%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU641^2 : 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 : n010.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 09:35:53 AM UTC 2026
% Result : Theorem 1.65s 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 204 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 221 ( 9 ~; 3 |; 11 &; 160 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 8 con; 0-2 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 20 ^; 32 !; 6 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f42,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f18]) ).
thf(f18,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setadjoinIL = $true )
& ( sK0 != sK1 )
& ( ( setadjoin @ sK0 @ emptyset )
= ( setadjoin @ sK1 @ emptyset ) )
& ( uniqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) ) )
=> ( ( sK0 != sK1 )
& ( ( setadjoin @ sK0 @ emptyset )
= ( setadjoin @ sK1 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setadjoinIL = $true )
& ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) ) )
& ( uniqinunit = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) ) )
& ( uniqinunit = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setadjoinIL = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setadjoinIL
=> ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( uniqinunit
=> ! [X1: $i,X0: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ! [X1: $i,X0: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',singletonsuniq) ).
thf(f41,plain,
sK0 = sK1,
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = $false )
| ( sK0 = sK1 ) ),
inference(superposition,[status(thm)],[f29,f34]) ).
thf(f34,plain,
( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(superposition,[status(thm)],[f33,f17]) ).
thf(f17,plain,
( ( setadjoin @ sK0 @ emptyset )
= ( setadjoin @ sK1 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f19]) ).
thf(f19,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f21,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',setadjoinIL) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( ( X2 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f16]) ).
thf(f16,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f20,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',uniqinunit) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU641^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n010.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:18 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU641^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Ordered Pairs - Singletons
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! x:i.! y:i.setadjoin x emptyset = setadjoin y emptyset -> x = y)
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC143l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.47 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.19/0.47 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 12 @)
% 0.19/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 6 ( 3 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=197
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyset_type,type,
% 0.19/0.47 emptyset: $i ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin_type,type,
% 0.19/0.47 setadjoin: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIL_type,type,
% 0.19/0.47 setadjoinIL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIL,definition,
% 0.19/0.47 ( setadjoinIL
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(uniqinunit_type,type,
% 0.19/0.47 uniqinunit: $o ).
% 0.19/0.47
% 0.19/0.47 thf(uniqinunit,definition,
% 0.19/0.47 ( uniqinunit
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsuniq,conjecture,
% 0.19/0.47 ( setadjoinIL
% 0.19/0.47 => ( uniqinunit
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.19/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 12:29:19 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2DTF4664.p
% See solution above
% 1.46/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(in_type,type,
% 1.65/1.30 in: $i > $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(emptyset_type,type,
% 1.65/1.30 emptyset: $i ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoin_type,type,
% 1.65/1.30 setadjoin: $i > $i > $i ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoinIL_type,type,
% 1.65/1.30 setadjoinIL: $o ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoinIL,definition,
% 1.65/1.30 ( setadjoinIL
% 1.65/1.30 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(uniqinunit_type,type,
% 1.65/1.30 uniqinunit: $o ).
% 1.65/1.30
% 1.65/1.30 thf(uniqinunit,definition,
% 1.65/1.30 ( uniqinunit
% 1.65/1.30 = ( ! [Xx: $i,Xy: $i] :
% 1.65/1.30 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.65/1.30 => ( Xx = Xy ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(singletonsuniq,conjecture,
% 1.65/1.30 ( setadjoinIL
% 1.65/1.30 => ( uniqinunit
% 1.65/1.30 => ! [Xx: $i,Xy: $i] :
% 1.65/1.30 ( ( ( setadjoin @ Xx @ emptyset )
% 1.65/1.30 = ( setadjoin @ Xy @ emptyset ) )
% 1.65/1.30 => ( Xx = Xy ) ) ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.31 % (4815)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4664 for (3000ds/183Mi)
% 1.65/1.31 % (4815)First to succeed.
% 1.65/1.31 % (4815)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_4664
% 1.65/1.31 % SZS output start Proof for DTF2THF_4664
% 1.65/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.31 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.65/1.31 thf(f42,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(subsumption_resolution,[status(thm)],[f41,f18])).
% 1.65/1.31 thf(f18,plain,(
% 1.65/1.31 (sK0 != sK1)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 (setadjoinIL = $true) & ((sK0 != sK1) & ((setadjoin @ sK0 @ emptyset) = (setadjoin @ sK1 @ emptyset))) & (uniqinunit = $true)),
% 1.65/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset))) => ((sK0 != sK1) & ((setadjoin @ sK0 @ emptyset) = (setadjoin @ sK1 @ emptyset)))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 (setadjoinIL = $true) & ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset))) & (uniqinunit = $true)),
% 1.65/1.31 inference(flattening,[status(thm)],[f12])).
% 1.65/1.31 thf(f12,plain,(
% 1.65/1.31 (? [X0 : $i,X1 : $i] : ((X0 != X1) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset))) & (uniqinunit = $true)) & (setadjoinIL = $true)),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f11,plain,(
% 1.65/1.31 ~((setadjoinIL = $true) => ((uniqinunit = $true) => ! [X0 : $i,X1 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.65/1.31 thf(f10,plain,(
% 1.65/1.31 ~(setadjoinIL => (uniqinunit => ! [X0 : $i,X1 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f4])).
% 1.65/1.31 thf(f4,negated_conjecture,(
% 1.65/1.31 ~(setadjoinIL => (uniqinunit => ! [X1 : $i,X0 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1))))),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.65/1.31 thf(f3,conjecture,(
% 1.65/1.31 setadjoinIL => (uniqinunit => ! [X1 : $i,X0 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',singletonsuniq)).
% 1.65/1.31 thf(f41,plain,(
% 1.65/1.31 (sK0 = sK1)),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.65/1.31 thf(f37,plain,(
% 1.65/1.31 ($true = $false) | (sK0 = sK1)),
% 1.65/1.31 inference(superposition,[status(thm)],[f29,f34])).
% 1.65/1.31 thf(f34,plain,(
% 1.65/1.31 ($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset)))),
% 1.65/1.31 inference(superposition,[status(thm)],[f33,f17])).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 ((setadjoin @ sK0 @ emptyset) = (setadjoin @ sK1 @ emptyset))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.31 thf(f33,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X2)))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.65/1.31 thf(f32,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0))) @ X2) = $true)) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f31])).
% 1.65/1.31 thf(f31,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0)))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.65/1.31 thf(f30,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))) @ X1))) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f23])).
% 1.65/1.31 thf(f23,plain,(
% 1.65/1.31 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) = $true)),
% 1.65/1.31 inference(definition_unfolding,[status(thm)],[f21,f19])).
% 1.65/1.31 thf(f19,plain,(
% 1.65/1.31 (setadjoinIL = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.31 thf(f21,plain,(
% 1.65/1.31 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.31 thf(f9,plain,(
% 1.65/1.31 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.65/1.31 thf(f8,plain,(
% 1.65/1.31 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f1])).
% 1.65/1.31 thf(f1,axiom,(
% 1.65/1.31 (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',setadjoinIL)).
% 1.65/1.31 thf(f29,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (X1 = X2)) )),
% 1.65/1.31 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.65/1.31 thf(f28,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | ((X2 = X1) = $true)) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.65/1.31 thf(f27,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)) = $true)) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.65/1.31 thf(f26,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2) = $true)) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f25])).
% 1.65/1.31 thf(f25,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.65/1.31 thf(f24,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f22])).
% 1.65/1.31 thf(f22,plain,(
% 1.65/1.31 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 1.65/1.31 inference(definition_unfolding,[status(thm)],[f20,f16])).
% 1.65/1.31 thf(f16,plain,(
% 1.65/1.31 (uniqinunit = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.31 thf(f20,plain,(
% 1.65/1.31 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.65/1.31 thf(f7,plain,(
% 1.65/1.31 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.65/1.31 thf(f6,plain,(
% 1.65/1.31 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f2])).
% 1.65/1.31 thf(f2,axiom,(
% 1.65/1.31 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.trbGw1F1qa/DTF2THF_4664.p',uniqinunit)).
% 1.65/1.31 % SZS output end Proof for DTF2THF_4664
% 1.65/1.31 % (4815)------------------------------
% 1.65/1.31 % (4815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (4815)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (4815)Memory used [KB]: 5500
% 1.65/1.31 % (4815)Time elapsed: 0.003 s
% 1.65/1.31 % (4815)Instructions burned: 2 (million)
% 1.65/1.31 % (4815)------------------------------
% 1.65/1.31 % (4815)------------------------------
% 1.65/1.31 % (4814)Success in time 0.013 s
%------------------------------------------------------------------------------