%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU516^2 : 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 : n018.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 09:35:02 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 369 ( 126 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 393 ( 57 ~; 56 |; 40 &; 226 @)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 42 !; 24 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(f44,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f43,f20]) ).
thf(f20,plain,
sK0 != sK2,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
= $true )
& ( sK0 != sK2 )
& ( setadjoinAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
& ( X0 != X2 ) )
=> ( ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
= $true )
& ( sK0 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
& ( X0 != X2 ) )
& ( setadjoinAx = $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
& ( X1 != X2 ) )
& ( setadjoinAx = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 )
& ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) )
& ( setadjoinAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( setadjoinAx = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
=> ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
=> ( ( X1 = X2 )
| ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X0 = X2 )
| ( in @ X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X0 = X2 )
| ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bnyOsRoS3x/DTF2THF_11950.p',setadjoinOr) ).
thf(f43,plain,
sK0 = sK2,
inference(subsumption_resolution,[status(thm)],[f42,f22]) ).
thf(f22,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f42,plain,
( ( ( in @ sK0 @ sK1 )
= $true )
| ( sK0 = sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( sK0 = sK2 )
| ( $true != $true )
| ( ( in @ sK0 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f36,f21]) ).
thf(f21,plain,
( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f36,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true )
| ( X1 = X2 ) ),
inference(definition_unfolding,[status(thm)],[f26,f19]) ).
thf(f19,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f26,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( ( ( in @ X2 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( ( in @ sK5 @ sK3 )
!= $true )
& ( sK5 != sK4 ) )
| ( ( in @ sK5 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true ) )
& ( ( ( in @ sK5 @ sK3 )
= $true )
| ( sK5 = sK4 )
| ( ( in @ sK5 @ ( setadjoin @ sK4 @ sK3 ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f17]) ).
thf(f17,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( ( in @ X5 @ X3 )
!= $true )
& ( X4 != X5 ) )
| ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
!= $true ) )
& ( ( ( in @ X5 @ X3 )
= $true )
| ( X4 = X5 )
| ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
= $true ) ) )
=> ( ( ( ( ( in @ sK5 @ sK3 )
!= $true )
& ( sK5 != sK4 ) )
| ( ( in @ sK5 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true ) )
& ( ( ( in @ sK5 @ sK3 )
= $true )
| ( sK5 = sK4 )
| ( ( in @ sK5 @ ( setadjoin @ sK4 @ sK3 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( ( ( in @ X2 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( ( in @ X5 @ X3 )
!= $true )
& ( X4 != X5 ) )
| ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
!= $true ) )
& ( ( ( in @ X5 @ X3 )
= $true )
| ( X4 = X5 )
| ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( X0 != X2 ) ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( ( ( in @ X0 @ X1 )
!= $true )
& ( X0 != X2 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( X0 != X2 ) ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( ( ( in @ X0 @ X1 )
!= $true )
& ( X0 != X2 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
<=> ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
<=> ( ( X0 = X2 )
| ( in @ X0 @ X1 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( X0 = X2 )
| ( in @ X2 @ X1 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox2/tmp/tmp.bnyOsRoS3x/DTF2THF_11950.p',setadjoinAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU516^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:25:16 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU516^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.20/0.45 % Version : Especial > Reduced > Especial.
% 0.20/0.45 % English : (! x:i.! A:i.! y:i.in y (setadjoin x A) -> y = x | in y A)
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC018l [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.20/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.45 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.45 % Number of connectives : 17 ( 0 ~; 2 |; 0 &; 12 @)
% 0.20/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 9 ( 5 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=457
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoin_type,type,
% 0.20/0.45 setadjoin: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx_type,type,
% 0.20/0.45 setadjoinAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx,definition,
% 0.20/0.45 ( setadjoinAx
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 <=> ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinOr,conjecture,
% 0.20/0.45 ( setadjoinAx
% 0.20/0.45 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 => ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:25:16 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.bnyOsRoS3x/DTF2DTF11950.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(in_type,type,
% 1.49/1.26 in: $i > $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(setadjoin_type,type,
% 1.49/1.26 setadjoin: $i > $i > $i ).
% 1.49/1.26
% 1.49/1.26 thf(setadjoinAx_type,type,
% 1.49/1.26 setadjoinAx: $o ).
% 1.49/1.26
% 1.49/1.26 thf(setadjoinAx,definition,
% 1.49/1.26 ( setadjoinAx
% 1.49/1.26 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.49/1.26 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.49/1.26 <=> ( ( Xy = Xx )
% 1.49/1.26 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf(setadjoinOr,conjecture,
% 1.49/1.26 ( setadjoinAx
% 1.49/1.26 => ! [Xx: $i,A: $i,Xy: $i] :
% 1.49/1.26 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.49/1.26 => ( ( Xy = Xx )
% 1.49/1.26 | ( in @ Xy @ A ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (12119)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_11950 for (3000ds/2Mi)
% 1.49/1.27 % (12120)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_11950 for (3000ds/275Mi)
% 1.49/1.27 % (12116)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_11950 for (3000ds/4Mi)
% 1.49/1.27 % (12119)Instruction limit reached!
% 1.49/1.27 % (12119)------------------------------
% 1.49/1.27 % (12119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (12119)Termination reason: Unknown
% 1.49/1.27 % (12119)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (12119)Memory used [KB]: 5500
% 1.49/1.27 % (12119)Time elapsed: 0.003 s
% 1.49/1.27 % (12119)Instructions burned: 3 (million)
% 1.49/1.27 % (12119)------------------------------
% 1.49/1.27 % (12119)------------------------------
% 1.49/1.27 % (12120)First to succeed.
% 1.49/1.27 % (12116)Instruction limit reached!
% 1.49/1.27 % (12116)------------------------------
% 1.49/1.27 % (12116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (12116)Termination reason: Unknown
% 1.49/1.27 % (12116)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (12116)Memory used [KB]: 5500
% 1.49/1.27 % (12116)Time elapsed: 0.003 s
% 1.49/1.27 % (12116)Instructions burned: 4 (million)
% 1.49/1.27 % (12116)------------------------------
% 1.49/1.27 % (12116)------------------------------
% 1.49/1.27 % (12120)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_11950
% 1.49/1.27 % SZS output start Proof for DTF2THF_11950
% 1.49/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.49/1.27 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.49/1.27 thf(f44,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f43,f20])).
% 1.49/1.27 thf(f20,plain,(
% 1.49/1.27 (sK0 != sK2)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 (((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (setadjoin @ sK2 @ sK1)) = $true) & (sK0 != sK2)) & (setadjoinAx = $true)),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ($true = (in @ X0 @ (setadjoin @ X2 @ X1))) & (X0 != X2)) => (((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (setadjoin @ sK2 @ sK1)) = $true) & (sK0 != sK2))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ($true = (in @ X0 @ (setadjoin @ X2 @ X1))) & (X0 != X2)) & (setadjoinAx = $true)),
% 1.49/1.27 inference(rectify,[status(thm)],[f10])).
% 1.49/1.27 thf(f10,plain,(
% 1.49/1.27 ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) & ((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) & (X1 != X2)) & (setadjoinAx = $true)),
% 1.49/1.27 inference(flattening,[status(thm)],[f9])).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0) != $true) & (X1 != X2)) & ((in @ X1 @ (setadjoin @ X2 @ X0)) = $true)) & (setadjoinAx = $true)),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.27 thf(f6,plain,(
% 1.49/1.27 ~((setadjoinAx = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) => (((in @ X1 @ X0) = $true) | (X1 = X2))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,plain,(
% 1.49/1.27 ~(setadjoinAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ X0)) => ((X1 = X2) | (in @ X1 @ X0))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f3])).
% 1.49/1.27 thf(f3,negated_conjecture,(
% 1.49/1.27 ~(setadjoinAx => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((X0 = X2) | (in @ X2 @ X1))))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.49/1.27 thf(f2,conjecture,(
% 1.49/1.27 setadjoinAx => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((X0 = X2) | (in @ X2 @ X1)))),
% 1.49/1.27 file('/export/starexec/sandbox2/tmp/tmp.bnyOsRoS3x/DTF2THF_11950.p',setadjoinOr)).
% 1.49/1.27 thf(f43,plain,(
% 1.49/1.27 (sK0 = sK2)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f42,f22])).
% 1.49/1.27 thf(f22,plain,(
% 1.49/1.27 ((in @ sK0 @ sK1) != $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.27 thf(f42,plain,(
% 1.49/1.27 ((in @ sK0 @ sK1) = $true) | (sK0 = sK2)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.49/1.27 thf(f39,plain,(
% 1.49/1.27 (sK0 = sK2) | ($true != $true) | ((in @ sK0 @ sK1) = $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f36,f21])).
% 1.49/1.27 thf(f21,plain,(
% 1.49/1.27 ((in @ sK0 @ (setadjoin @ sK2 @ sK1)) = $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.27 thf(f36,plain,(
% 1.49/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ X0)) != $true) | ((in @ X2 @ X0) = $true) | (X1 = X2)) )),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.49/1.27 thf(f31,plain,(
% 1.49/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true) | (X1 = X2)) )),
% 1.49/1.27 inference(definition_unfolding,[status(thm)],[f26,f19])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 (setadjoinAx = $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.27 thf(f26,plain,(
% 1.49/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | (X1 = X2) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true) | (setadjoinAx != $true)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ X0)) = $true) | (((in @ X2 @ X0) != $true) & (X1 != X2))) & (((in @ X2 @ X0) = $true) | (X1 = X2) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | (((((in @ sK5 @ sK3) != $true) & (sK5 != sK4)) | ((in @ sK5 @ (setadjoin @ sK4 @ sK3)) != $true)) & (((in @ sK5 @ sK3) = $true) | (sK5 = sK4) | ((in @ sK5 @ (setadjoin @ sK4 @ sK3)) = $true))))),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f17])).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 ? [X3 : $i,X4 : $i,X5 : $i] : (((((in @ X5 @ X3) != $true) & (X4 != X5)) | ((in @ X5 @ (setadjoin @ X4 @ X3)) != $true)) & (((in @ X5 @ X3) = $true) | (X4 = X5) | ((in @ X5 @ (setadjoin @ X4 @ X3)) = $true))) => (((((in @ sK5 @ sK3) != $true) & (sK5 != sK4)) | ((in @ sK5 @ (setadjoin @ sK4 @ sK3)) != $true)) & (((in @ sK5 @ sK3) = $true) | (sK5 = sK4) | ((in @ sK5 @ (setadjoin @ sK4 @ sK3)) = $true)))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ X0)) = $true) | (((in @ X2 @ X0) != $true) & (X1 != X2))) & (((in @ X2 @ X0) = $true) | (X1 = X2) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((((in @ X5 @ X3) != $true) & (X4 != X5)) | ((in @ X5 @ (setadjoin @ X4 @ X3)) != $true)) & (((in @ X5 @ X3) = $true) | (X4 = X5) | ((in @ X5 @ (setadjoin @ X4 @ X3)) = $true))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f15])).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 (! [X1 : $i,X2 : $i,X0 : $i] : ((($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (((in @ X0 @ X1) != $true) & (X0 != X2))) & (((in @ X0 @ X1) = $true) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1))))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((((in @ X0 @ X1) != $true) & (X0 != X2)) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & (((in @ X0 @ X1) = $true) | (X0 = X2) | ($true = (in @ X0 @ (setadjoin @ X2 @ X1))))))),
% 1.49/1.27 inference(flattening,[status(thm)],[f14])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 (! [X1 : $i,X2 : $i,X0 : $i] : ((($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (((in @ X0 @ X1) != $true) & (X0 != X2))) & ((((in @ X0 @ X1) = $true) | (X0 = X2)) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1))))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((((in @ X0 @ X1) != $true) & (X0 != X2)) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & ((((in @ X0 @ X1) = $true) | (X0 = X2)) | ($true = (in @ X0 @ (setadjoin @ X2 @ X1))))))),
% 1.49/1.27 inference(nnf_transformation,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) <=> (((in @ X0 @ X1) = $true) | (X0 = X2))) <=> (setadjoinAx = $true)),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X2 @ X1)) <=> ((X0 = X2) | (in @ X0 @ X1))) = setadjoinAx)),
% 1.49/1.27 inference(rectify,[status(thm)],[f1])).
% 1.49/1.27 thf(f1,axiom,(
% 1.49/1.27 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) <=> ((X0 = X2) | (in @ X2 @ X1))) = setadjoinAx)),
% 1.49/1.27 file('/export/starexec/sandbox2/tmp/tmp.bnyOsRoS3x/DTF2THF_11950.p',setadjoinAx)).
% 1.49/1.27 % SZS output end Proof for DTF2THF_11950
% 1.49/1.27 % (12120)------------------------------
% 1.49/1.27 % (12120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (12120)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (12120)Memory used [KB]: 5500
% 1.49/1.27 % (12120)Time elapsed: 0.004 s
% 1.49/1.27 % (12120)Instructions burned: 3 (million)
% 1.49/1.27 % (12120)------------------------------
% 1.49/1.27 % (12120)------------------------------
% 1.49/1.27 % (12114)Success in time 0.012 s
%------------------------------------------------------------------------------