%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU665^2 : 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 : n031.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 09:36:03 AM UTC 2026
% Result : Theorem 1.67s 1.33s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 39 unt; 0 typ; 5 def)
% Number of atoms : 833 ( 169 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 1204 ( 41 ~; 68 |; 69 &; 885 @)
% ( 5 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 16 con; 0-3 aty)
% ( 43 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 240 ( 123 ^; 96 !; 21 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_22,type,
sK0: $i > $i > $o ).
thf(func_def_28,type,
sK6: $i > $i > $i ).
thf(func_def_29,type,
sK7: $i > $i > $i ).
thf(func_def_31,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f158,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f112,f126,f132,f139,f146,f157]) ).
thf(f157,plain,
( ~ spl5_1
| spl5_3
| spl5_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f156]) ).
thf(f156,plain,
( $false
| ~ spl5_1
| spl5_3
| spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f155,f116]) ).
thf(f116,plain,
( ( $false
!= ( in @ sK4 @ sK1 ) )
| spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f115,definition,
( spl5_3
<=> ( $false
= ( in @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f155,plain,
( ( $false
= ( in @ sK4 @ sK1 ) )
| ~ spl5_1
| spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f150,f124]) ).
thf(f124,plain,
( ( $false
!= ( in @ sK2 @ sK3 ) )
| spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl5_5
<=> ( $false
= ( in @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f150,plain,
( ( $false
= ( in @ sK2 @ sK3 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $false
= ( in @ sK2 @ sK3 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false = $true )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f75,f108]) ).
thf(f108,plain,
( ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f106]) ).
thf(f106,definition,
( spl5_1
<=> ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X4 ) @ ( cartprod @ X1 @ X3 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( in @ X4 @ X3 )
=> ( in @ ( kpair @ X2 @ X4 ) @ ( cartprod @ X1 @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( cartprod @ X1 @ X3 ) ) )
@ X4 )
= $true )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( cartprod @ X1 @ X3 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( cartprod @ X1 @ X3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( kpair @ X2 @ Y1 ) @ ( cartprod @ X1 @ Y0 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( kpair @ X2 @ Y1 ) @ ( cartprod @ X1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y2 ) @ ( cartprod @ X1 @ Y1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y2 ) @ ( cartprod @ X1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( cartprod @ Y0 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( cartprod @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f24]) ).
thf(f24,plain,
( cartprodpairin
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( cartprod @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cartprodpairin
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( cartprod @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X2 @ X0 ) ) ) )
= cartprodpairin ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X4 ) ) ) )
= cartprodpairin ),
file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',cartprodpairin) ).
thf(f33,plain,
cartprodpairin = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( cartprodpairin = $true )
& ( setext = $true )
& ( $true
= ( in @ sK2 @ sK3 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK2 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) ) )
& ( ( sK0 @ sK2 @ sK4 )
= $true )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( $true
!= ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( X0 @ X2 @ X4 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ sK3 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( ( in @ ( kpair @ sK2 @ X4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
!= $true )
& ( $true
= ( sK0 @ sK2 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( ( in @ ( kpair @ sK2 @ X4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
!= $true )
& ( $true
= ( sK0 @ sK2 @ X4 ) ) )
=> ( ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK2 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) ) )
& ( ( sK0 @ sK2 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( cartprodpairin = $true )
& ( setext = $true )
& ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( $true
!= ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( X0 @ X2 @ X4 ) ) ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( X0 @ X2 @ X4 ) )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X2 @ X3 )
= $true ) )
& ( cartprodpairin = $true )
& ( setext = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( dsetconstrI = $true )
=> ( ( setext = $true )
=> ( ( cartprodpairin = $true )
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( X0 @ X2 @ X4 ) )
=> ( $true
= ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X0 @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X1: $i > $i > $o,X4: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X0 @ X4
@ ^ [X6: $i,X5: $i] : ( X1 @ X6 @ X5 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X1: $i > $i > $o,X4: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X0 @ X4
@ ^ [X6: $i,X5: $i] : ( X1 @ X6 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dpsetconstrI) ).
thf(f146,plain,
~ spl5_5,
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $false = $true )
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f31,f125]) ).
thf(f125,plain,
( ( $false
= ( in @ sK2 @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f31,plain,
( $true
= ( in @ sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f139,plain,
~ spl5_4,
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f28,f121]) ).
thf(f121,plain,
( ( ( sK0 @ sK2 @ sK4 )
= $false )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl5_4
<=> ( ( sK0 @ sK2 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f28,plain,
( ( sK0 @ sK2 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f132,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f131]) ).
thf(f131,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $false = $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f117,f30]) ).
thf(f30,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f117,plain,
( ( $false
= ( in @ sK4 @ sK1 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f126,plain,
( spl5_3
| spl5_4
| spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f113,f110,f123,f119,f115]) ).
thf(f110,definition,
( spl5_2
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK3 ) )
| ( ( kpair @ X1 @ X2 )
!= ( kpair @ sK2 @ sK4 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( in @ X2 @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f113,plain,
( ( ( sK0 @ sK2 @ sK4 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 ) )
| ~ spl5_2 ),
inference(equality_resolution,[status(thm)],[f111]) ).
thf(f111,plain,
( ! [X2: $i,X1: $i] :
( ( ( kpair @ X1 @ X2 )
!= ( kpair @ sK2 @ sK4 ) )
| ( $false
= ( in @ X1 @ sK3 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f112,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f104,f110,f106]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK3 ) )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( kpair @ X1 @ X2 )
!= ( kpair @ sK2 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK3 ) )
| ( ( kpair @ X1 @ X2 )
!= ( kpair @ sK2 @ sK4 ) )
| ( $false
= ( ( in @ X2 @ sK1 )
& ( sK0 @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK3 ) )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( ( ( kpair @ X1 @ X2 )
= ( kpair @ sK2 @ sK4 ) )
= $false )
| ( $false
= ( ( in @ X2 @ sK1 )
& ( sK0 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ sK1 )
& ( sK0 @ X1 @ X2 )
& ( ( kpair @ X1 @ X2 )
= ( kpair @ sK2 @ sK4 ) ) )
= $false )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK3 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK0 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK2 @ sK4 ) ) )
@ X2 )
= $false )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK0 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK2 @ sK4 ) ) ) )
= $false )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: $i] :
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK0 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK2 @ sK4 ) ) ) )
& ( in @ X1 @ sK3 ) )
= $false )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
& ( sK0 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK2 @ sK4 ) ) ) )
& ( in @ Y0 @ sK3 ) )
@ X1 ) )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
& ( sK0 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK2 @ sK4 ) ) ) )
& ( in @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) )
@ ( kpair @ sK2 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true != $true )
| ( $false
= ( in @ ( kpair @ sK2 @ sK4 ) @ ( cartprod @ sK3 @ sK1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) )
@ ( kpair @ sK2 @ sK4 ) ) ) ),
inference(superposition,[status(thm)],[f65,f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f27,f26]) ).
thf(f26,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dsetconstrI) ).
thf(f27,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f65,plain,
( ( in @ ( kpair @ sK2 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK3 @ sK1 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( ( in @ ( kpair @ sK2 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK3
@ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f29,f25]) ).
thf(f25,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( ( kpair @ X4 @ X5 )
= X3 )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) ) ) ) )
= dpsetconstr ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X4: $i,X1: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X4 )
@ ^ [X5: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ? [X3: $i] :
( ( ( kpair @ X2 @ X3 )
= X5 )
& ( X1 @ X2 @ X3 )
& ( in @ X3 @ X4 ) ) ) ) )
= dpsetconstr ),
file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dpsetconstr) ).
thf(f29,plain,
( $true
!= ( in @ ( kpair @ sK2 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU665^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU665^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Sets of Pairs
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.in x A -> (! y:i.in y B ->
% 0.30/0.46 % phi x y -> in (kpair x y) (dpsetconstr A B (^ z,u:i.phi z u))))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC167l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.46 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
% 0.30/0.46 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.30/0.46 % Number of atoms : 26 ( 6 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 6 ( 5 avg)
% 0.30/0.46 % Number of connectives : 70 ( 0 ~; 0 |; 3 &; 53 @)
% 0.30/0.46 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 18 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 25 ( 7 ^; 16 !; 2 ?; 25 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=229
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpair_type,type,
% 0.30/0.46 kpair: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(cartprod_type,type,
% 0.30/0.46 cartprod: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin_type,type,
% 0.30/0.46 cartprodpairin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin,definition,
% 0.30/0.46 ( cartprodpairin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstr_type,type,
% 0.30/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstr,definition,
% 0.30/0.46 ( dpsetconstr
% 0.30/0.46 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( dsetconstr @ ( cartprod @ A @ B )
% 0.30/0.46 @ ^ [Xu: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 & ( Xphi @ Xx @ Xy )
% 0.30/0.46 & ( Xu
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrI,conjecture,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 => ( setext
% 0.30/0.46 => ( cartprodpairin
% 0.30/0.46 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 12:31:19 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2DTF20496.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(in_type,type,
% 1.50/1.29 in: $i > $i > $o ).
% 1.50/1.29
% 1.50/1.29 thf(dsetconstr_type,type,
% 1.50/1.29 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.50/1.29
% 1.50/1.29 thf(dsetconstrI_type,type,
% 1.50/1.29 dsetconstrI: $o ).
% 1.50/1.29
% 1.50/1.29 thf(dsetconstrI,definition,
% 1.50/1.29 ( dsetconstrI
% 1.50/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ A )
% 1.50/1.29 => ( ( Xphi @ Xx )
% 1.50/1.29 => ( in @ Xx
% 1.50/1.29 @ ( dsetconstr @ A
% 1.50/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(setext_type,type,
% 1.50/1.29 setext: $o ).
% 1.50/1.29
% 1.50/1.29 thf(setext,definition,
% 1.50/1.29 ( setext
% 1.50/1.29 = ( ! [A: $i,B: $i] :
% 1.50/1.29 ( ! [Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ A )
% 1.50/1.29 => ( in @ Xx @ B ) )
% 1.50/1.29 => ( ! [Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ B )
% 1.50/1.29 => ( in @ Xx @ A ) )
% 1.50/1.29 => ( A = B ) ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(kpair_type,type,
% 1.50/1.29 kpair: $i > $i > $i ).
% 1.50/1.29
% 1.50/1.29 thf(cartprod_type,type,
% 1.50/1.29 cartprod: $i > $i > $i ).
% 1.50/1.29
% 1.50/1.29 thf(cartprodpairin_type,type,
% 1.50/1.29 cartprodpairin: $o ).
% 1.50/1.29
% 1.50/1.29 thf(cartprodpairin,definition,
% 1.50/1.29 ( cartprodpairin
% 1.50/1.29 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ A )
% 1.50/1.29 => ! [Xy: $i] :
% 1.50/1.29 ( ( in @ Xy @ B )
% 1.50/1.29 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(dpsetconstr_type,type,
% 1.50/1.29 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.50/1.29
% 1.50/1.29 thf(dpsetconstr,definition,
% 1.50/1.29 ( dpsetconstr
% 1.50/1.29 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.50/1.29 ( dsetconstr @ ( cartprod @ A @ B )
% 1.50/1.29 @ ^ [Xu: $i] :
% 1.50/1.29 ? [Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ A )
% 1.50/1.29 & ? [Xy: $i] :
% 1.50/1.29 ( ( in @ Xy @ B )
% 1.50/1.29 & ( Xphi @ Xx @ Xy )
% 1.50/1.29 & ( Xu
% 1.50/1.29 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(dpsetconstrI,conjecture,
% 1.50/1.29 ( dsetconstrI
% 1.50/1.29 => ( setext
% 1.50/1.29 => ( cartprodpairin
% 1.50/1.29 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.50/1.29 ( ( in @ Xx @ A )
% 1.50/1.29 => ! [Xy: $i] :
% 1.50/1.29 ( ( in @ Xy @ B )
% 1.50/1.29 => ( ( Xphi @ Xx @ Xy )
% 1.50/1.29 => ( in @ ( kpair @ Xx @ Xy )
% 1.50/1.29 @ ( dpsetconstr @ A @ B
% 1.50/1.29 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ) ).
% 1.50/1.29 ------------------------
% 1.67/1.30 % (20762)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_20496 for (3000ds/4Mi)
% 1.67/1.31 % (20762)Instruction limit reached!
% 1.67/1.31 % (20762)------------------------------
% 1.67/1.31 % (20762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (20762)Termination reason: Unknown
% 1.67/1.31 % (20762)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (20762)Memory used [KB]: 5500
% 1.67/1.31 % (20762)Time elapsed: 0.003 s
% 1.67/1.31 % (20762)Instructions burned: 5 (million)
% 1.67/1.31 % (20762)------------------------------
% 1.67/1.31 % (20762)------------------------------
% 1.67/1.31 % (20761)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20496 for (3000ds/183Mi)
% 1.67/1.31 % (20764)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20496 for (3000ds/2Mi)
% 1.67/1.31 % (20763)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_20496 for (3000ds/27Mi)
% 1.67/1.31 % (20765)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_20496 for (3000ds/2Mi)
% 1.67/1.31 % (20767)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20496 for (3000ds/18Mi)
% 1.67/1.31 % (20766)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_20496 for (3000ds/275Mi)
% 1.67/1.31 % (20764)Instruction limit reached!
% 1.67/1.31 % (20764)------------------------------
% 1.67/1.31 % (20764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (20764)Termination reason: Unknown
% 1.67/1.31 % (20764)Termination phase: shuffling
% 1.67/1.31
% 1.67/1.31 % (20764)Memory used [KB]: 1023
% 1.67/1.31 % (20764)Time elapsed: 0.003 s
% 1.67/1.31 % (20764)Instructions burned: 2 (million)
% 1.67/1.31 % (20764)------------------------------
% 1.67/1.31 % (20764)------------------------------
% 1.67/1.31 % (20765)Instruction limit reached!
% 1.67/1.31 % (20765)------------------------------
% 1.67/1.31 % (20765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (20765)Termination reason: Unknown
% 1.67/1.31 % (20765)Termination phase: shuffling
% 1.67/1.31
% 1.67/1.31 % (20765)Memory used [KB]: 1023
% 1.67/1.31 % (20765)Time elapsed: 0.003 s
% 1.67/1.31 % (20765)Instructions burned: 2 (million)
% 1.67/1.31 % (20765)------------------------------
% 1.67/1.31 % (20765)------------------------------
% 1.67/1.32 % (20768)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20496 for (2999ds/3Mi)
% 1.67/1.32 % (20768)Instruction limit reached!
% 1.67/1.32 % (20768)------------------------------
% 1.67/1.32 % (20768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (20768)Termination reason: Unknown
% 1.67/1.32 % (20768)Termination phase: Property scanning
% 1.67/1.32
% 1.67/1.32 % (20768)Memory used [KB]: 1023
% 1.67/1.32 % (20768)Time elapsed: 0.002 s
% 1.67/1.32 % (20768)Instructions burned: 4 (million)
% 1.67/1.32 % (20768)------------------------------
% 1.67/1.32 % (20768)------------------------------
% 1.67/1.32 % (20767)Instruction limit reached!
% 1.67/1.32 % (20767)------------------------------
% 1.67/1.32 % (20767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (20767)Termination reason: Unknown
% 1.67/1.32 % (20767)Termination phase: Saturation
% 1.67/1.32
% 1.67/1.32 % (20767)Memory used [KB]: 5628
% 1.67/1.32 % (20767)Time elapsed: 0.013 s
% 1.67/1.32 % (20767)Instructions burned: 18 (million)
% 1.67/1.32 % (20767)------------------------------
% 1.67/1.32 % (20767)------------------------------
% 1.67/1.32 % (20761)First to succeed.
% 1.67/1.33 % (20771)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20496 for (2999ds/3Mi)
% 1.67/1.33 % (20771)Instruction limit reached!
% 1.67/1.33 % (20771)------------------------------
% 1.67/1.33 % (20771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20771)Termination reason: Unknown
% 1.67/1.33 % (20771)Termination phase: Function definition elimination
% 1.67/1.33
% 1.67/1.33 % (20771)Memory used [KB]: 1023
% 1.67/1.33 % (20771)Time elapsed: 0.002 s
% 1.67/1.33 % (20771)Instructions burned: 4 (million)
% 1.67/1.33 % (20771)------------------------------
% 1.67/1.33 % (20771)------------------------------
% 1.67/1.33 % (20763)Also succeeded, but the first one will report.
% 1.67/1.33 % (20761)Refutation found. Thanks to Tanya!
% 1.67/1.33 % SZS status Theorem for DTF2THF_20496
% 1.67/1.33 % SZS output start Proof for DTF2THF_20496
% 1.67/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.33 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.67/1.33 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.67/1.33 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.67/1.33 thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.67/1.33 thf(func_def_22, type, sK0: $i > $i > $o).
% 1.67/1.33 thf(func_def_28, type, sK6: $i > $i > $i).
% 1.67/1.33 thf(func_def_29, type, sK7: $i > $i > $i).
% 1.67/1.33 thf(func_def_31, type, ph8: !>[X0: $tType]:(X0)).
% 1.67/1.33 thf(f158,plain,(
% 1.67/1.33 $false),
% 1.67/1.33 inference(avatar_sat_refutation,[status(thm)],[f112,f126,f132,f139,f146,f157])).
% 1.67/1.33 thf(f157,plain,(
% 1.67/1.33 ~spl5_1 | spl5_3 | spl5_5),
% 1.67/1.33 inference(avatar_contradiction_clause,[status(thm)],[f156])).
% 1.67/1.33 thf(f156,plain,(
% 1.67/1.33 $false | (~spl5_1 | spl5_3 | spl5_5)),
% 1.67/1.33 inference(subsumption_resolution,[status(thm)],[f155,f116])).
% 1.67/1.33 thf(f116,plain,(
% 1.67/1.33 ($false != (in @ sK4 @ sK1)) | spl5_3),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.67/1.33 thf(f115,definition,(
% 1.67/1.33 spl5_3 <=> ($false = (in @ sK4 @ sK1))),
% 1.67/1.33 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.67/1.33 thf(f155,plain,(
% 1.67/1.33 ($false = (in @ sK4 @ sK1)) | (~spl5_1 | spl5_5)),
% 1.67/1.33 inference(subsumption_resolution,[status(thm)],[f150,f124])).
% 1.67/1.33 thf(f124,plain,(
% 1.67/1.33 ($false != (in @ sK2 @ sK3)) | spl5_5),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.67/1.33 thf(f123,definition,(
% 1.67/1.33 spl5_5 <=> ($false = (in @ sK2 @ sK3))),
% 1.67/1.33 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.67/1.33 thf(f150,plain,(
% 1.67/1.33 ($false = (in @ sK2 @ sK3)) | ($false = (in @ sK4 @ sK1)) | ~spl5_1),
% 1.67/1.33 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.67/1.33 thf(f149,plain,(
% 1.67/1.33 ($false = (in @ sK2 @ sK3)) | ($false = (in @ sK4 @ sK1)) | ($false = $true) | ~spl5_1),
% 1.67/1.33 inference(superposition,[status(thm)],[f75,f108])).
% 1.67/1.33 thf(f108,plain,(
% 1.67/1.33 ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ~spl5_1),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f106])).
% 1.67/1.33 thf(f106,definition,(
% 1.67/1.33 spl5_1 <=> ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1)))),
% 1.67/1.33 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.67/1.33 thf(f75,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (kpair @ X2 @ X4) @ (cartprod @ X1 @ X3))) | ((in @ X2 @ X1) = $false) | ($false = (in @ X4 @ X3))) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.67/1.33 thf(f74,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X2 @ X1) = $false) | (((in @ X4 @ X3) => (in @ (kpair @ X2 @ X4) @ (cartprod @ X1 @ X3))) = $true)) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.67/1.33 thf(f73,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ X2 @ Y0) @ (cartprod @ X1 @ X3)))) @ X4) = $true) | ((in @ X2 @ X1) = $false)) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f72])).
% 1.67/1.33 thf(f72,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ X2 @ Y0) @ (cartprod @ X1 @ X3))))) = $true)) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.67/1.33 thf(f71,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ X2 @ Y0) @ (cartprod @ X1 @ X3)))))))) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.67/1.33 thf(f70,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (kpair @ X2 @ Y1) @ (cartprod @ X1 @ Y0))))))) @ X3))) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f69])).
% 1.67/1.33 thf(f69,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (kpair @ X2 @ Y1) @ (cartprod @ X1 @ Y0)))))))) = $true)) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.67/1.33 thf(f68,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (kpair @ Y0 @ Y2) @ (cartprod @ X1 @ Y1))))))))) @ X2) = $true)) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f67])).
% 1.67/1.33 thf(f67,plain,(
% 1.67/1.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (kpair @ Y0 @ Y2) @ (cartprod @ X1 @ Y1)))))))))))) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.67/1.33 thf(f66,plain,(
% 1.67/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2))))))))))) @ X1) = $true)) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f34])).
% 1.67/1.33 thf(f34,plain,(
% 1.67/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)))))))))))))),
% 1.67/1.33 inference(definition_unfolding,[status(thm)],[f33,f24])).
% 1.67/1.33 thf(f24,plain,(
% 1.67/1.33 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)))))))))))))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.67/1.33 thf(f9,plain,(
% 1.67/1.33 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)))))))))))))),
% 1.67/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.33 thf(f8,plain,(
% 1.67/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)))) = cartprodpairin)),
% 1.67/1.33 inference(rectify,[status(thm)],[f3])).
% 1.67/1.33 thf(f3,axiom,(
% 1.67/1.33 (! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))) = cartprodpairin)),
% 1.67/1.33 file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',cartprodpairin)).
% 1.67/1.33 thf(f33,plain,(
% 1.67/1.33 (cartprodpairin = $true)),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 thf(f22,plain,(
% 1.67/1.33 (cartprodpairin = $true) & (setext = $true) & (($true = (in @ sK2 @ sK3)) & (($true = (in @ sK4 @ sK1)) & ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1))))))) & ((sK0 @ sK2 @ sK4) = $true))) & (dsetconstrI = $true)),
% 1.67/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f21,f20])).
% 1.67/1.33 thf(f20,plain,(
% 1.67/1.33 ? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : (((in @ X2 @ X3) = $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) & ($true = (X0 @ X2 @ X4)))) => (($true = (in @ sK2 @ sK3)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ((in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) != $true) & ($true = (sK0 @ sK2 @ X4))))),
% 1.67/1.33 introduced(definition,[],[choice_axiom])).
% 1.67/1.33 thf(f21,plain,(
% 1.67/1.33 ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ((in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) != $true) & ($true = (sK0 @ sK2 @ X4))) => (($true = (in @ sK4 @ sK1)) & ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1))))))) & ((sK0 @ sK2 @ sK4) = $true))),
% 1.67/1.33 introduced(definition,[],[choice_axiom])).
% 1.67/1.33 thf(f19,plain,(
% 1.67/1.33 (cartprodpairin = $true) & (setext = $true) & ? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : (((in @ X2 @ X3) = $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) & ($true = (X0 @ X2 @ X4)))) & (dsetconstrI = $true)),
% 1.67/1.33 inference(flattening,[status(thm)],[f18])).
% 1.67/1.33 thf(f18,plain,(
% 1.67/1.33 ((? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : (? [X4 : $i] : ((($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) & ($true = (X0 @ X2 @ X4))) & ((in @ X4 @ X1) = $true)) & ((in @ X2 @ X3) = $true)) & (cartprodpairin = $true)) & (setext = $true)) & (dsetconstrI = $true)),
% 1.67/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.33 thf(f11,plain,(
% 1.67/1.33 ~((dsetconstrI = $true) => ((setext = $true) => ((cartprodpairin = $true) => ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : (((in @ X2 @ X3) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (($true = (X0 @ X2 @ X4)) => ($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))))))))),
% 1.67/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.33 thf(f10,plain,(
% 1.67/1.33 ~(dsetconstrI => (setext => (cartprodpairin => ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : ((in @ X2 @ X3) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X0 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6))))))))))),
% 1.67/1.33 inference(rectify,[status(thm)],[f6])).
% 1.67/1.33 thf(f6,negated_conjecture,(
% 1.67/1.33 ~(dsetconstrI => (setext => (cartprodpairin => ! [X1 : $i > $i > $o,X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((X1 @ X2 @ X3) => (in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5))))))))))),
% 1.67/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 1.67/1.33 thf(f5,conjecture,(
% 1.67/1.33 dsetconstrI => (setext => (cartprodpairin => ! [X1 : $i > $i > $o,X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((X1 @ X2 @ X3) => (in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5)))))))))),
% 1.67/1.33 file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dpsetconstrI)).
% 1.67/1.33 thf(f146,plain,(
% 1.67/1.33 ~spl5_5),
% 1.67/1.33 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.67/1.33 thf(f145,plain,(
% 1.67/1.33 $false | ~spl5_5),
% 1.67/1.33 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.67/1.33 thf(f142,plain,(
% 1.67/1.33 ($false = $true) | ~spl5_5),
% 1.67/1.33 inference(superposition,[status(thm)],[f31,f125])).
% 1.67/1.33 thf(f125,plain,(
% 1.67/1.33 ($false = (in @ sK2 @ sK3)) | ~spl5_5),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.67/1.33 thf(f31,plain,(
% 1.67/1.33 ($true = (in @ sK2 @ sK3))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 thf(f139,plain,(
% 1.67/1.33 ~spl5_4),
% 1.67/1.33 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.67/1.33 thf(f138,plain,(
% 1.67/1.33 $false | ~spl5_4),
% 1.67/1.33 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.67/1.33 thf(f135,plain,(
% 1.67/1.33 ($false = $true) | ~spl5_4),
% 1.67/1.33 inference(superposition,[status(thm)],[f28,f121])).
% 1.67/1.33 thf(f121,plain,(
% 1.67/1.33 ((sK0 @ sK2 @ sK4) = $false) | ~spl5_4),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f119])).
% 1.67/1.33 thf(f119,definition,(
% 1.67/1.33 spl5_4 <=> ((sK0 @ sK2 @ sK4) = $false)),
% 1.67/1.33 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.67/1.33 thf(f28,plain,(
% 1.67/1.33 ((sK0 @ sK2 @ sK4) = $true)),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 thf(f132,plain,(
% 1.67/1.33 ~spl5_3),
% 1.67/1.33 inference(avatar_contradiction_clause,[status(thm)],[f131])).
% 1.67/1.33 thf(f131,plain,(
% 1.67/1.33 $false | ~spl5_3),
% 1.67/1.33 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.67/1.33 thf(f127,plain,(
% 1.67/1.33 ($false = $true) | ~spl5_3),
% 1.67/1.33 inference(superposition,[status(thm)],[f117,f30])).
% 1.67/1.33 thf(f30,plain,(
% 1.67/1.33 ($true = (in @ sK4 @ sK1))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 thf(f117,plain,(
% 1.67/1.33 ($false = (in @ sK4 @ sK1)) | ~spl5_3),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.67/1.33 thf(f126,plain,(
% 1.67/1.33 spl5_3 | spl5_4 | spl5_5 | ~spl5_2),
% 1.67/1.33 inference(avatar_split_clause,[status(thm)],[f113,f110,f123,f119,f115])).
% 1.67/1.33 thf(f110,definition,(
% 1.67/1.33 spl5_2 <=> ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ sK3)) | ((kpair @ X1 @ X2) != (kpair @ sK2 @ sK4)) | ($false = (sK0 @ X1 @ X2)) | ((in @ X2 @ sK1) = $false))),
% 1.67/1.33 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.67/1.33 thf(f113,plain,(
% 1.67/1.33 ((sK0 @ sK2 @ sK4) = $false) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ sK2 @ sK3)) | ~spl5_2),
% 1.67/1.33 inference(equality_resolution,[status(thm)],[f111])).
% 1.67/1.33 thf(f111,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (((kpair @ X1 @ X2) != (kpair @ sK2 @ sK4)) | ($false = (in @ X1 @ sK3)) | ((in @ X2 @ sK1) = $false) | ($false = (sK0 @ X1 @ X2))) ) | ~spl5_2),
% 1.67/1.33 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.67/1.33 thf(f112,plain,(
% 1.67/1.33 spl5_1 | spl5_2),
% 1.67/1.33 inference(avatar_split_clause,[status(thm)],[f104,f110,f106])).
% 1.67/1.33 thf(f104,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ sK3)) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ((in @ X2 @ sK1) = $false) | ($false = (sK0 @ X1 @ X2)) | ((kpair @ X1 @ X2) != (kpair @ sK2 @ sK4))) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.67/1.33 thf(f103,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ($false = (in @ X1 @ sK3)) | ((kpair @ X1 @ X2) != (kpair @ sK2 @ sK4)) | ($false = ((in @ X2 @ sK1) & (sK0 @ X1 @ X2)))) )),
% 1.67/1.33 inference(equality_proxy_clausification,[status(thm)],[f102])).
% 1.67/1.33 thf(f102,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ sK3)) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | (((kpair @ X1 @ X2) = (kpair @ sK2 @ sK4)) = $false) | ($false = ((in @ X2 @ sK1) & (sK0 @ X1 @ X2)))) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.67/1.33 thf(f101,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (((((in @ X2 @ sK1) & (sK0 @ X1 @ X2)) & ((kpair @ X1 @ X2) = (kpair @ sK2 @ sK4))) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ($false = (in @ X1 @ sK3))) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.67/1.33 thf(f100,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ sK3)) | (((^[Y0 : $i]: (((in @ Y0 @ sK1) & (sK0 @ X1 @ Y0)) & ((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4)))) @ X2) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1)))) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f99])).
% 1.67/1.33 thf(f99,plain,(
% 1.67/1.33 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK1) & (sK0 @ X1 @ Y0)) & ((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4))))) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ($false = (in @ X1 @ sK3))) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.67/1.33 thf(f98,plain,(
% 1.67/1.33 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK1) & (sK0 @ X1 @ Y0)) & ((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4))))) & (in @ X1 @ sK3)) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1)))) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.67/1.33 thf(f97,plain,(
% 1.67/1.33 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK1) & (sK0 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4))))) & (in @ Y0 @ sK3))) @ X1)) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1)))) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f96])).
% 1.67/1.33 thf(f96,plain,(
% 1.67/1.33 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK1) & (sK0 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4))))) & (in @ Y0 @ sK3)))) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1)))),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.67/1.33 thf(f95,plain,(
% 1.67/1.33 ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))) @ (kpair @ sK2 @ sK4)))),
% 1.67/1.33 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.67/1.33 thf(f94,plain,(
% 1.67/1.33 ($true != $true) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK3 @ sK1))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))) @ (kpair @ sK2 @ sK4)))),
% 1.67/1.33 inference(superposition,[status(thm)],[f65,f46])).
% 1.67/1.33 thf(f46,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ X3))) | ($false = (X3 @ X2)) | ((in @ X2 @ X1) = $false)) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.67/1.33 thf(f45,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ X1) = $false) | (((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3))) = $true)) )),
% 1.67/1.33 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.67/1.33 thf(f44,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))))) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.67/1.33 thf(f43,plain,(
% 1.67/1.33 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f42])).
% 1.67/1.33 thf(f42,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))) = $true)) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.67/1.33 thf(f41,plain,(
% 1.67/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f40])).
% 1.67/1.33 thf(f40,plain,(
% 1.67/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))) = $true)) )),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.67/1.33 thf(f39,plain,(
% 1.67/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1))) )),
% 1.67/1.33 inference(pi_clausification,[status(thm)],[f38])).
% 1.67/1.33 thf(f38,plain,(
% 1.67/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))))),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.67/1.33 thf(f37,plain,(
% 1.67/1.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 1.67/1.33 inference(definition_unfolding,[status(thm)],[f27,f26])).
% 1.67/1.33 thf(f26,plain,(
% 1.67/1.33 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.33 thf(f17,plain,(
% 1.67/1.33 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.67/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.33 thf(f16,plain,(
% 1.67/1.33 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 1.67/1.33 inference(rectify,[status(thm)],[f1])).
% 1.67/1.33 thf(f1,axiom,(
% 1.67/1.33 (dsetconstrI = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.67/1.33 file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dsetconstrI)).
% 1.67/1.33 thf(f27,plain,(
% 1.67/1.33 (dsetconstrI = $true)),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 thf(f65,plain,(
% 1.67/1.33 ((in @ (kpair @ sK2 @ sK4) @ (dsetconstr @ (cartprod @ sK3 @ sK1) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))))) != $true)),
% 1.67/1.33 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.67/1.33 thf(f36,plain,(
% 1.67/1.33 ((in @ (kpair @ sK2 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))) @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) != $true)),
% 1.67/1.33 inference(definition_unfolding,[status(thm)],[f29,f25])).
% 1.67/1.33 thf(f25,plain,(
% 1.67/1.33 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.33 thf(f15,plain,(
% 1.67/1.33 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.67/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.67/1.33 thf(f14,plain,(
% 1.67/1.33 ((^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X0) & ? [X5 : $i] : (((kpair @ X4 @ X5) = X3) & (X2 @ X4 @ X5) & (in @ X5 @ X1))))))) = dpsetconstr)),
% 1.67/1.33 inference(rectify,[status(thm)],[f4])).
% 1.67/1.33 thf(f4,axiom,(
% 1.67/1.33 ((^[X0 : $i, X4 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X4) @ (^[X5 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ? [X3 : $i] : (((kpair @ X2 @ X3) = X5) & (X1 @ X2 @ X3) & (in @ X3 @ X4))))))) = dpsetconstr)),
% 1.67/1.33 file('/export/starexec/sandbox2/tmp/tmp.1bAVzfu2yk/DTF2THF_20496.p',dpsetconstr)).
% 1.67/1.33 thf(f29,plain,(
% 1.67/1.33 ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))))),
% 1.67/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.33 % SZS output end Proof for DTF2THF_20496
% 1.67/1.33 % (20761)------------------------------
% 1.67/1.33 % (20761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20761)Termination reason: Refutation
% 1.67/1.33
% 1.67/1.33 % (20761)Memory used [KB]: 5628
% 1.67/1.33 % (20761)Time elapsed: 0.017 s
% 1.67/1.33 % (20761)Instructions burned: 17 (million)
% 1.67/1.33 % (20761)------------------------------
% 1.67/1.33 % (20761)------------------------------
% 1.67/1.33 % (20760)Success in time 0.03 s
%------------------------------------------------------------------------------