1.31 => ( in @ Xx
% 0.30/1.31 @ ( dsetconstr @ A
% 0.30/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(binunion_type,type,
% 0.30/1.31 binunion: $i > $i > $i ).
% 0.30/1.31
% 0.30/1.31 thf(kpair_type,type,
% 0.30/1.31 kpair: $i > $i > $i ).
% 0.30/1.31
% 0.30/1.31 thf(kpair,definition,
% 0.30/1.31 ( kpair
% 0.30/1.31 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(cartprod_type,type,
% 0.30/1.31 cartprod: $i > $i > $i ).
% 0.30/1.31
% 0.30/1.31 thf(cartprod,definition,
% 0.30/1.31 ( cartprod
% 0.30/1.31 = ( ^ [A: $i,B: $i] :
% 0.30/1.31 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.30/1.31 @ ^ [Xx: $i] :
% 0.30/1.31 ? [Xy: $i] :
% 0.30/1.31 ( ( in @ Xy @ A )
% 0.30/1.31 & ? [Xz: $i] :
% 0.30/1.31 ( ( in @ Xz @ B )
% 0.30/1.31 & ( Xx
% 0.30/1.31 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(ubforcartprodlem3_type,type,
% 0.30/1.31 ubforcartprodlem3: $o ).
% 0.30/1.31
% 0.30/1.31 thf(ubforcartprodlem3,definition,
% 0.30/1.31 ( ubforcartprodlem3
% 0.30/1.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.31 ( ( in @ Xx @ A )
% 0.30/1.31 => ! [Xy: $i] :
% 0.30/1.31 ( ( in @ Xy @ B )
% 0.30/1.31 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(cartprodpairin,conjecture,
% 0.30/1.31 ( dsetconstrI
% 0.30/1.31 => ( ubforcartprodlem3
% 0.30/1.31 => ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.31 ( ( in @ Xx @ A )
% 0.30/1.31 => ! [Xy: $i] :
% 0.30/1.31 ( ( in @ Xy @ B )
% 0.30/1.31 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/1.31 ------------------------
% 0.30/1.33 % (32300)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/2Mi)
% 0.30/1.33 % (32300)Instruction limit reached!
% 0.30/1.33 % (32300)------------------------------
% 0.30/1.33 % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (32300)Termination reason: Unknown
% 0.30/1.33 % (32300)Termination phase: Property scanning
% 0.30/1.33
% 0.30/1.33 % (32300)Memory used [KB]: 1023
% 0.30/1.33 % (32300)Time elapsed: 0.002 s
% 0.30/1.33 % (32300)Instructions burned: 3 (million)
% 0.30/1.33 % (32300)------------------------------
% 0.30/1.33 % (32300)------------------------------
% 0.30/1.34 % (32296)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/183Mi)
% 0.30/1.34 % (32297)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/4Mi)
% 0.30/1.34 % (32298)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/27Mi)
% 0.30/1.34 % (32299)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/2Mi)
% 0.30/1.34 % (32301)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/275Mi)
% 0.30/1.34 % (32302)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/18Mi)
% 0.30/1.34 % (32299)Instruction limit reached!
% 0.30/1.34 % (32299)------------------------------
% 0.30/1.34 % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (32299)Termination reason: Unknown
% 0.30/1.34 % (32299)Termination phase: Property scanning
% 0.30/1.34
% 0.30/1.34 % (32299)Memory used [KB]: 1023
% 0.30/1.34 % (32299)Time elapsed: 0.003 s
% 0.30/1.34 % (32299)Instructions burned: 2 (million)
% 0.30/1.34 % (32299)------------------------------
% 0.30/1.34 % (32299)------------------------------
% 0.30/1.34 % (32297)Instruction limit reached!
% 0.30/1.34 % (32297)------------------------------
% 0.30/1.34 % (32297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (32297)Termination reason: Unknown
% 0.30/1.34 % (32297)Termination phase: Property scanning
% 0.30/1.34
% 0.30/1.34 % (32297)Memory used [KB]: 1023
% 0.30/1.34 % (32297)Time elapsed: 0.004 s
% 0.30/1.34 % (32297)Instructions burned: 4 (million)
% 0.30/1.34 % (32297)------------------------------
% 0.30/1.34 % (32297)------------------------------
% 0.30/1.34 % (32301)Refutation not found, incomplete strategy
% 0.30/1.34 % (32301)------------------------------
% 0.30/1.34 % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (32301)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.34
% 0.30/1.34
% 0.30/1.34 % (32301)Memory used [KB]: 5500
% 0.30/1.34 % (32301)Time elapsed: 0.005 s
% 0.30/1.34 % (32301)Instructions burned: 4 (million)
% 0.30/1.34 % (32301)------------------------------
% 0.30/1.34 % (32301)------------------------------
% 0.30/1.34 % (32303)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32199 for (2999ds/3Mi)
% 0.30/1.34 % (32303)Instruction limit reached!
% 0.30/1.34 % (32303)------------------------------
% 0.30/1.34 % (32303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (32303)Termination reason: Unknown
% 0.30/1.34 % (32303)Termination phase: Saturation
% 0.30/1.34
% 0.30/1.34 % (32303)Memory used [KB]: 5500
% 0.30/1.34 % (32303)Time elapsed: 0.003 s
% 0.30/1.34 % (32303)Instructions burned: 4 (million)
% 0.30/1.34 % (32303)------------------------------
% 0.30/1.34 % (32303)------------------------------
% 0.30/1.35 % (32296)First to succeed.
% 0.30/1.35 % (32302)Instruction limit reached!
% 0.30/1.35 % (32302)------------------------------
% 0.30/1.35 % (32302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.35 % (32302)Termination reason: Unknown
% 0.30/1.35 % (32302)Termination phase: Saturation
% 0.30/1.35
% 0.30/1.35 % (32302)Memory used [KB]: 5628
% 0.30/1.35 % (32302)Time elapsed: 0.014 s
% 0.30/1.35 % (32302)Instructions burned: 19 (million)
% 0.30/1.35 % (32302)------------------------------
% 0.30/1.35 % (32302)------------------------------
% 0.30/1.35 % (32298)Also succeeded, but the first one will report.
% 0.30/1.35 % (32296)Refutation found. Thanks to Tanya!
% 0.30/1.35 % SZS status Theorem for DTF2THF_32199
% 0.30/1.35 % SZS output start Proof for DTF2THF_32199
% 0.30/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.30/1.35 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.30/1.35 thf(func_def_3, type, powerset: $i > $i).
% 0.30/1.35 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.30/1.35 thf(func_def_7, type, binunion: $i > $i > $i).
% 0.30/1.35 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.30/1.35 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.30/1.35 thf(func_def_29, type, ph5: !>[X0: $tType]:(X0)).
% 0.30/1.35 thf(f110,plain,(
% 0.30/1.35 $false),
% 0.30/1.35 inference(avatar_sat_refutation,[status(thm)],[f76,f86,f92,f99,f109])).
% 0.30/1.35 thf(f109,plain,(
% 0.30/1.35 ~spl4_1 | spl4_3 | spl4_4),
% 0.30/1.35 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 0.30/1.35 thf(f108,plain,(
% 0.30/1.35 $false | (~spl4_1 | spl4_3 | spl4_4)),
% 0.30/1.35 inference(subsumption_resolution,[status(thm)],[f107,f80])).
% 0.30/1.35 thf(f80,plain,(
% 0.30/1.35 ($false != (in @ sK3 @ sK2)) | spl4_3),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f79])).
% 0.30/1.35 thf(f79,definition,(
% 0.30/1.35 spl4_3 <=> ($false = (in @ sK3 @ sK2))),
% 0.30/1.35 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 0.30/1.35 thf(f107,plain,(
% 0.30/1.35 ($false = (in @ sK3 @ sK2)) | (~spl4_1 | spl4_4)),
% 0.30/1.35 inference(subsumption_resolution,[status(thm)],[f102,f84])).
% 0.30/1.35 thf(f84,plain,(
% 0.30/1.35 ($false != (in @ sK0 @ sK1)) | spl4_4),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f83])).
% 0.30/1.35 thf(f83,definition,(
% 0.30/1.35 spl4_4 <=> ($false = (in @ sK0 @ sK1))),
% 0.30/1.35 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 0.30/1.35 thf(f102,plain,(
% 0.30/1.35 ($false = (in @ sK0 @ sK1)) | ($false = (in @ sK3 @ sK2)) | ~spl4_1),
% 0.30/1.35 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 0.30/1.35 thf(f101,plain,(
% 0.30/1.35 ($false = (in @ sK0 @ sK1)) | ($false = (in @ sK3 @ sK2)) | ($false = $true) | ~spl4_1),
% 0.30/1.35 inference(superposition,[status(thm)],[f46,f72])).
% 0.30/1.35 thf(f72,plain,(
% 0.30/1.35 ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ~spl4_1),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f70])).
% 0.30/1.35 thf(f70,definition,(
% 0.30/1.35 spl4_1 <=> ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2)))))),
% 0.30/1.35 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 0.30/1.35 thf(f46,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2))))) | ($false = (in @ X3 @ X1)) | ($false = (in @ X4 @ X2))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 0.30/1.35 thf(f45,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ X2) => (in @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))) | ($false = (in @ X3 @ X1))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f44])).
% 0.30/1.35 thf(f44,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))) @ X4)) | ($false = (in @ X3 @ X1))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f43])).
% 0.30/1.35 thf(f43,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))))) | ($false = (in @ X3 @ X1))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 0.30/1.35 thf(f42,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))))) = $true)) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f41])).
% 0.30/1.35 thf(f41,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2))))))))) @ X3))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f40])).
% 0.30/1.35 thf(f40,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))))))))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f39])).
% 0.30/1.35 thf(f39,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ Y0))))))))))) @ X2))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f38])).
% 0.30/1.35 thf(f38,plain,(
% 0.30/1.35 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ Y0)))))))))))))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f37])).
% 0.30/1.35 thf(f37,plain,(
% 0.30/1.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))))))))))))) @ X1))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f36])).
% 0.30/1.35 thf(f36,plain,(
% 0.30/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f34])).
% 0.30/1.35 thf(f34,plain,(
% 0.30/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 0.30/1.35 inference(definition_unfolding,[status(thm)],[f30,f24,f23])).
% 0.30/1.35 thf(f23,plain,(
% 0.30/1.35 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 0.30/1.35 thf(f15,plain,(
% 0.30/1.35 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.30/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 0.30/1.35 thf(f14,plain,(
% 0.30/1.35 ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)),
% 0.30/1.35 inference(rectify,[status(thm)],[f2])).
% 0.30/1.35 thf(f2,axiom,(
% 0.30/1.35 ((^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) = kpair)),
% 0.30/1.35 file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',kpair)).
% 0.30/1.35 thf(f24,plain,(
% 0.30/1.35 (ubforcartprodlem3 = $true)),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.30/1.35 thf(f22,plain,(
% 0.30/1.35 (($true = (in @ sK0 @ sK1)) & (($true = (in @ sK3 @ sK2)) & ($true != (in @ (kpair @ sK0 @ sK3) @ (cartprod @ sK1 @ sK2))))) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true)),
% 0.30/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
% 0.30/1.35 thf(f20,plain,(
% 0.30/1.35 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2))))) => (($true = (in @ sK0 @ sK1)) & ? [X3 : $i] : (((in @ X3 @ sK2) = $true) & ($true != (in @ (kpair @ sK0 @ X3) @ (cartprod @ sK1 @ sK2)))))),
% 0.30/1.35 introduced(definition,[],[choice_axiom])).
% 0.30/1.35 thf(f21,plain,(
% 0.30/1.35 ? [X3 : $i] : (((in @ X3 @ sK2) = $true) & ($true != (in @ (kpair @ sK0 @ X3) @ (cartprod @ sK1 @ sK2)))) => (($true = (in @ sK3 @ sK2)) & ($true != (in @ (kpair @ sK0 @ sK3) @ (cartprod @ sK1 @ sK2))))),
% 0.30/1.35 introduced(definition,[],[choice_axiom])).
% 0.30/1.35 thf(f19,plain,(
% 0.30/1.35 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2))))) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true)),
% 0.30/1.35 inference(flattening,[status(thm)],[f18])).
% 0.30/1.35 thf(f18,plain,(
% 0.30/1.35 (? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2))))) & (ubforcartprodlem3 = $true)) & (dsetconstrI = $true)),
% 0.30/1.35 inference(ennf_transformation,[status(thm)],[f13])).
% 0.30/1.35 thf(f13,plain,(
% 0.30/1.35 ~((dsetconstrI = $true) => ((ubforcartprodlem3 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ($true = (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2)))))))),
% 0.30/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 0.30/1.35 thf(f12,plain,(
% 0.30/1.35 ~(dsetconstrI => (ubforcartprodlem3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2))))))),
% 0.30/1.35 inference(rectify,[status(thm)],[f6])).
% 0.30/1.35 thf(f6,negated_conjecture,(
% 0.30/1.35 ~(dsetconstrI => (ubforcartprodlem3 => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4))))))),
% 0.30/1.35 inference(negated_conjecture,[status(cth)],[f5])).
% 0.30/1.35 thf(f5,conjecture,(
% 0.30/1.35 dsetconstrI => (ubforcartprodlem3 => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))))),
% 0.30/1.35 file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',cartprodpairin)).
% 0.30/1.35 thf(f30,plain,(
% 0.30/1.35 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 0.30/1.35 thf(f11,plain,(
% 0.30/1.35 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 0.30/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 0.30/1.35 thf(f10,plain,(
% 0.30/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X0 @ X3) @ (powerset @ (powerset @ (binunion @ X2 @ X1)))))) = ubforcartprodlem3)),
% 0.30/1.35 inference(rectify,[status(thm)],[f4])).
% 0.30/1.35 thf(f4,axiom,(
% 0.30/1.35 (! [X2 : $i,X4 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X4)))))) = ubforcartprodlem3)),
% 0.30/1.35 file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',ubforcartprodlem3)).
% 0.30/1.35 thf(f99,plain,(
% 0.30/1.35 ~spl4_4),
% 0.30/1.35 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 0.30/1.35 thf(f98,plain,(
% 0.30/1.35 $false | ~spl4_4),
% 0.30/1.35 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 0.30/1.35 thf(f95,plain,(
% 0.30/1.35 ($false = $true) | ~spl4_4),
% 0.30/1.35 inference(superposition,[status(thm)],[f28,f85])).
% 0.30/1.35 thf(f85,plain,(
% 0.30/1.35 ($false = (in @ sK0 @ sK1)) | ~spl4_4),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f83])).
% 0.30/1.35 thf(f28,plain,(
% 0.30/1.35 ($true = (in @ sK0 @ sK1))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.30/1.35 thf(f92,plain,(
% 0.30/1.35 ~spl4_3),
% 0.30/1.35 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 0.30/1.35 thf(f91,plain,(
% 0.30/1.35 $false | ~spl4_3),
% 0.30/1.35 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 0.30/1.35 thf(f87,plain,(
% 0.30/1.35 ($false = $true) | ~spl4_3),
% 0.30/1.35 inference(superposition,[status(thm)],[f81,f27])).
% 0.30/1.35 thf(f27,plain,(
% 0.30/1.35 ($true = (in @ sK3 @ sK2))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.30/1.35 thf(f81,plain,(
% 0.30/1.35 ($false = (in @ sK3 @ sK2)) | ~spl4_3),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f79])).
% 0.30/1.35 thf(f86,plain,(
% 0.30/1.35 spl4_3 | spl4_4 | ~spl4_2),
% 0.30/1.35 inference(avatar_split_clause,[status(thm)],[f77,f74,f83,f79])).
% 0.30/1.35 thf(f74,definition,(
% 0.30/1.35 spl4_2 <=> ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X2 @ sK2)))),
% 0.30/1.35 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 0.30/1.35 thf(f77,plain,(
% 0.30/1.35 ($false = (in @ sK0 @ sK1)) | ($false = (in @ sK3 @ sK2)) | ~spl4_2),
% 0.30/1.35 inference(equality_resolution,[status(thm)],[f75])).
% 0.30/1.35 thf(f75,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ sK2)) | ($false = (in @ X1 @ sK1))) ) | ~spl4_2),
% 0.30/1.35 inference(avatar_component_clause,[status(thm)],[f74])).
% 0.30/1.35 thf(f76,plain,(
% 0.30/1.35 spl4_1 | spl4_2),
% 0.30/1.35 inference(avatar_split_clause,[status(thm)],[f68,f74,f70])).
% 0.30/1.35 thf(f68,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ sK2)) | ($false = (in @ X1 @ sK1))) )),
% 0.30/1.35 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 0.30/1.35 thf(f67,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ sK2)) | ($false = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ($false = (in @ X1 @ sK1)) | ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2)))))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 0.30/1.35 thf(f66,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (((((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ X2 @ sK2)) = $false) | ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($false = (in @ X1 @ sK1))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f65])).
% 0.30/1.35 thf(f65,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($false = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK2))) @ X2)) | ($false = (in @ X1 @ sK1))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f64])).
% 0.30/1.35 thf(f64,plain,(
% 0.30/1.35 ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($false = (in @ X1 @ sK1)) | ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK2)))))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 0.30/1.35 thf(f63,plain,(
% 0.30/1.35 ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($false = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK2)))) & (in @ X1 @ sK1)))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f62])).
% 0.30/1.35 thf(f62,plain,(
% 0.30/1.35 ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK2)))) & (in @ Y0 @ sK1))) @ X1))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f61])).
% 0.30/1.35 thf(f61,plain,(
% 0.30/1.35 ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK2)))) & (in @ Y0 @ sK1))))) | ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2)))))),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f60])).
% 0.30/1.35 thf(f60,plain,(
% 0.30/1.35 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK2)))) & (in @ Y1 @ sK1))))) @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2)))))),
% 0.30/1.35 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.30/1.35 thf(f59,plain,(
% 0.30/1.35 ($false = (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))))) | ($true != $true) | ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK2)))) & (in @ Y1 @ sK1))))) @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))),
% 0.30/1.35 inference(superposition,[status(thm)],[f47,f56])).
% 0.30/1.35 thf(f56,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (in @ X2 @ (dsetconstr @ X3 @ X1))) | ((X1 @ X2) = $false) | ($false = (in @ X2 @ X3))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 0.30/1.35 thf(f55,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1)))) | ($false = (in @ X2 @ X3))) )),
% 0.30/1.35 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 0.30/1.35 thf(f54,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X2 @ X3) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1)))))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f53])).
% 0.30/1.35 thf(f53,plain,(
% 0.30/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1))))) @ X3) = $true)) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f52])).
% 0.30/1.35 thf(f52,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1)))))))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f51])).
% 0.30/1.35 thf(f51,plain,(
% 0.30/1.35 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1))))))) @ X2))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f50])).
% 0.30/1.35 thf(f50,plain,(
% 0.30/1.35 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1)))))))))) )),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f49])).
% 0.30/1.35 thf(f49,plain,(
% 0.30/1.35 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0))))))))) @ X1))) )),
% 0.30/1.35 inference(pi_clausification,[status(thm)],[f48])).
% 0.30/1.35 thf(f48,plain,(
% 0.30/1.35 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0)))))))))))),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f35])).
% 0.30/1.35 thf(f35,plain,(
% 0.30/1.35 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 0.30/1.35 inference(definition_unfolding,[status(thm)],[f31,f25])).
% 0.30/1.35 thf(f25,plain,(
% 0.30/1.35 (dsetconstrI = $true)),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.30/1.35 thf(f31,plain,(
% 0.30/1.35 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f9])).
% 0.30/1.35 thf(f9,plain,(
% 0.30/1.35 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 0.30/1.35 inference(fool_elimination,[status(thm)],[f8])).
% 0.30/1.35 thf(f8,plain,(
% 0.30/1.35 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 0.30/1.35 inference(rectify,[status(thm)],[f1])).
% 0.30/1.35 thf(f1,axiom,(
% 0.30/1.35 (! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 0.30/1.35 file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',dsetconstrI)).
% 0.30/1.35 thf(f47,plain,(
% 0.30/1.35 ($true != (in @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK1 @ sK2))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK2)))) & (in @ Y1 @ sK1))))))))),
% 0.30/1.35 inference(beta_eta_normalization,[status(thm)],[f33])).
% 0.30/1.35 thf(f33,plain,(
% 0.30/1.35 ($true != (in @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK0 @ sK3) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))) @ sK1 @ sK2)))),
% 0.30/1.35 inference(definition_unfolding,[status(thm)],[f26,f23,f32])).
% 0.30/1.35 thf(f32,plain,(
% 0.30/1.35 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.30/1.35 inference(definition_unfolding,[status(thm)],[f29,f23])).
% 0.30/1.35 thf(f29,plain,(
% 0.30/1.35 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f17])).
% 0.30/1.35 thf(f17,plain,(
% 0.30/1.35 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.30/1.35 inference(fool_elimination,[status(thm)],[f16])).
% 0.30/1.35 thf(f16,plain,(
% 0.30/1.35 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2))))))) = cartprod)),
% 0.30/1.35 inference(rectify,[status(thm)],[f3])).
% 0.30/1.35 thf(f3,axiom,(
% 0.30/1.35 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X4))) @ (^[X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ? [X5 : $i] : ((in @ X5 @ X4) & ((kpair @ X3 @ X5) = X2))))))) = cartprod)),
% 0.30/1.35 file('/export/starexec/sandbox2/tmp/tmp.dIXC5wQ0ce/DTF2THF_32199.p',cartprod)).
% 0.30/1.35 thf(f26,plain,(
% 0.30/1.35 ($true != (in @ (kpair @ sK0 @ sK3) @ (cartprod @ sK1 @ sK2)))),
% 0.30/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.30/1.35 % SZS output end Proof for DTF2THF_32199
% 0.30/1.35 % (32296)------------------------------
% 0.30/1.35 % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.35 % (32296)Termination reason: Refutation
% 0.30/1.35
% 0.30/1.35 % (32296)Memory used [KB]: 5628
% 0.30/1.35 % (32296)Time elapsed: 0.014 s
% 0.30/1.35 % (32296)Instructions burned: 13 (million)
% 0.30/1.35 % (32296)------------------------------
% 0.30/1.35 % (32296)------------------------------
% 0.30/1.35 % (32295)Success in time 0.022 s
%------------------------------------------------------------------------------