%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU654^2 : 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 : n008.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 09:35:59 AM UTC 2026
% Result : Theorem 1.44s 1.16s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 287 ( 78 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 569 ( 11 ~; 4 |; 6 &; 502 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 9 con; 0-2 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 104 ( 38 ^; 58 !; 8 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(f50,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f40,f15]) ).
thf(f15,plain,
sK1 != sK2,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setukpairinjR2 = $true )
& ( ( kpair @ sK3 @ sK2 )
= ( kpair @ sK0 @ sK1 ) )
& ( sK1 != sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
& ( X1 != X2 ) )
=> ( ( ( kpair @ sK3 @ sK2 )
= ( kpair @ sK0 @ sK1 ) )
& ( sK1 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( setukpairinjR2 = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
& ( X1 != X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setukpairinjR2 = $true )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
=> ( X1 = X2 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( setukpairinjR2
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
=> ( X1 = X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setukpairinjR2
=> ! [X2: $i,X3: $i,X1: $i,X0: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setukpairinjR2
=> ! [X2: $i,X3: $i,X1: $i,X0: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',setukpairinjR) ).
thf(f40,plain,
sK1 = sK2,
inference(equality_resolution,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( sK2 = X1 ) ),
inference(superposition,[status(thm)],[f31,f32]) ).
thf(f32,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 )
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK3
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f16,f18,f18]) ).
thf(f18,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',kpair) ).
thf(f16,plain,
( ( kpair @ sK3 @ sK2 )
= ( kpair @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 = X1 ) )
| ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f14]) ).
thf(f14,plain,
( setukpairinjR2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( setukpairinjR2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setukpairinjR2
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setukpairinjR2
= ( ! [X0: $i,X2: $i,X1: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',setukpairinjR2) ).
thf(f17,plain,
setukpairinjR2 = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU654^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:29:39 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.43 thf(spec,logic,$$dhol).
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % File : SEU654^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.43 % Domain : Set Theory
% 0.18/0.43 % Problem : Ordered Pairs - Properties of Pairs
% 0.18/0.43 % Version : Especial > Reduced > Especial.
% 0.18/0.43 % English : (! x:i.! y:i.! z:i.! u:i.kpair x y = kpair z u -> y = u)
% 0.18/0.43
% 0.18/0.43 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.43 % Source : [Bro08]
% 0.18/0.43 % Names : ZFC156l [Bro08]
% 0.18/0.43
% 0.18/0.43 % Status : Theorem
% 0.18/0.43 % 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 v3.7.0
% 0.18/0.43 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.18/0.43 % Number of atoms : 8 ( 6 equ; 0 cnn)
% 0.18/0.43 % Maximal formula atoms : 3 ( 2 avg)
% 0.18/0.43 % Number of connectives : 37 ( 0 ~; 0 |; 0 &; 34 @)
% 0.18/0.43 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.43 % Maximal formula depth : 7 ( 3 avg)
% 0.18/0.43 % Number of types : 2 ( 0 usr)
% 0.18/0.43 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.43 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.43 % Number of variables : 10 ( 2 ^; 8 !; 0 ?; 10 :)
% 0.18/0.43 % SPC : TH0_THM_EQU_NAR
% 0.18/0.43
% 0.18/0.43 % Comments : http://mathgate.info/detsetitem.php?id=210
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 thf(emptyset_type,type,
% 0.18/0.43 emptyset: $i ).
% 0.18/0.43
% 0.18/0.43 thf(setadjoin_type,type,
% 0.18/0.43 setadjoin: $i > $i > $i ).
% 0.18/0.43
% 0.18/0.43 thf(kpair_type,type,
% 0.18/0.43 kpair: $i > $i > $i ).
% 0.18/0.43
% 0.18/0.43 thf(kpair,definition,
% 0.18/0.43 ( kpair
% 0.18/0.43 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 thf(setukpairinjR2_type,type,
% 0.18/0.43 setukpairinjR2: $o ).
% 0.18/0.43
% 0.18/0.43 thf(setukpairinjR2,definition,
% 0.18/0.43 ( setukpairinjR2
% 0.18/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.43 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.43 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.43 => ( Xy = Xu ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 thf(setukpairinjR,conjecture,
% 0.18/0.43 ( setukpairinjR2
% 0.18/0.43 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.43 ( ( ( kpair @ Xx @ Xy )
% 0.18/0.43 = ( kpair @ Xz @ Xu ) )
% 0.18/0.43 => ( Xy = Xu ) ) ) ).
% 0.18/0.43
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 ------------------------
% 1.24/1.12 ---- Embedded in THF ---
% 1.24/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.24/1.12 %%% Generated on Tue Feb 24 12:29:40 EST 2026
% 1.24/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.24/1.12 %%% Logic specification used:
% 1.24/1.12 %%% thf(spec, logic, $$dhol).
% 1.24/1.12
% 1.24/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2DTF31541.p
% See solution above
% 1.24/1.12 ------------------------
% 1.44/1.13 ---- Cleaned THF ---
% 1.44/1.13 thf(emptyset_type,type,
% 1.44/1.13 emptyset: $i ).
% 1.44/1.13
% 1.44/1.13 thf(setadjoin_type,type,
% 1.44/1.13 setadjoin: $i > $i > $i ).
% 1.44/1.13
% 1.44/1.13 thf(kpair_type,type,
% 1.44/1.13 kpair: $i > $i > $i ).
% 1.44/1.13
% 1.44/1.13 thf(kpair,definition,
% 1.44/1.13 ( kpair
% 1.44/1.13 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 1.44/1.13
% 1.44/1.13 thf(setukpairinjR2_type,type,
% 1.44/1.13 setukpairinjR2: $o ).
% 1.44/1.13
% 1.44/1.13 thf(setukpairinjR2,definition,
% 1.44/1.13 ( setukpairinjR2
% 1.44/1.13 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.44/1.13 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 1.44/1.13 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 1.44/1.13 => ( Xy = Xu ) ) ) ) ).
% 1.44/1.13
% 1.44/1.13 thf(setukpairinjR,conjecture,
% 1.44/1.13 ( setukpairinjR2
% 1.44/1.13 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.44/1.13 ( ( ( kpair @ Xx @ Xy )
% 1.44/1.13 = ( kpair @ Xz @ Xu ) )
% 1.44/1.13 => ( Xy = Xu ) ) ) ).
% 1.44/1.13 ------------------------
% 1.44/1.14 % (31817)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_31541 for (2999ds/4Mi)
% 1.44/1.14 % (31821)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_31541 for (2999ds/275Mi)
% 1.44/1.14 % (31817)Instruction limit reached!
% 1.44/1.14 % (31817)------------------------------
% 1.44/1.14 % (31817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.14 % (31817)Termination reason: Unknown
% 1.44/1.14 % (31817)Termination phase: Saturation
% 1.44/1.14
% 1.44/1.14 % (31817)Memory used [KB]: 5500
% 1.44/1.14 % (31817)Time elapsed: 0.003 s
% 1.44/1.14 % (31817)Instructions burned: 4 (million)
% 1.44/1.14 % (31817)------------------------------
% 1.44/1.14 % (31817)------------------------------
% 1.44/1.14 % (31821)Refutation not found, incomplete strategy
% 1.44/1.14 % (31821)------------------------------
% 1.44/1.14 % (31821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.14 % (31821)Termination reason: Refutation not found, incomplete strategy
% 1.44/1.14
% 1.44/1.14
% 1.44/1.14 % (31821)Memory used [KB]: 5500
% 1.44/1.14 % (31821)Time elapsed: 0.002 s
% 1.44/1.14 % (31821)Instructions burned: 3 (million)
% 1.44/1.14 % (31821)------------------------------
% 1.44/1.14 % (31821)------------------------------
% 1.44/1.15 % (31816)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31541 for (2999ds/183Mi)
% 1.44/1.15 % (31818)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_31541 for (2999ds/27Mi)
% 1.44/1.15 % (31819)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31541 for (2999ds/2Mi)
% 1.44/1.15 % (31820)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_31541 for (2999ds/2Mi)
% 1.44/1.15 % (31822)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31541 for (2999ds/18Mi)
% 1.44/1.15 % (31819)Instruction limit reached!
% 1.44/1.15 % (31819)------------------------------
% 1.44/1.15 % (31819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.15 % (31819)Termination reason: Unknown
% 1.44/1.15 % (31819)Termination phase: Preprocessing 1
% 1.44/1.15
% 1.44/1.15 % (31819)Memory used [KB]: 895
% 1.44/1.15 % (31819)Time elapsed: 0.003 s
% 1.44/1.15 % (31819)Instructions burned: 2 (million)
% 1.44/1.15 % (31819)------------------------------
% 1.44/1.15 % (31819)------------------------------
% 1.44/1.15 % (31820)Instruction limit reached!
% 1.44/1.15 % (31820)------------------------------
% 1.44/1.15 % (31820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.15 % (31820)Termination reason: Unknown
% 1.44/1.15 % (31820)Termination phase: Property scanning
% 1.44/1.15
% 1.44/1.15 % (31820)Memory used [KB]: 895
% 1.44/1.15 % (31820)Time elapsed: 0.003 s
% 1.44/1.15 % (31820)Instructions burned: 2 (million)
% 1.44/1.15 % (31820)------------------------------
% 1.44/1.15 % (31820)------------------------------
% 1.44/1.15 % (31823)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31541 for (2999ds/3Mi)
% 1.44/1.15 % (31823)Instruction limit reached!
% 1.44/1.15 % (31823)------------------------------
% 1.44/1.15 % (31823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.15 % (31823)Termination reason: Unknown
% 1.44/1.15 % (31823)Termination phase: Saturation
% 1.44/1.15
% 1.44/1.15 % (31823)Memory used [KB]: 5500
% 1.44/1.15 % (31823)Time elapsed: 0.002 s
% 1.44/1.15 % (31823)Instructions burned: 3 (million)
% 1.44/1.15 % (31823)------------------------------
% 1.44/1.15 % (31823)------------------------------
% 1.44/1.15 % (31816)First to succeed.
% 1.44/1.15 % (31824)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_31541 for (2999ds/37Mi)
% 1.44/1.16 % (31818)Also succeeded, but the first one will report.
% 1.44/1.16 % (31816)Refutation found. Thanks to Tanya!
% 1.44/1.16 % SZS status Theorem for DTF2THF_31541
% 1.44/1.16 % SZS output start Proof for DTF2THF_31541
% 1.44/1.16 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.44/1.16 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.44/1.16 thf(f50,plain,(
% 1.44/1.16 $false),
% 1.44/1.16 inference(subsumption_resolution,[status(thm)],[f40,f15])).
% 1.44/1.16 thf(f15,plain,(
% 1.44/1.16 (sK1 != sK2)),
% 1.44/1.16 inference(cnf_transformation,[status(thm)],[f13])).
% 1.44/1.16 thf(f13,plain,(
% 1.44/1.16 (setukpairinjR2 = $true) & (((kpair @ sK3 @ sK2) = (kpair @ sK0 @ sK1)) & (sK1 != sK2))),
% 1.44/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f12])).
% 1.44/1.16 thf(f12,plain,(
% 1.44/1.16 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) & (X1 != X2)) => (((kpair @ sK3 @ sK2) = (kpair @ sK0 @ sK1)) & (sK1 != sK2))),
% 1.44/1.16 introduced(definition,[],[choice_axiom])).
% 1.44/1.16 thf(f11,plain,(
% 1.44/1.16 (setukpairinjR2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) & (X1 != X2))),
% 1.44/1.16 inference(ennf_transformation,[status(thm)],[f9])).
% 1.44/1.16 thf(f9,plain,(
% 1.44/1.16 ~((setukpairinjR2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) => (X1 = X2)))),
% 1.44/1.16 inference(fool_elimination,[status(thm)],[f8])).
% 1.44/1.16 thf(f8,plain,(
% 1.44/1.16 ~(setukpairinjR2 => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) => (X1 = X2)))),
% 1.44/1.16 inference(rectify,[status(thm)],[f4])).
% 1.44/1.16 thf(f4,negated_conjecture,(
% 1.44/1.16 ~(setukpairinjR2 => ! [X2 : $i,X3 : $i,X1 : $i,X0 : $i] : (((kpair @ X0 @ X1) = (kpair @ X2 @ X3)) => (X1 = X3)))),
% 1.44/1.16 inference(negated_conjecture,[status(cth)],[f3])).
% 1.44/1.16 thf(f3,conjecture,(
% 1.44/1.16 setukpairinjR2 => ! [X2 : $i,X3 : $i,X1 : $i,X0 : $i] : (((kpair @ X0 @ X1) = (kpair @ X2 @ X3)) => (X1 = X3))),
% 1.44/1.16 file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',setukpairinjR)).
% 1.44/1.16 thf(f40,plain,(
% 1.44/1.16 (sK1 = sK2)),
% 1.44/1.16 inference(equality_resolution,[status(thm)],[f36])).
% 1.44/1.16 thf(f36,plain,(
% 1.44/1.16 ( ! [X0 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset))) | (sK2 = X1)) )),
% 1.44/1.16 inference(superposition,[status(thm)],[f31,f32])).
% 1.44/1.16 thf(f32,plain,(
% 1.44/1.16 ((setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset)) @ emptyset)))),
% 1.44/1.16 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.44/1.16 thf(f20,plain,(
% 1.44/1.16 (((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK0 @ sK1) = ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK3 @ sK2))),
% 1.44/1.16 inference(definition_unfolding,[status(thm)],[f16,f18,f18])).
% 1.44/1.16 thf(f18,plain,(
% 1.44/1.16 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.44/1.16 inference(cnf_transformation,[status(thm)],[f10])).
% 1.44/1.16 thf(f10,plain,(
% 1.44/1.16 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.44/1.16 inference(fool_elimination,[status(thm)],[f1])).
% 1.44/1.16 thf(f1,axiom,(
% 1.44/1.16 ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)),
% 1.44/1.16 file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',kpair)).
% 1.44/1.16 thf(f16,plain,(
% 1.44/1.16 ((kpair @ sK3 @ sK2) = (kpair @ sK0 @ sK1))),
% 1.44/1.16 inference(cnf_transformation,[status(thm)],[f13])).
% 1.44/1.16 thf(f31,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | (X1 = X2)) )),
% 1.44/1.16 inference(equality_proxy_clausification,[status(thm)],[f30])).
% 1.44/1.16 thf(f30,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (X2 = X1)) | ((setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) )),
% 1.44/1.16 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.44/1.16 thf(f29,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = $false) | ($true = (X2 = X1))) )),
% 1.44/1.16 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.44/1.16 thf(f28,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X2 = X1)))) )),
% 1.44/1.16 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.44/1.16 thf(f27,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X2 = X1))) @ X4) = $true)) )),
% 1.44/1.16 inference(pi_clausification,[status(thm)],[f26])).
% 1.44/1.16 thf(f26,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X2 = X1)))))) )),
% 1.44/1.16 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.44/1.16 thf(f25,plain,(
% 1.44/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X2 = X1))))) @ X3))) )),
% 1.44/1.16 inference(pi_clausification,[status(thm)],[f24])).
% 1.44/1.16 thf(f24,plain,(
% 1.44/1.16 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X2 = X1)))))))) )),
% 1.44/1.16 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.44/1.16 thf(f23,plain,(
% 1.44/1.16 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y0 = X1))))))) @ X2))) )),
% 1.44/1.16 inference(pi_clausification,[status(thm)],[f22])).
% 1.44/1.16 thf(f22,plain,(
% 1.44/1.16 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y0 = X1)))))))))) )),
% 1.44/1.16 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.44/1.16 thf(f21,plain,(
% 1.44/1.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0))))))))) @ X1))) )),
% 1.44/1.16 inference(pi_clausification,[status(thm)],[f19])).
% 1.44/1.16 thf(f19,plain,(
% 1.44/1.16 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))),
% 1.44/1.16 inference(definition_unfolding,[status(thm)],[f17,f14])).
% 1.44/1.16 thf(f14,plain,(
% 1.44/1.16 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))),
% 1.44/1.16 inference(cnf_transformation,[status(thm)],[f7])).
% 1.44/1.16 thf(f7,plain,(
% 1.44/1.16 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))),
% 1.44/1.16 inference(fool_elimination,[status(thm)],[f6])).
% 1.44/1.16 thf(f6,plain,(
% 1.44/1.16 (setukpairinjR2 = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X2 = X3)))),
% 1.44/1.16 inference(rectify,[status(thm)],[f2])).
% 1.44/1.16 thf(f2,axiom,(
% 1.44/1.16 (setukpairinjR2 = ! [X0 : $i,X2 : $i,X1 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X1 = X3)))),
% 1.44/1.16 file('/export/starexec/sandbox/tmp/tmp.MT8tj4l9pS/DTF2THF_31541.p',setukpairinjR2)).
% 1.44/1.16 thf(f17,plain,(
% 1.44/1.16 (setukpairinjR2 = $true)),
% 1.44/1.16 inference(cnf_transformation,[status(thm)],[f13])).
% 1.44/1.16 % SZS output end Proof for DTF2THF_31541
% 1.44/1.16 % (31816)------------------------------
% 1.44/1.16 % (31816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.16 % (31816)Termination reason: Refutation
% 1.44/1.16
% 1.44/1.16 % (31816)Memory used [KB]: 5500
% 1.44/1.16 % (31816)Time elapsed: 0.008 s
% 1.44/1.16 % (31816)Instructions burned: 6 (million)
% 1.44/1.16 % (31816)------------------------------
% 1.44/1.16 % (31816)------------------------------
% 1.44/1.16 % (31815)Success in time 0.023 s
%------------------------------------------------------------------------------