%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU528^2 : 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 : 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 09:35:06 AM UTC 2026
% Result : Theorem 1.56s 1.34s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 184 ( 37 ~; 16 |; 14 &; 100 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 30 !; 10 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f29,f23]) ).
thf(f23,plain,
sK2 != sK3,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( sK2 != sK3 )
& ( $true
= ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
& ( uniqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
=> ( ( sK2 != sK3 )
& ( $true
= ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( uniqinunit
=> ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( uniqinunit
=> ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.G3rQCU26J8/DTF2THF_23941.p',notinsingleton) ).
thf(f29,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true != $true )
| ( sK2 = sK3 ) ),
inference(superposition,[status(thm)],[f27,f22]) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f20,f21]) ).
thf(f21,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK1 != sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
& ( X2 != X3 ) )
=> ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox/tmp/tmp.G3rQCU26J8/DTF2THF_23941.p',uniqinunit) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU528^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n010.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:25:33 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SEU528^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.40 % Domain : Set Theory
% 0.16/0.40 % Problem : Preliminary Notions - Equality Laws
% 0.16/0.40 % Version : Especial > Reduced > Especial.
% 0.16/0.40 % English : (! x:i.! y:i.~(x = y) -> ~(in y (setadjoin x emptyset)))
% 0.16/0.40
% 0.16/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.40 % Source : [Bro08]
% 0.16/0.40 % Names : ZFC030l [Bro08]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % 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
% 0.16/0.40 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.16/0.40 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.40 % Number of connectives : 13 ( 2 ~; 0 |; 0 &; 8 @)
% 0.16/0.40 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 9 ( 5 avg)
% 0.16/0.40 % Number of types : 2 ( 0 usr)
% 0.16/0.40 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.16/0.40 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.16/0.40 % SPC : TH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : http://mathgate.info/detsetitem.php?id=437
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(in_type,type,
% 0.16/0.40 in: $i > $i > $o ).
% 0.16/0.40
% 0.16/0.40 thf(emptyset_type,type,
% 0.16/0.40 emptyset: $i ).
% 0.16/0.40
% 0.16/0.40 thf(setadjoin_type,type,
% 0.16/0.40 setadjoin: $i > $i > $i ).
% 0.16/0.40
% 0.16/0.40 thf(uniqinunit_type,type,
% 0.16/0.40 uniqinunit: $o ).
% 0.16/0.40
% 0.16/0.40 thf(uniqinunit,definition,
% 0.16/0.40 ( uniqinunit
% 0.16/0.40 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.40 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.40 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(notinsingleton,conjecture,
% 0.16/0.40 ( uniqinunit
% 0.16/0.40 => ! [Xx: $i,Xy: $i] :
% 0.16/0.40 ( ( Xx != Xy )
% 0.16/0.40 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.56/1.31 ---- Embedded in THF ---
% 1.56/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.31 %%% Generated on Tue Feb 24 12:25:34 EST 2026
% 1.56/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.31 %%% Logic specification used:
% 1.56/1.31 %%% thf(spec, logic, $$dhol).
% 1.56/1.31
% 1.56/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.G3rQCU26J8/DTF2DTF23941.p
% See solution above
% 1.56/1.31 ------------------------
% 1.56/1.32 ---- Cleaned THF ---
% 1.56/1.32 thf(in_type,type,
% 1.56/1.32 in: $i > $i > $o ).
% 1.56/1.32
% 1.56/1.32 thf(emptyset_type,type,
% 1.56/1.32 emptyset: $i ).
% 1.56/1.32
% 1.56/1.32 thf(setadjoin_type,type,
% 1.56/1.32 setadjoin: $i > $i > $i ).
% 1.56/1.32
% 1.56/1.32 thf(uniqinunit_type,type,
% 1.56/1.32 uniqinunit: $o ).
% 1.56/1.32
% 1.56/1.32 thf(uniqinunit,definition,
% 1.56/1.32 ( uniqinunit
% 1.56/1.32 = ( ! [Xx: $i,Xy: $i] :
% 1.56/1.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.56/1.32 => ( Xx = Xy ) ) ) ) ).
% 1.56/1.32
% 1.56/1.32 thf(notinsingleton,conjecture,
% 1.56/1.32 ( uniqinunit
% 1.56/1.32 => ! [Xx: $i,Xy: $i] :
% 1.56/1.32 ( ( Xx != Xy )
% 1.56/1.32 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ).
% 1.56/1.32 ------------------------
% 1.56/1.34 % (24041)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23941 for (2999ds/2Mi)
% 1.56/1.34 % (24043)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_23941 for (2999ds/275Mi)
% 1.56/1.34 % (24039)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_23941 for (2999ds/4Mi)
% 1.56/1.34 % (24044)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23941 for (2999ds/18Mi)
% 1.56/1.34 % (24038)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23941 for (2999ds/183Mi)
% 1.56/1.34 % (24042)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_23941 for (2999ds/2Mi)
% 1.56/1.34 % (24041)Instruction limit reached!
% 1.56/1.34 % (24041)------------------------------
% 1.56/1.34 % (24041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (24041)Termination reason: Unknown
% 1.56/1.34 % (24041)Termination phase: Saturation
% 1.56/1.34 % (24042)Instruction limit reached!
% 1.56/1.34 % (24042)------------------------------
% 1.56/1.34 % (24042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34
% 1.56/1.34 % (24041)Memory used [KB]: 5500
% 1.56/1.34 % (24041)Time elapsed: 0.003 s
% 1.56/1.34 % (24041)Instructions burned: 2 (million)
% 1.56/1.34 % (24041)------------------------------
% 1.56/1.34 % (24041)------------------------------
% 1.56/1.34 % (24042)Termination reason: Unknown
% 1.56/1.34 % (24042)Termination phase: Saturation
% 1.56/1.34
% 1.56/1.34 % (24042)Memory used [KB]: 5500
% 1.56/1.34 % (24042)Time elapsed: 0.003 s
% 1.56/1.34 % (24042)Instructions burned: 2 (million)
% 1.56/1.34 % (24042)------------------------------
% 1.56/1.34 % (24042)------------------------------
% 1.56/1.34 % (24043)First to succeed.
% 1.56/1.34 % (24044)Also succeeded, but the first one will report.
% 1.56/1.34 % (24040)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_23941 for (2999ds/27Mi)
% 1.56/1.34 % (24038)Also succeeded, but the first one will report.
% 1.56/1.34 % (24043)Refutation found. Thanks to Tanya!
% 1.56/1.34 % SZS status Theorem for DTF2THF_23941
% 1.56/1.34 % SZS output start Proof for DTF2THF_23941
% 1.56/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.34 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.56/1.34 thf(f30,plain,(
% 1.56/1.34 $false),
% 1.56/1.34 inference(subsumption_resolution,[status(thm)],[f29,f23])).
% 1.56/1.34 thf(f23,plain,(
% 1.56/1.34 (sK2 != sK3)),
% 1.56/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.34 thf(f17,plain,(
% 1.56/1.34 ((sK2 != sK3) & ($true = (in @ sK2 @ (setadjoin @ sK3 @ emptyset)))) & (uniqinunit = $true)),
% 1.56/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16])).
% 1.56/1.34 thf(f16,plain,(
% 1.56/1.34 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) => ((sK2 != sK3) & ($true = (in @ sK2 @ (setadjoin @ sK3 @ emptyset))))),
% 1.56/1.34 introduced(definition,[],[choice_axiom])).
% 1.56/1.34 thf(f10,plain,(
% 1.56/1.34 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) & (uniqinunit = $true)),
% 1.56/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.56/1.34 thf(f9,plain,(
% 1.56/1.34 ~((uniqinunit = $true) => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)))),
% 1.56/1.34 inference(flattening,[status(thm)],[f8])).
% 1.56/1.34 thf(f8,plain,(
% 1.56/1.34 ~((uniqinunit = $true) => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)))),
% 1.56/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.34 thf(f7,plain,(
% 1.56/1.34 ~(uniqinunit => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.56/1.34 inference(rectify,[status(thm)],[f3])).
% 1.56/1.34 thf(f3,negated_conjecture,(
% 1.56/1.34 ~(uniqinunit => ! [X1 : $i,X0 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.56/1.34 inference(negated_conjecture,[status(cth)],[f2])).
% 1.56/1.34 thf(f2,conjecture,(
% 1.56/1.34 uniqinunit => ! [X1 : $i,X0 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset)))),
% 1.56/1.34 file('/export/starexec/sandbox/tmp/tmp.G3rQCU26J8/DTF2THF_23941.p',notinsingleton)).
% 1.56/1.34 thf(f29,plain,(
% 1.56/1.34 (sK2 = sK3)),
% 1.56/1.34 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.56/1.34 thf(f28,plain,(
% 1.56/1.34 ($true != $true) | (sK2 = sK3)),
% 1.56/1.34 inference(superposition,[status(thm)],[f27,f22])).
% 1.56/1.34 thf(f22,plain,(
% 1.56/1.34 ($true = (in @ sK2 @ (setadjoin @ sK3 @ emptyset)))),
% 1.56/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.34 thf(f27,plain,(
% 1.56/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) )),
% 1.56/1.34 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.56/1.34 thf(f24,plain,(
% 1.56/1.34 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (X0 = X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true)) )),
% 1.56/1.34 inference(definition_unfolding,[status(thm)],[f20,f21])).
% 1.56/1.34 thf(f21,plain,(
% 1.56/1.34 (uniqinunit = $true)),
% 1.56/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.34 thf(f20,plain,(
% 1.56/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1) | (uniqinunit != $true)) )),
% 1.56/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 1.56/1.34 thf(f15,plain,(
% 1.56/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK1 != sK0)))),
% 1.56/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.56/1.34 thf(f14,plain,(
% 1.56/1.34 ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X2 @ emptyset))) & (X2 != X3)) => (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK1 != sK0))),
% 1.56/1.34 introduced(definition,[],[choice_axiom])).
% 1.56/1.34 thf(f13,plain,(
% 1.56/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X2 @ emptyset))) & (X2 != X3)))),
% 1.56/1.34 inference(rectify,[status(thm)],[f12])).
% 1.56/1.34 thf(f12,plain,(
% 1.56/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1)))),
% 1.56/1.34 inference(nnf_transformation,[status(thm)],[f11])).
% 1.56/1.34 thf(f11,plain,(
% 1.56/1.34 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) <=> (uniqinunit = $true)),
% 1.56/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 1.56/1.34 thf(f6,plain,(
% 1.56/1.34 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 1.56/1.34 inference(fool_elimination,[status(thm)],[f5])).
% 1.56/1.34 thf(f5,plain,(
% 1.56/1.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.56/1.34 inference(rectify,[status(thm)],[f1])).
% 1.56/1.34 thf(f1,axiom,(
% 1.56/1.34 (! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.56/1.34 file('/export/starexec/sandbox/tmp/tmp.G3rQCU26J8/DTF2THF_23941.p',uniqinunit)).
% 1.56/1.34 % SZS output end Proof for DTF2THF_23941
% 1.56/1.34 % (24043)------------------------------
% 1.56/1.34 % (24043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (24043)Termination reason: Refutation
% 1.56/1.34
% 1.56/1.34 % (24043)Memory used [KB]: 5500
% 1.56/1.34 % (24043)Time elapsed: 0.004 s
% 1.56/1.34 % (24043)Instructions burned: 2 (million)
% 1.56/1.34 % (24043)------------------------------
% 1.56/1.34 % (24043)------------------------------
% 1.56/1.34 % (24037)Success in time 0.019 s
%------------------------------------------------------------------------------