%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU574^2 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:21 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 84 ( 27 unt; 0 typ; 3 def)
% Number of atoms : 704 ( 185 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 821 ( 29 ~; 87 |; 16 &; 548 @)
% ( 3 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 10 con; 0-2 aty)
% ( 46 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 148 ( 54 ^; 88 !; 6 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK3: $i > $i > $i ).
thf(func_def_19,type,
sK4: $i > $i > $i ).
thf(func_def_20,type,
sK5: $i > $i > $i ).
thf(f190,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f109,f120,f163,f189]) ).
thf(f189,plain,
( spl2_2
| ~ spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f188,f159,f101,f105]) ).
thf(f105,definition,
( spl2_2
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f101,definition,
( spl2_1
<=> ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f159,definition,
( spl2_3
<=> ( ( in @ ( sK4 @ sK0 @ sK1 ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f188,plain,
( ( sK1 = sK0 )
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ( sK1 = sK0 )
| ( $true = $false )
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[status(thm)],[f182,f151]) ).
thf(f151,plain,
( ( $false
= ( in @ ( sK3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f60,f103]) ).
thf(f103,plain,
( ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f60,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f32,f17]) ).
thf(f17,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setext = $true )
& ( subsetE = $true )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( sK1 != sK0 )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( $true
= ( subset @ sK0 @ sK1 ) )
& ( sK1 != sK0 )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setext = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) )
& ( subsetE = $true )
& ( setext = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setext = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( subset @ X0 @ X1 )
= $true )
=> ( X0 = X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setext
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setext
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setext
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',setextsub) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X1 @ X3 )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) ) )
| ( ( subset @ X1 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f20]) ).
thf(f20,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f22,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',subsetE) ).
thf(f182,plain,
( ( $true
= ( in @ ( sK3 @ sK0 @ sK1 ) @ sK1 ) )
| ( sK1 = sK0 )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ( $true = $false )
| ( sK1 = sK0 )
| ( $true
= ( in @ ( sK3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f161,f73]) ).
thf(f73,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ sK0 @ X0 ) @ sK1 ) )
| ( $true
= ( in @ ( sK3 @ sK0 @ X0 ) @ X0 ) )
| ( sK0 = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK3 @ sK0 @ X0 ) @ X0 ) )
| ( $true = $false )
| ( sK0 = X0 )
| ( $true
= ( in @ ( sK4 @ sK0 @ X0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f47,f58]) ).
thf(f58,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f32,f19]) ).
thf(f19,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK4 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X1 @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( X2 = X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f16]) ).
thf(f16,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) )
= setext ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) )
= setext ),
file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',setext) ).
thf(f21,plain,
setext = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f161,plain,
( ( ( in @ ( sK4 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f159]) ).
thf(f163,plain,
( spl2_3
| spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f156,f101,f105,f159]) ).
thf(f156,plain,
( ( sK1 = sK0 )
| ( ( in @ ( sK4 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( in @ ( sK4 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ( $true = $false )
| ( sK1 = sK0 )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f151,f46]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 )
| ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f120,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f119]) ).
thf(f119,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( sK0 != sK0 )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f18,f107]) ).
thf(f107,plain,
( ( sK1 = sK0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f18,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f109,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f97,f101,f105]) ).
thf(f97,plain,
( ( sK1 = sK0 )
| ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( sK1 = sK0 )
| ( $true = $false )
| ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( sK1 = sK0 )
| ( sK1 = sK0 )
| ( $true = $false )
| ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK3 @ sK0 @ sK1 ) @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f53,f77]) ).
thf(f77,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK5 @ sK0 @ X0 ) @ sK1 ) )
| ( sK0 = X0 )
| ( ( in @ ( sK3 @ sK0 @ X0 ) @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i] :
( ( sK0 = X0 )
| ( $true = $false )
| ( ( in @ ( sK3 @ sK0 @ X0 ) @ sK0 )
= $false )
| ( $true
= ( in @ ( sK5 @ sK0 @ X0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f52,f58]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK5 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK5 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK5 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK5 @ X1 @ X2 ) )
= $false )
| ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK5 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU574^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n016.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 12:27:51 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
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEU574^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.29/0.47 % Version : Especial > Reduced > Especial.
% 0.29/0.47 % English : (! A:i.! B:i.subset A B -> subset B A -> A = B)
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.47 % Source : [Bro08]
% 0.29/0.47 % Names : ZFC076l [Bro08]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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
% 0.29/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.29/0.47 % Number of atoms : 17 ( 4 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.29/0.47 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 18 @)
% 0.29/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 9 ( 4 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : http://mathgate.info/detsetitem.php?id=154
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(in_type,type,
% 0.29/0.47 in: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setext_type,type,
% 0.29/0.47 setext: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setext,definition,
% 0.29/0.47 ( setext
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset_type,type,
% 0.29/0.47 subset: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE_type,type,
% 0.29/0.47 subsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE,definition,
% 0.29/0.47 ( subsetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub,conjecture,
% 0.29/0.47 ( setext
% 0.29/0.47 => ( subsetE
% 0.29/0.47 => ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 12:27:52 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2DTF9378.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(in_type,type,
% 1.47/1.28 in: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(setext_type,type,
% 1.47/1.28 setext: $o ).
% 1.47/1.28
% 1.47/1.28 thf(setext,definition,
% 1.47/1.28 ( setext
% 1.47/1.28 = ( ! [A: $i,B: $i] :
% 1.47/1.28 ( ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( in @ Xx @ B ) )
% 1.47/1.28 => ( ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ B )
% 1.47/1.28 => ( in @ Xx @ A ) )
% 1.47/1.28 => ( A = B ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(subset_type,type,
% 1.47/1.28 subset: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(subsetE_type,type,
% 1.47/1.28 subsetE: $o ).
% 1.47/1.28
% 1.47/1.28 thf(subsetE,definition,
% 1.47/1.28 ( subsetE
% 1.47/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.28 ( ( subset @ A @ B )
% 1.47/1.28 => ( ( in @ Xx @ A )
% 1.47/1.28 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(setextsub,conjecture,
% 1.47/1.28 ( setext
% 1.47/1.28 => ( subsetE
% 1.47/1.28 => ! [A: $i,B: $i] :
% 1.47/1.28 ( ( subset @ A @ B )
% 1.47/1.28 => ( ( subset @ B @ A )
% 1.47/1.28 => ( A = B ) ) ) ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (9599)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_9378 for (2999ds/2Mi)
% 1.47/1.29 % (9599)Instruction limit reached!
% 1.47/1.29 % (9599)------------------------------
% 1.47/1.29 % (9599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (9599)Termination reason: Unknown
% 1.47/1.29 % (9599)Termination phase: shuffling
% 1.47/1.29
% 1.47/1.29 % (9599)Memory used [KB]: 895
% 1.47/1.29 % (9599)Time elapsed: 0.002 s
% 1.47/1.29 % (9599)Instructions burned: 2 (million)
% 1.47/1.29 % (9599)------------------------------
% 1.47/1.29 % (9599)------------------------------
% 1.47/1.29 % (9597)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_9378 for (2999ds/27Mi)
% 1.64/1.30 % (9595)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9378 for (2999ds/183Mi)
% 1.64/1.30 % (9596)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_9378 for (2999ds/4Mi)
% 1.64/1.30 % (9598)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9378 for (2999ds/2Mi)
% 1.64/1.30 % (9600)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_9378 for (2999ds/275Mi)
% 1.64/1.30 % (9601)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9378 for (2999ds/18Mi)
% 1.64/1.30 % (9598)Instruction limit reached!
% 1.64/1.30 % (9598)------------------------------
% 1.64/1.30 % (9598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (9598)Termination reason: Unknown
% 1.64/1.30 % (9598)Termination phase: Property scanning
% 1.64/1.30
% 1.64/1.30 % (9598)Memory used [KB]: 895
% 1.64/1.30 % (9598)Time elapsed: 0.003 s
% 1.64/1.30 % (9598)Instructions burned: 2 (million)
% 1.64/1.30 % (9598)------------------------------
% 1.64/1.30 % (9598)------------------------------
% 1.64/1.30 % (9602)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9378 for (2999ds/3Mi)
% 1.64/1.30 % (9596)Instruction limit reached!
% 1.64/1.30 % (9596)------------------------------
% 1.64/1.30 % (9596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (9596)Termination reason: Unknown
% 1.64/1.30 % (9596)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (9596)Memory used [KB]: 5500
% 1.64/1.30 % (9596)Time elapsed: 0.005 s
% 1.64/1.30 % (9596)Instructions burned: 5 (million)
% 1.64/1.30 % (9596)------------------------------
% 1.64/1.30 % (9596)------------------------------
% 1.64/1.30 % (9602)Instruction limit reached!
% 1.64/1.30 % (9602)------------------------------
% 1.64/1.30 % (9602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (9602)Termination reason: Unknown
% 1.64/1.30 % (9602)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (9602)Memory used [KB]: 5500
% 1.64/1.30 % (9602)Time elapsed: 0.002 s
% 1.64/1.30 % (9602)Instructions burned: 3 (million)
% 1.64/1.30 % (9602)------------------------------
% 1.64/1.30 % (9602)------------------------------
% 1.64/1.30 % (9597)First to succeed.
% 1.64/1.31 % (9597)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_9378
% 1.64/1.31 % SZS output start Proof for DTF2THF_9378
% 1.64/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.31 thf(func_def_3, type, subset: $i > $i > $o).
% 1.64/1.31 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.31 thf(func_def_18, type, sK3: $i > $i > $i).
% 1.64/1.31 thf(func_def_19, type, sK4: $i > $i > $i).
% 1.64/1.31 thf(func_def_20, type, sK5: $i > $i > $i).
% 1.64/1.31 thf(f190,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(avatar_sat_refutation,[status(thm)],[f109,f120,f163,f189])).
% 1.64/1.31 thf(f189,plain,(
% 1.64/1.31 spl2_2 | ~spl2_1 | ~spl2_3),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f188,f159,f101,f105])).
% 1.64/1.31 thf(f105,definition,(
% 1.64/1.31 spl2_2 <=> (sK1 = sK0)),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.64/1.31 thf(f101,definition,(
% 1.64/1.31 spl2_1 <=> ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false)),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.64/1.31 thf(f159,definition,(
% 1.64/1.31 spl2_3 <=> ((in @ (sK4 @ sK0 @ sK1) @ sK1) = $false)),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.64/1.31 thf(f188,plain,(
% 1.64/1.31 (sK1 = sK0) | (~spl2_1 | ~spl2_3)),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 1.64/1.31 thf(f187,plain,(
% 1.64/1.31 (sK1 = sK0) | ($true = $false) | (~spl2_1 | ~spl2_3)),
% 1.64/1.31 inference(forward_demodulation,[status(thm)],[f182,f151])).
% 1.64/1.31 thf(f151,plain,(
% 1.64/1.31 ($false = (in @ (sK3 @ sK0 @ sK1) @ sK1)) | ~spl2_1),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.64/1.31 thf(f143,plain,(
% 1.64/1.31 ($true = $false) | ($false = (in @ (sK3 @ sK0 @ sK1) @ sK1)) | ~spl2_1),
% 1.64/1.31 inference(superposition,[status(thm)],[f60,f103])).
% 1.64/1.31 thf(f103,plain,(
% 1.64/1.31 ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false) | ~spl2_1),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.64/1.31 thf(f60,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = (in @ X0 @ sK0)) | ((in @ X0 @ sK1) = $false)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.64/1.31 thf(f54,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = (in @ X0 @ sK0)) | ((in @ X0 @ sK1) = $false) | ($true = $false)) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f32,f17])).
% 1.64/1.31 thf(f17,plain,(
% 1.64/1.31 ($true = (subset @ sK1 @ sK0))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 (setext = $true) & (subsetE = $true) & (($true = (subset @ sK0 @ sK1)) & (sK1 != sK0) & ($true = (subset @ sK1 @ sK0)))),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & (X0 != X1) & ((subset @ X1 @ X0) = $true)) => (($true = (subset @ sK0 @ sK1)) & (sK1 != sK0) & ($true = (subset @ sK1 @ sK0)))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 (setext = $true) & (subsetE = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & (X0 != X1) & ((subset @ X1 @ X0) = $true))),
% 1.64/1.31 inference(flattening,[status(thm)],[f12])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 (? [X0 : $i,X1 : $i] : (((X0 != X1) & ((subset @ X0 @ X1) = $true)) & ((subset @ X1 @ X0) = $true)) & (subsetE = $true)) & (setext = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 ~((setext = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (((subset @ X0 @ X1) = $true) => (X0 = X1)))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 ~(setext => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1)))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f4])).
% 1.64/1.31 thf(f4,negated_conjecture,(
% 1.64/1.31 ~(setext => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1)))))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.31 thf(f3,conjecture,(
% 1.64/1.31 setext => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',setextsub)).
% 1.64/1.31 thf(f32,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X1 @ X3) = $false) | ((in @ X2 @ X1) = $false) | ((in @ X2 @ X3) = $true)) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.64/1.31 thf(f31,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => (in @ X2 @ X3))) | ((subset @ X1 @ X3) = $false)) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.31 thf(f30,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3) => ((in @ X2 @ X1) => (in @ X2 @ X3))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.64/1.31 thf(f29,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ Y0)))) @ X3))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f28])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ Y0))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ Y1)))))) @ X2))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ Y1))))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.64/1.31 thf(f25,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2)))))))) @ X1))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f24])).
% 1.64/1.31 thf(f24,plain,(
% 1.64/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f22,f20])).
% 1.64/1.31 thf(f20,plain,(
% 1.64/1.31 (subsetE = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f22,plain,(
% 1.64/1.31 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = subsetE)),
% 1.64/1.31 inference(rectify,[status(thm)],[f2])).
% 1.64/1.31 thf(f2,axiom,(
% 1.64/1.31 (! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',subsetE)).
% 1.64/1.31 thf(f182,plain,(
% 1.64/1.31 ($true = (in @ (sK3 @ sK0 @ sK1) @ sK1)) | (sK1 = sK0) | ~spl2_3),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.64/1.31 thf(f181,plain,(
% 1.64/1.31 ($true = $false) | (sK1 = sK0) | ($true = (in @ (sK3 @ sK0 @ sK1) @ sK1)) | ~spl2_3),
% 1.64/1.31 inference(superposition,[status(thm)],[f161,f73])).
% 1.64/1.31 thf(f73,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = (in @ (sK4 @ sK0 @ X0) @ sK1)) | ($true = (in @ (sK3 @ sK0 @ X0) @ X0)) | (sK0 = X0)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.64/1.31 thf(f71,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = (in @ (sK3 @ sK0 @ X0) @ X0)) | ($true = $false) | (sK0 = X0) | ($true = (in @ (sK4 @ sK0 @ X0) @ sK1))) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f47,f58])).
% 1.64/1.31 thf(f58,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($false = (in @ X0 @ sK0)) | ((in @ X0 @ sK1) = $true)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.64/1.31 thf(f55,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = $false) | ($false = (in @ X0 @ sK0)) | ((in @ X0 @ sK1) = $true)) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f32,f19])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 ($true = (subset @ sK0 @ sK1))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f47,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK4 @ X1 @ X2) @ X1)) | (X1 = X2) | ($true = (in @ (sK3 @ X1 @ X2) @ X2))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.64/1.31 thf(f45,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | ($true = (in @ (sK3 @ X1 @ X2) @ X2)) | ($false = ((in @ (sK4 @ X1 @ X2) @ X1) => (in @ (sK4 @ X1 @ X2) @ X2)))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.64/1.31 thf(f44,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK4 @ X1 @ X2))) | ($true = (in @ (sK3 @ X1 @ X2) @ X2))) )),
% 1.64/1.31 inference(sigma_clausification,[status(thm)],[f43])).
% 1.64/1.31 thf(f43,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK3 @ X1 @ X2) @ X2)) | (X1 = X2) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false)) )),
% 1.64/1.31 inference(equality_proxy_clausification,[status(thm)],[f42])).
% 1.64/1.31 thf(f42,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK3 @ X1 @ X2) @ X2)) | ($true = (X2 = X1)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false)) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.64/1.31 thf(f40,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK3 @ X1 @ X2) @ X2) => (in @ (sK3 @ X1 @ X2) @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.31 thf(f39,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(sigma_clausification,[status(thm)],[f38])).
% 1.64/1.31 thf(f38,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.64/1.31 thf(f37,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = $false)) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.64/1.31 thf(f36,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.64/1.31 thf(f35,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f34])).
% 1.64/1.31 thf(f34,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.64/1.31 thf(f33,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f23])).
% 1.64/1.31 thf(f23,plain,(
% 1.64/1.31 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) = $true)),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f21,f16])).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.qhkNoSK9xX/DTF2THF_9378.p',setext)).
% 1.64/1.31 thf(f21,plain,(
% 1.64/1.31 (setext = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f161,plain,(
% 1.64/1.31 ((in @ (sK4 @ sK0 @ sK1) @ sK1) = $false) | ~spl2_3),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f159])).
% 1.64/1.31 thf(f163,plain,(
% 1.64/1.31 spl2_3 | spl2_2 | ~spl2_1),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f156,f101,f105,f159])).
% 1.64/1.31 thf(f156,plain,(
% 1.64/1.31 (sK1 = sK0) | ((in @ (sK4 @ sK0 @ sK1) @ sK1) = $false) | ~spl2_1),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.64/1.31 thf(f154,plain,(
% 1.64/1.31 ((in @ (sK4 @ sK0 @ sK1) @ sK1) = $false) | ($true = $false) | (sK1 = sK0) | ~spl2_1),
% 1.64/1.31 inference(superposition,[status(thm)],[f151,f46])).
% 1.64/1.31 thf(f46,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK3 @ X1 @ X2) @ X2)) | (X1 = X2) | ((in @ (sK4 @ X1 @ X2) @ X2) = $false)) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.64/1.31 thf(f120,plain,(
% 1.64/1.31 ~spl2_2),
% 1.64/1.31 inference(avatar_contradiction_clause,[status(thm)],[f119])).
% 1.64/1.31 thf(f119,plain,(
% 1.64/1.31 $false | ~spl2_2),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.64/1.31 thf(f118,plain,(
% 1.64/1.31 (sK0 != sK0) | ~spl2_2),
% 1.64/1.31 inference(superposition,[status(thm)],[f18,f107])).
% 1.64/1.31 thf(f107,plain,(
% 1.64/1.31 (sK1 = sK0) | ~spl2_2),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 (sK1 != sK0)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f109,plain,(
% 1.64/1.31 spl2_2 | spl2_1),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f97,f101,f105])).
% 1.64/1.31 thf(f97,plain,(
% 1.64/1.31 (sK1 = sK0) | ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false)),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.64/1.31 thf(f96,plain,(
% 1.64/1.31 (sK1 = sK0) | ($true = $false) | ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false)),
% 1.64/1.31 inference(duplicate_literal_removal,[status(thm)],[f95])).
% 1.64/1.31 thf(f95,plain,(
% 1.64/1.31 (sK1 = sK0) | (sK1 = sK0) | ($true = $false) | ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false) | ((in @ (sK3 @ sK0 @ sK1) @ sK0) = $false)),
% 1.64/1.31 inference(superposition,[status(thm)],[f53,f77])).
% 1.64/1.31 thf(f77,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true = (in @ (sK5 @ sK0 @ X0) @ sK1)) | (sK0 = X0) | ((in @ (sK3 @ sK0 @ X0) @ sK0) = $false)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.64/1.31 thf(f75,plain,(
% 1.64/1.31 ( ! [X0 : $i] : ((sK0 = X0) | ($true = $false) | ((in @ (sK3 @ sK0 @ X0) @ sK0) = $false) | ($true = (in @ (sK5 @ sK0 @ X0) @ sK1))) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f52,f58])).
% 1.64/1.31 thf(f52,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK5 @ X1 @ X2) @ X1)) | (X1 = X2) | ($false = (in @ (sK3 @ X1 @ X2) @ X1))) )),
% 1.64/1.31 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.64/1.31 thf(f51,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK3 @ X1 @ X2) @ X1)) | ($true = (in @ (sK5 @ X1 @ X2) @ X1)) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.64/1.31 thf(f49,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X2) @ X1) => (in @ (sK5 @ X1 @ X2) @ X2)) = $false) | ($false = (in @ (sK3 @ X1 @ X2) @ X1)) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.64/1.31 thf(f48,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK5 @ X1 @ X2)) = $false) | ($true = (X2 = X1)) | ($false = (in @ (sK3 @ X1 @ X2) @ X1))) )),
% 1.64/1.31 inference(sigma_clausification,[status(thm)],[f41])).
% 1.64/1.31 thf(f41,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ($true = (X2 = X1)) | ($false = (in @ (sK3 @ X1 @ X2) @ X1))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.64/1.31 thf(f53,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK5 @ X1 @ X2) @ X2)) | ($false = (in @ (sK3 @ X1 @ X2) @ X1)) | (X1 = X2)) )),
% 1.64/1.31 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.64/1.31 thf(f50,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK3 @ X1 @ X2) @ X1)) | ($false = (in @ (sK5 @ X1 @ X2) @ X2)) | ($true = (X2 = X1))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_9378
% 1.64/1.31 % (9597)------------------------------
% 1.64/1.31 % (9597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (9597)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (9597)Memory used [KB]: 5628
% 1.64/1.31 % (9597)Time elapsed: 0.013 s
% 1.64/1.31 % (9597)Instructions burned: 26 (million)
% 1.64/1.31 % (9597)------------------------------
% 1.64/1.31 % (9597)------------------------------
% 1.64/1.31 % (9594)Success in time 0.021 s
%------------------------------------------------------------------------------