%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU768^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 09:37:02 AM UTC 2026
% Result : Theorem 1.58s 1.33s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 9
% Syntax : Number of formulae : 82 ( 29 unt; 0 typ; 2 def)
% Number of atoms : 1117 ( 268 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 1836 ( 64 ~; 169 |; 28 &;1345 @)
% ( 2 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 9 con; 0-4 aty)
% ( 79 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 339 ( 116 ^; 201 !; 22 ?; 339 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_7,type,
breln1: $i > $i > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK2: $i > $o ).
thf(func_def_24,type,
sK5: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_25,type,
sK6: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f126,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f100,f122,f125]) ).
thf(f125,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f124]) ).
thf(f124,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(backward_demodulation,[status(thm)],[f57,f85]) ).
thf(f85,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl4_1
<=> ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f57,plain,
( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f29]) ).
thf(f29,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f21]) ).
thf(f21,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln) ).
thf(f28,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( breln1
= ( ^ [X0: $i,X3: $i] : ( breln @ X0 @ X0 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln1) ).
thf(f23,plain,
( $true
= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK0 ) )
| ( ( sK2 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK1 )
!= $true ) ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( brelnall2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f19,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK0 ) )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK1 )
!= $true ) ) ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK0 ) )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK1 )
!= $true ) ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
!= ( sK2 @ X3 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK0 ) )
| ( ( sK2 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK1 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
!= ( sK2 @ X3 ) ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
!= ( sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( brelnall2 = $true ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( brelnall2 = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( brelnall2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( brelnall2 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( X2 @ X5 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( brelnall2
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X2 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( brelnall2
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( brelnall2
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln1all2) ).
thf(f122,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f121]) ).
thf(f121,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true != $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f25,f112]) ).
thf(f112,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $false = $true )
| ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f88,f26]) ).
thf(f26,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f88,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl4_2
<=> ! [X0: $i] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f25,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f100,plain,
( spl4_1
| spl4_2
| spl4_2
| spl4_2
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f78,f87,f87,f87,f87,f83]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( sK2 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( sK2 @ X0 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false = $true )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $true
= ( sK2 @ X1 ) )
| ( ( sK2 @ X2 )
= $true )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f71,f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) ) ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( ( in @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) )
| ( ( X4 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) )
@ ( sK6 @ X1 @ X2 @ X3 @ X4 ) )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) )
@ X5 ) ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) ) )
| ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) ) )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) )
@ X4 ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 @ ( kpair @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 @ ( kpair @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( Y2 @ ( kpair @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( Y2 @ Y3 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( Y2 @ ( kpair @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f22,f21]) ).
thf(f22,plain,
brelnall2 = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f27,plain,
( brelnall2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( brelnall2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( brelnall2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X1 @ X0 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( X3 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( brelnall2
= ( ! [X3: $i,X1: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',brelnall2) ).
thf(f71,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ sK0 @ X0 @ sK0 ) @ ( sK6 @ sK0 @ sK0 @ sK1 @ X0 ) ) ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( ( X0 @ X1 )
= $true )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( X0 @ X2 ) )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ sK1 )
= $false )
| ( ( X0 @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ sK0 @ X0 @ sK0 ) @ ( sK6 @ sK0 @ sK0 @ sK1 @ X0 ) ) ) )
| ( $true
= ( X0 @ X2 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f69,f57]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ sK0 @ X0 @ sK0 ) @ ( sK6 @ sK0 @ sK0 @ sK1 @ X0 ) ) ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $true
= ( X0 @ X3 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ sK1 )
= $false )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( X0 @ X1 )
= $true )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ sK0 @ X0 @ sK0 ) @ ( sK6 @ sK0 @ sK0 @ sK1 @ X0 ) ) ) )
| ( $true != $true )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $true
= ( X0 @ X2 ) )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( in @ X3 @ sK1 ) )
| ( ( X0 @ X1 )
= $true )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $true
= ( X0 @ X2 ) )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ sK0 @ X0 @ sK0 ) @ ( sK6 @ sK0 @ sK0 @ sK1 @ X0 ) ) ) )
| ( $true != $true )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $true
= ( X0 @ X3 ) ) ),
inference(superposition,[status(thm)],[f66,f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) )
| ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ ( sK6 @ X0 @ sK0 @ sK1 @ X1 ) ) ) )
| ( $true
= ( X1 @ X3 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $true
= ( X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ ( sK6 @ X0 @ sK0 @ sK1 @ X1 ) ) ) )
| ( $true
= ( X1 @ X3 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
!= ( in @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true != $true )
| ( ( in @ X2 @ sK1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ X0 @ X1 @ sK0 ) @ ( sK6 @ X0 @ sK0 @ sK1 @ X1 ) ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( ( in @ X2 @ sK1 )
= $false )
| ( $true
= ( X1 @ X3 ) ) ),
inference(superposition,[status(thm)],[f63,f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( in @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
= $true )
| ( ( X4 @ X5 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ ( sK6 @ X0 @ X2 @ sK1 @ X1 ) @ sK0 ) )
| ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ X0 @ X1 @ X2 ) @ ( sK6 @ X0 @ X2 @ sK1 @ X1 ) ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( ( in @ ( sK5 @ sK1 @ X0 @ X1 @ X2 ) @ sK0 )
!= $true )
| ( $true
= ( X1 @ X3 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( sK2 @ ( kpair @ ( sK5 @ sK1 @ X0 @ X1 @ X2 ) @ ( sK6 @ X0 @ X2 @ sK1 @ X1 ) ) ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X2 @ sK1 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ X2 ) ) )
| ( ( in @ ( sK5 @ sK1 @ X0 @ X1 @ X2 ) @ sK0 )
!= $true )
| ( $true != $true )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( X1 @ X3 ) ) ),
inference(superposition,[status(thm)],[f24,f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ X5 @ X3 )
= $false )
| ( ( X4 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f24,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK1 )
!= $true )
| ( $true
!= ( in @ X4 @ sK0 ) )
| ( ( sK2 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU768^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n022.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:33:21 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU768^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Binary Relations on a Set
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! R:i.breln1 A R -> (! phi:i>o.(! x:i.in x A ->
% 0.18/0.38 % (! y:i.in y A -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.18/0.38 % (! x:i.in x R -> phi x)))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC270l [Bro08]
% 0.18/0.38 % : ZFC274l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.38 % Number of atoms : 19 ( 3 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 6 ( 4 avg)
% 0.18/0.38 % Number of connectives : 53 ( 0 ~; 0 |; 0 &; 40 @)
% 0.18/0.38 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 16 ( 5 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.18/0.38 % Number of variables : 18 ( 5 ^; 13 !; 0 ?; 18 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=378
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subset_type,type,
% 0.18/0.38 subset: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(kpair_type,type,
% 0.18/0.38 kpair: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(cartprod_type,type,
% 0.18/0.38 cartprod: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(breln_type,type,
% 0.18/0.38 breln: $i > $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln,definition,
% 0.18/0.38 ( breln
% 0.18/0.38 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(brelnall2_type,type,
% 0.18/0.38 brelnall2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(brelnall2,definition,
% 0.18/0.38 ( brelnall2
% 0.18/0.38 = ( ! [A: $i,B: $i,R: $i] :
% 0.18/0.38 ( ( breln @ A @ B @ R )
% 0.18/0.38 => ! [Xphi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ B )
% 0.18/0.38 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.38 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ R )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(breln1_type,type,
% 0.18/0.38 breln1: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln1,definition,
% 0.18/0.38 ( breln1
% 0.18/0.38 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(breln1all2,conjecture,
% 0.18/0.38 ( brelnall2
% 0.18/0.38 => ! [A: $i,R: $i] :
% 0.18/0.38 ( ( breln1 @ A @ R )
% 0.18/0.38 => ! [Xphi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.38 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ R )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.39/1.28 ---- Embedded in THF ---
% 1.39/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.28 %%% Generated on Tue Feb 24 12:33:22 EST 2026
% 1.39/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.28 %%% Logic specification used:
% 1.39/1.28 %%% thf(spec, logic, $$dhol).
% 1.39/1.28
% 1.39/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2DTF27684.p
% See solution above
% 1.39/1.28 ------------------------
% 1.39/1.29 ---- Cleaned THF ---
% 1.39/1.29 thf(in_type,type,
% 1.39/1.29 in: $i > $i > $o ).
% 1.39/1.29
% 1.39/1.29 thf(subset_type,type,
% 1.39/1.29 subset: $i > $i > $o ).
% 1.39/1.29
% 1.39/1.29 thf(kpair_type,type,
% 1.39/1.29 kpair: $i > $i > $i ).
% 1.39/1.29
% 1.39/1.29 thf(cartprod_type,type,
% 1.39/1.29 cartprod: $i > $i > $i ).
% 1.39/1.29
% 1.39/1.29 thf(breln_type,type,
% 1.39/1.29 breln: $i > $i > $i > $o ).
% 1.39/1.29
% 1.39/1.29 thf(breln,definition,
% 1.39/1.29 ( breln
% 1.39/1.29 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(brelnall2_type,type,
% 1.39/1.29 brelnall2: $o ).
% 1.39/1.29
% 1.39/1.29 thf(brelnall2,definition,
% 1.39/1.29 ( brelnall2
% 1.39/1.29 = ( ! [A: $i,B: $i,R: $i] :
% 1.39/1.29 ( ( breln @ A @ B @ R )
% 1.39/1.29 => ! [Xphi: $i > $o] :
% 1.39/1.29 ( ! [Xx: $i] :
% 1.39/1.29 ( ( in @ Xx @ A )
% 1.39/1.29 => ! [Xy: $i] :
% 1.39/1.29 ( ( in @ Xy @ B )
% 1.39/1.29 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.39/1.29 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 1.39/1.29 => ! [Xx: $i] :
% 1.39/1.29 ( ( in @ Xx @ R )
% 1.39/1.29 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(breln1_type,type,
% 1.39/1.29 breln1: $i > $i > $o ).
% 1.39/1.29
% 1.39/1.29 thf(breln1,definition,
% 1.39/1.29 ( breln1
% 1.39/1.29 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(breln1all2,conjecture,
% 1.39/1.29 ( brelnall2
% 1.39/1.29 => ! [A: $i,R: $i] :
% 1.39/1.29 ( ( breln1 @ A @ R )
% 1.39/1.29 => ! [Xphi: $i > $o] :
% 1.39/1.29 ( ! [Xx: $i] :
% 1.39/1.29 ( ( in @ Xx @ A )
% 1.39/1.29 => ! [Xy: $i] :
% 1.39/1.29 ( ( in @ Xy @ A )
% 1.39/1.29 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.39/1.29 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 1.39/1.29 => ! [Xx: $i] :
% 1.39/1.29 ( ( in @ Xx @ R )
% 1.39/1.29 => ( Xphi @ Xx ) ) ) ) ) ).
% 1.39/1.29 ------------------------
% 1.58/1.31 % (27784)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_27684 for (2999ds/27Mi)
% 1.58/1.31 % (27782)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/183Mi)
% 1.58/1.31 % (27785)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/2Mi)
% 1.58/1.31 % (27786)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_27684 for (2999ds/2Mi)
% 1.58/1.31 % (27787)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_27684 for (2999ds/275Mi)
% 1.58/1.31 % (27783)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_27684 for (2999ds/4Mi)
% 1.58/1.31 % (27788)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/18Mi)
% 1.58/1.31 % (27785)Instruction limit reached!
% 1.58/1.31 % (27785)------------------------------
% 1.58/1.31 % (27785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (27785)Termination reason: Unknown
% 1.58/1.31 % (27785)Termination phase: Preprocessing 3
% 1.58/1.31
% 1.58/1.31 % (27785)Memory used [KB]: 1023
% 1.58/1.31 % (27785)Time elapsed: 0.003 s
% 1.58/1.31 % (27785)Instructions burned: 2 (million)
% 1.58/1.31 % (27785)------------------------------
% 1.58/1.31 % (27785)------------------------------
% 1.58/1.31 % (27786)Instruction limit reached!
% 1.58/1.31 % (27786)------------------------------
% 1.58/1.31 % (27786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (27786)Termination reason: Unknown
% 1.58/1.31 % (27786)Termination phase: Property scanning
% 1.58/1.31
% 1.58/1.31 % (27786)Memory used [KB]: 1023
% 1.58/1.31 % (27786)Time elapsed: 0.003 s
% 1.58/1.31 % (27786)Instructions burned: 3 (million)
% 1.58/1.31 % (27786)------------------------------
% 1.58/1.31 % (27786)------------------------------
% 1.58/1.31 % (27783)Instruction limit reached!
% 1.58/1.31 % (27783)------------------------------
% 1.58/1.31 % (27783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (27783)Termination reason: Unknown
% 1.58/1.31 % (27783)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (27783)Memory used [KB]: 5500
% 1.58/1.31 % (27783)Time elapsed: 0.004 s
% 1.58/1.31 % (27783)Instructions burned: 4 (million)
% 1.58/1.31 % (27783)------------------------------
% 1.58/1.31 % (27783)------------------------------
% 1.58/1.32 % (27788)Instruction limit reached!
% 1.58/1.32 % (27788)------------------------------
% 1.58/1.32 % (27788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27788)Termination reason: Unknown
% 1.58/1.32 % (27788)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27788)Memory used [KB]: 5628
% 1.58/1.32 % (27788)Time elapsed: 0.011 s
% 1.58/1.32 % (27788)Instructions burned: 18 (million)
% 1.58/1.32 % (27788)------------------------------
% 1.58/1.32 % (27788)------------------------------
% 1.58/1.32 % (27784)First to succeed.
% 1.58/1.33 % (27789)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/3Mi)
% 1.58/1.33 % (27790)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/37Mi)
% 1.58/1.33 % (27787)Also succeeded, but the first one will report.
% 1.58/1.33 % (27791)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_27684 for (2999ds/15Mi)
% 1.58/1.33 % (27784)Refutation found. Thanks to Tanya!
% 1.58/1.33 % SZS status Theorem for DTF2THF_27684
% 1.58/1.33 % SZS output start Proof for DTF2THF_27684
% 1.58/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.58/1.33 thf(func_def_1, type, subset: $i > $i > $o).
% 1.58/1.33 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.58/1.33 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.58/1.33 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.58/1.33 thf(func_def_7, type, breln1: $i > $i > $o).
% 1.58/1.33 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.58/1.33 thf(func_def_21, type, sK2: $i > $o).
% 1.58/1.33 thf(func_def_24, type, sK5: $i > $i > ($i > $o) > $i > $i).
% 1.58/1.33 thf(func_def_25, type, sK6: $i > $i > $i > ($i > $o) > $i).
% 1.58/1.33 thf(func_def_26, type, ph7: !>[X0: $tType]:(X0)).
% 1.58/1.33 thf(f126,plain,(
% 1.58/1.33 $false),
% 1.58/1.33 inference(avatar_sat_refutation,[status(thm)],[f100,f122,f125])).
% 1.58/1.33 thf(f125,plain,(
% 1.58/1.33 ~spl4_1),
% 1.58/1.33 inference(avatar_contradiction_clause,[status(thm)],[f124])).
% 1.58/1.33 thf(f124,plain,(
% 1.58/1.33 $false | ~spl4_1),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.58/1.33 thf(f123,plain,(
% 1.58/1.33 ($false = $true) | ~spl4_1),
% 1.58/1.33 inference(backward_demodulation,[status(thm)],[f57,f85])).
% 1.58/1.33 thf(f85,plain,(
% 1.58/1.33 ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ~spl4_1),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.58/1.33 thf(f83,definition,(
% 1.58/1.33 spl4_1 <=> ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false)),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.58/1.33 thf(f57,plain,(
% 1.58/1.33 ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $true)),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.58/1.33 thf(f30,plain,(
% 1.58/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK1) = $true)),
% 1.58/1.33 inference(definition_unfolding,[status(thm)],[f23,f29])).
% 1.58/1.33 thf(f29,plain,(
% 1.58/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.58/1.33 inference(definition_unfolding,[status(thm)],[f28,f21])).
% 1.58/1.33 thf(f21,plain,(
% 1.58/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.33 thf(f13,plain,(
% 1.58/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f1])).
% 1.58/1.33 thf(f1,axiom,(
% 1.58/1.33 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln)).
% 1.58/1.33 thf(f28,plain,(
% 1.58/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 1.58/1.33 thf(f10,plain,(
% 1.58/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f9])).
% 1.58/1.33 thf(f9,plain,(
% 1.58/1.33 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 1.58/1.33 inference(rectify,[status(thm)],[f3])).
% 1.58/1.33 thf(f3,axiom,(
% 1.58/1.33 (breln1 = (^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln1)).
% 1.58/1.33 thf(f23,plain,(
% 1.58/1.33 ($true = (breln1 @ sK0 @ sK1))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.58/1.33 thf(f20,plain,(
% 1.58/1.33 (((($true = (in @ sK3 @ sK1)) & ($true != (sK2 @ sK3))) & ! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true != (in @ X5 @ sK0)) | ((sK2 @ (kpair @ X4 @ X5)) = $true) | ((in @ (kpair @ X4 @ X5) @ sK1) != $true)))) & ($true = (breln1 @ sK0 @ sK1))) & (brelnall2 = $true)),
% 1.58/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f19,f18,f17])).
% 1.58/1.33 thf(f17,plain,(
% 1.58/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((X2 @ X3) != $true)) & ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (((in @ X5 @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i > $o] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ((X2 @ X3) != $true)) & ! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true != (in @ X5 @ sK0)) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ sK1) != $true)))) & ($true = (breln1 @ sK0 @ sK1)))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f18,plain,(
% 1.58/1.33 ? [X2 : $i > $o] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ((X2 @ X3) != $true)) & ! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true != (in @ X5 @ sK0)) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ sK1) != $true)))) => (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true != (sK2 @ X3))) & ! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true != (in @ X5 @ sK0)) | ((sK2 @ (kpair @ X4 @ X5)) = $true) | ((in @ (kpair @ X4 @ X5) @ sK1) != $true))))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f19,plain,(
% 1.58/1.33 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true != (sK2 @ X3))) => (($true = (in @ sK3 @ sK1)) & ($true != (sK2 @ sK3)))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f16,plain,(
% 1.58/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((X2 @ X3) != $true)) & ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (((in @ X5 @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)))) & ($true = (breln1 @ X0 @ X1))) & (brelnall2 = $true)),
% 1.58/1.33 inference(rectify,[status(thm)],[f15])).
% 1.58/1.33 thf(f15,plain,(
% 1.58/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((X2 @ X5) != $true)) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ($true = (X2 @ (kpair @ X3 @ X4))) | ($true != (in @ (kpair @ X3 @ X4) @ X1))))) & ($true = (breln1 @ X0 @ X1))) & (brelnall2 = $true)),
% 1.58/1.33 inference(flattening,[status(thm)],[f14])).
% 1.58/1.33 thf(f14,plain,(
% 1.58/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((X2 @ X5) != $true)) & ! [X3 : $i] : (! [X4 : $i] : ((($true = (X2 @ (kpair @ X3 @ X4))) | ($true != (in @ (kpair @ X3 @ X4) @ X1))) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X0)))) & ($true = (breln1 @ X0 @ X1))) & (brelnall2 = $true)),
% 1.58/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.58/1.33 thf(f8,plain,(
% 1.58/1.33 ~((brelnall2 = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i > $o] : (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (($true = (in @ (kpair @ X3 @ X4) @ X1)) => ($true = (X2 @ (kpair @ X3 @ X4)))))) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => ((X2 @ X5) = $true)))))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.58/1.33 thf(f7,plain,(
% 1.58/1.33 ~(brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i > $o] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))))),
% 1.58/1.33 inference(rectify,[status(thm)],[f5])).
% 1.58/1.33 thf(f5,negated_conjecture,(
% 1.58/1.33 ~(brelnall2 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 1.58/1.33 inference(negated_conjecture,[status(cth)],[f4])).
% 1.58/1.33 thf(f4,conjecture,(
% 1.58/1.33 brelnall2 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5))))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',breln1all2)).
% 1.58/1.33 thf(f122,plain,(
% 1.58/1.33 ~spl4_2),
% 1.58/1.33 inference(avatar_contradiction_clause,[status(thm)],[f121])).
% 1.58/1.33 thf(f121,plain,(
% 1.58/1.33 $false | ~spl4_2),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.58/1.33 thf(f120,plain,(
% 1.58/1.33 ($true != $true) | ~spl4_2),
% 1.58/1.33 inference(superposition,[status(thm)],[f25,f112])).
% 1.58/1.33 thf(f112,plain,(
% 1.58/1.33 ($true = (sK2 @ sK3)) | ~spl4_2),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.58/1.33 thf(f102,plain,(
% 1.58/1.33 ($false = $true) | ($true = (sK2 @ sK3)) | ~spl4_2),
% 1.58/1.33 inference(superposition,[status(thm)],[f88,f26])).
% 1.58/1.33 thf(f26,plain,(
% 1.58/1.33 ($true = (in @ sK3 @ sK1))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.58/1.33 thf(f88,plain,(
% 1.58/1.33 ( ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ($true = (sK2 @ X0))) ) | ~spl4_2),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.58/1.33 thf(f87,definition,(
% 1.58/1.33 spl4_2 <=> ! [X0 : $i] : (($true = (sK2 @ X0)) | ($false = (in @ X0 @ sK1)))),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.58/1.33 thf(f25,plain,(
% 1.58/1.33 ($true != (sK2 @ sK3))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.58/1.33 thf(f100,plain,(
% 1.58/1.33 spl4_1 | spl4_2 | spl4_2 | spl4_2 | spl4_2),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f78,f87,f87,f87,f87,f83])).
% 1.58/1.33 thf(f78,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ X0 @ sK1)) | ($true = (sK2 @ X3)) | ((in @ X2 @ sK1) = $false) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($false = (in @ X3 @ sK1)) | ($true = (sK2 @ X1)) | ($true = (sK2 @ X0)) | ($false = (in @ X1 @ sK1)) | ((sK2 @ X2) = $true)) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.58/1.33 thf(f72,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (sK2 @ X0)) | ($true = (sK2 @ X3)) | ($false = $true) | ((in @ X2 @ sK1) = $false) | ($true = (sK2 @ X1)) | ((sK2 @ X2) = $true) | ($false = (in @ X3 @ sK1)) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X0 @ sK1))) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f71,f55])).
% 1.58/1.33 thf(f55,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.58/1.33 thf(f53,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4))))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false)) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.58/1.33 thf(f52,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false) | ($false = ((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)))))) | ((X4 @ X5) = $true)) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.58/1.33 thf(f51,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK6 @ X1 @ X2 @ X3 @ X4)) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false)) )),
% 1.58/1.33 inference(sigma_clausification,[status(thm)],[f50])).
% 1.58/1.33 thf(f50,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.58/1.33 thf(f47,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = ((in @ X5 @ X3) => (X4 @ X5))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.58/1.33 thf(f46,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ($true = ((in @ X5 @ X3) => (X4 @ X5)))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.58/1.33 thf(f45,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))) @ X5))) )),
% 1.58/1.33 inference(pi_clausification,[status(thm)],[f44])).
% 1.58/1.33 thf(f44,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))))) | ($false = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.58/1.33 thf(f43,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0)))))) )),
% 1.58/1.33 inference(sigma_clausification,[status(thm)],[f42])).
% 1.58/1.33 thf(f42,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.58/1.33 thf(f41,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))))) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.58/1.33 thf(f40,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))) @ X4)) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(pi_clausification,[status(thm)],[f39])).
% 1.58/1.33 thf(f39,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1))))))))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.58/1.33 thf(f38,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))))))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.58/1.33 thf(f37,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))))))) @ X3) = $true)) )),
% 1.58/1.33 inference(pi_clausification,[status(thm)],[f36])).
% 1.58/1.33 thf(f36,plain,(
% 1.58/1.33 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.58/1.33 thf(f35,plain,(
% 1.58/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))) @ X2))) )),
% 1.58/1.33 inference(pi_clausification,[status(thm)],[f34])).
% 1.58/1.33 thf(f34,plain,(
% 1.58/1.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3)))))))))))))) )),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.58/1.33 thf(f33,plain,(
% 1.58/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))) @ X1))) )),
% 1.58/1.33 inference(pi_clausification,[status(thm)],[f32])).
% 1.58/1.33 thf(f32,plain,(
% 1.58/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 1.58/1.33 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.58/1.33 thf(f31,plain,(
% 1.58/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 1.58/1.33 inference(definition_unfolding,[status(thm)],[f27,f22,f21])).
% 1.58/1.33 thf(f22,plain,(
% 1.58/1.33 (brelnall2 = $true)),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.58/1.33 thf(f27,plain,(
% 1.58/1.33 (brelnall2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f12,plain,(
% 1.58/1.33 (brelnall2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.58/1.33 thf(f11,plain,(
% 1.58/1.33 (brelnall2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6)))))),
% 1.58/1.33 inference(rectify,[status(thm)],[f2])).
% 1.58/1.33 thf(f2,axiom,(
% 1.58/1.33 (brelnall2 = ! [X3 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.n7w8YK9uer/DTF2THF_27684.p',brelnall2)).
% 1.58/1.33 thf(f71,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0)))) | ((in @ X2 @ sK1) = $false) | ((X0 @ X1) = $true) | ($true = (X0 @ X3)) | ($false = (in @ X1 @ sK1)) | ($true = (X0 @ X2)) | ($false = (in @ X3 @ sK1))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.58/1.33 thf(f70,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ sK1) = $false) | ((X0 @ X1) = $true) | ($false = $true) | ($false = (in @ X3 @ sK1)) | ($true = (X0 @ X3)) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0)))) | ($true = (X0 @ X2)) | ($false = (in @ X1 @ sK1))) )),
% 1.58/1.33 inference(forward_demodulation,[status(thm)],[f69,f57])).
% 1.58/1.33 thf(f69,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X1) = $true) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0)))) | ($false = (in @ X1 @ sK1)) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($true = (X0 @ X3)) | ((in @ X2 @ sK1) = $false) | ($false = (in @ X3 @ sK1)) | ($true = (X0 @ X2))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.58/1.33 thf(f68,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ sK1) = $false) | ($true = (X0 @ X3)) | ($false = (in @ X1 @ sK1)) | ((X0 @ X1) = $true) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0)))) | ($true != $true) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($true = (X0 @ X2)) | ($false = (in @ X3 @ sK1))) )),
% 1.58/1.33 inference(duplicate_literal_removal,[status(thm)],[f67])).
% 1.58/1.33 thf(f67,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (in @ X3 @ sK1)) | ((X0 @ X1) = $true) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($true = (X0 @ X2)) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0)))) | ($true != $true) | ($false = (in @ X1 @ sK1)) | ((in @ X2 @ sK1) = $false) | ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($true = (X0 @ X3))) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f66,f49])).
% 1.58/1.33 thf(f49,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1)) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.58/1.33 thf(f48,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($true = ((in @ X5 @ X3) => (X4 @ X5))) | ($true = (in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.58/1.33 thf(f66,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($false = (in @ X3 @ sK1)) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1)))) | ($true = (X1 @ X3)) | ((in @ X2 @ sK1) = $false) | ($true = (X1 @ X2))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.58/1.33 thf(f65,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1)))) | ($true = (X1 @ X3)) | ($false = (in @ X3 @ sK1)) | ($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0)) | ($true = (X1 @ X2)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true != $true) | ((in @ X2 @ sK1) = $false)) )),
% 1.58/1.33 inference(duplicate_literal_removal,[status(thm)],[f64])).
% 1.58/1.33 thf(f64,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true != $true) | ($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true = (X1 @ X2)) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1)))) | ($false = (in @ X3 @ sK1)) | ((in @ X2 @ sK1) = $false) | ($true = (X1 @ X3))) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f63,f54])).
% 1.58/1.33 thf(f54,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2) = $true) | ((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false)) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.58/1.33 thf(f63,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK6 @ X0 @ X2 @ sK1 @ X1) @ sK0)) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X2 @ sK1 @ X1)))) | ($false = (in @ X3 @ sK1)) | ((in @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ sK0) != $true) | ($true = (X1 @ X3)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ X2)))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.58/1.33 thf(f61,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X2 @ sK1 @ X1)))) | ($true != (in @ (sK6 @ X0 @ X2 @ sK1 @ X1) @ sK0)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ X2))) | ((in @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ sK0) != $true) | ($true != $true) | ($false = (in @ X3 @ sK1)) | ($true = (X1 @ X3))) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f24,f56])).
% 1.58/1.33 thf(f56,plain,(
% 1.58/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3)) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false) | ((X4 @ X5) = $true)) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.58/1.33 thf(f24,plain,(
% 1.58/1.33 ( ! [X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK1) != $true) | ($true != (in @ X4 @ sK0)) | ((sK2 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK0))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.58/1.33 % SZS output end Proof for DTF2THF_27684
% 1.58/1.33 % (27784)------------------------------
% 1.58/1.33 % (27784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (27784)Termination reason: Refutation
% 1.58/1.33
% 1.58/1.33 % (27784)Memory used [KB]: 5756
% 1.58/1.33 % (27784)Time elapsed: 0.019 s
% 1.58/1.33 % (27784)Instructions burned: 26 (million)
% 1.58/1.33 % (27784)------------------------------
% 1.58/1.33 % (27784)------------------------------
% 1.58/1.33 % (27781)Success in time 0.034 s
%------------------------------------------------------------------------------