%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU650^2 : 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 : n005.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 09:35:57 AM UTC 2026
% Result : Theorem 1.52s 1.27s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 208 ( 61 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 300 ( 16 ~; 5 |; 6 &; 248 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 7 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 36 ( 10 ^; 22 !; 4 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( sK1 != sK1 )
| ( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ emptyset ) ) ),
inference(superposition,[status(thm)],[f27,f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f12,f11]) ).
thf(f11,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( setukpairinjR11
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gWPwuWSs1N/DTF2THF_6577.p',setukpairinjR11) ).
thf(f12,plain,
setukpairinjR11 = $true,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK0 = sK1 )
& ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) )
& ( setukpairinjR11 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
=> ( ( sK0 = sK1 )
& ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
& ( setukpairinjR11 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( setukpairinjR11 = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gWPwuWSs1N/DTF2THF_6577.p',setukpairinjR12) ).
thf(f27,plain,
( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset ) )
| ( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
inference(superposition,[status(thm)],[f15,f23]) ).
thf(f15,plain,
( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f14,f14,f14]) ).
thf(f14,plain,
sK0 = sK1,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU650^2 : 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 : n005.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 12:29:14 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
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU650^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.19/0.46 % Version : Especial > Reduced > Especial.
% 0.19/0.46 % English : (! x:i.! y:i.x = y -> setadjoin (setadjoin x emptyset) (setadjoin
% 0.19/0.46 % (setadjoin x (setadjoin y emptyset)) emptyset) = setadjoin
% 0.19/0.46 % (setadjoin x emptyset) emptyset)
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.46 % Source : [Bro08]
% 0.19/0.46 % Names : ZFC152l [Bro08]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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 v4.0.0, 0.33 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.19/0.46 % Number of atoms : 7 ( 5 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.46 % Number of connectives : 23 ( 0 ~; 0 |; 0 &; 20 @)
% 0.19/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : http://mathgate.info/detsetitem.php?id=206
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(emptyset_type,type,
% 0.19/0.46 emptyset: $i ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoin_type,type,
% 0.19/0.46 setadjoin: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(setukpairinjR11_type,type,
% 0.19/0.46 setukpairinjR11: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setukpairinjR11,definition,
% 0.19/0.46 ( setukpairinjR11
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setukpairinjR12,conjecture,
% 0.19/0.46 ( setukpairinjR11
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.52/1.24 ---- Embedded in THF ---
% 1.52/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.24 %%% Generated on Tue Feb 24 12:29:15 EST 2026
% 1.52/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.24 %%% Logic specification used:
% 1.52/1.24 %%% thf(spec, logic, $$dhol).
% 1.52/1.24
% 1.52/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gWPwuWSs1N/DTF2DTF6577.p
% See solution above
% 1.52/1.24 ------------------------
% 1.52/1.25 ---- Cleaned THF ---
% 1.52/1.25 thf(emptyset_type,type,
% 1.52/1.25 emptyset: $i ).
% 1.52/1.25
% 1.52/1.25 thf(setadjoin_type,type,
% 1.52/1.25 setadjoin: $i > $i > $i ).
% 1.52/1.25
% 1.52/1.25 thf(setukpairinjR11_type,type,
% 1.52/1.25 setukpairinjR11: $o ).
% 1.52/1.25
% 1.52/1.25 thf(setukpairinjR11,definition,
% 1.52/1.25 ( setukpairinjR11
% 1.52/1.25 = ( ! [Xx: $i,Xy: $i] :
% 1.52/1.25 ( ( Xx = Xy )
% 1.52/1.25 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.52/1.25 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.52/1.25
% 1.52/1.25 thf(setukpairinjR12,conjecture,
% 1.52/1.25 ( setukpairinjR11
% 1.52/1.25 => ! [Xx: $i,Xy: $i] :
% 1.52/1.25 ( ( Xx = Xy )
% 1.52/1.25 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 1.52/1.25 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ).
% 1.52/1.25 ------------------------
% 1.52/1.26 % (6727)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_6577 for (3000ds/4Mi)
% 1.52/1.27 % (6732)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6577 for (3000ds/18Mi)
% 1.52/1.27 % (6727)First to succeed.
% 1.52/1.27 % (6732)Also succeeded, but the first one will report.
% 1.52/1.27 % (6727)Refutation found. Thanks to Tanya!
% 1.52/1.27 % SZS status Theorem for DTF2THF_6577
% 1.52/1.27 % SZS output start Proof for DTF2THF_6577
% 1.52/1.27 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.52/1.27 thf(f29,plain,(
% 1.52/1.27 $false),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.52/1.27 thf(f28,plain,(
% 1.52/1.27 (sK1 != sK1) | ((setadjoin @ sK1 @ emptyset) != (setadjoin @ sK1 @ emptyset))),
% 1.52/1.27 inference(superposition,[status(thm)],[f27,f23])).
% 1.52/1.27 thf(f23,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset)) | (X1 != X2)) )),
% 1.52/1.27 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.52/1.27 thf(f22,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : ((X1 != X2) | ($true = ((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset)))) )),
% 1.52/1.27 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.52/1.27 thf(f21,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : (($false = (X2 = X1)) | ($true = ((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset)))) )),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.52/1.27 thf(f20,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : (($true = ((X2 = X1) => ((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset))))) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.52/1.27 thf(f19,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => ((setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ Y0 @ emptyset)))) @ X2) = $true)) )),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f18])).
% 1.52/1.27 thf(f18,plain,(
% 1.52/1.27 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => ((setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ Y0 @ emptyset))))))) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.52/1.27 thf(f17,plain,(
% 1.52/1.27 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset)))))) @ X1))) )),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f16])).
% 1.52/1.27 thf(f16,plain,(
% 1.52/1.27 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))),
% 1.52/1.27 inference(definition_unfolding,[status(thm)],[f12,f11])).
% 1.52/1.27 thf(f11,plain,(
% 1.52/1.27 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f5])).
% 1.52/1.27 thf(f5,plain,(
% 1.52/1.27 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f1])).
% 1.52/1.27 thf(f1,axiom,(
% 1.52/1.27 (setukpairinjR11 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X0 @ emptyset))))),
% 1.52/1.27 file('/export/starexec/sandbox2/tmp/tmp.gWPwuWSs1N/DTF2THF_6577.p',setukpairinjR11)).
% 1.52/1.27 thf(f12,plain,(
% 1.52/1.27 (setukpairinjR11 = $true)),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.27 thf(f10,plain,(
% 1.52/1.27 ((sK0 = sK1) & ((setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ emptyset))) & (setukpairinjR11 = $true)),
% 1.52/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9])).
% 1.52/1.27 thf(f9,plain,(
% 1.52/1.27 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) => ((sK0 = sK1) & ((setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ emptyset)))),
% 1.52/1.27 introduced(definition,[],[choice_axiom])).
% 1.52/1.27 thf(f8,plain,(
% 1.52/1.27 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) & (setukpairinjR11 = $true)),
% 1.52/1.27 inference(ennf_transformation,[status(thm)],[f7])).
% 1.52/1.27 thf(f7,plain,(
% 1.52/1.27 ~((setukpairinjR11 = $true) => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f6])).
% 1.52/1.27 thf(f6,plain,(
% 1.52/1.27 ~(setukpairinjR11 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 1.52/1.27 inference(rectify,[status(thm)],[f3])).
% 1.52/1.27 thf(f3,negated_conjecture,(
% 1.52/1.27 ~(setukpairinjR11 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 1.52/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.52/1.27 thf(f2,conjecture,(
% 1.52/1.27 setukpairinjR11 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)))),
% 1.52/1.27 file('/export/starexec/sandbox2/tmp/tmp.gWPwuWSs1N/DTF2THF_6577.p',setukpairinjR12)).
% 1.52/1.27 thf(f27,plain,(
% 1.52/1.27 ((setadjoin @ sK1 @ emptyset) != (setadjoin @ sK1 @ (setadjoin @ sK1 @ emptyset)))),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.52/1.27 thf(f25,plain,(
% 1.52/1.27 ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset)) | ((setadjoin @ sK1 @ emptyset) != (setadjoin @ sK1 @ (setadjoin @ sK1 @ emptyset)))),
% 1.52/1.27 inference(superposition,[status(thm)],[f15,f23])).
% 1.52/1.27 thf(f15,plain,(
% 1.52/1.27 ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)))),
% 1.52/1.27 inference(definition_unfolding,[status(thm)],[f13,f14,f14,f14])).
% 1.52/1.27 thf(f14,plain,(
% 1.52/1.27 (sK0 = sK1)),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.27 thf(f13,plain,(
% 1.52/1.27 ((setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK0 @ emptyset) @ emptyset))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.27 % SZS output end Proof for DTF2THF_6577
% 1.52/1.27 % (6727)------------------------------
% 1.52/1.27 % (6727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (6727)Termination reason: Refutation
% 1.52/1.27
% 1.52/1.27 % (6727)Memory used [KB]: 5500
% 1.52/1.27 % (6727)Time elapsed: 0.003 s
% 1.52/1.27 % (6727)Instructions burned: 2 (million)
% 1.52/1.27 % (6727)------------------------------
% 1.52/1.27 % (6727)------------------------------
% 1.52/1.27 % (6725)Success in time 0.004 s
%------------------------------------------------------------------------------