%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU514^2 : 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 : n025.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 09:35:01 AM UTC 2026
% Result : Theorem 0.32s 1.43s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 322 ( 103 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 355 ( 50 ~; 47 |; 30 &; 214 @)
% ( 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 : 60 ( 0 ^; 42 !; 18 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f37,f23]) ).
thf(f23,plain,
( $true
= ( in @ sK5 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setadjoinAx = $true )
& ( $true
!= ( in @ sK5 @ ( setadjoin @ sK3 @ sK4 ) ) )
& ( $true
= ( in @ sK5 @ sK4 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f9,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( $true
!= ( in @ sK5 @ ( setadjoin @ sK3 @ sK4 ) ) )
& ( $true
= ( in @ sK5 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( setadjoinAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setadjoinAx = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2HjOLh0nb5/DTF2THF_1323.p',setadjoinIR) ).
thf(f37,plain,
( $true
!= ( in @ sK5 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
!= ( in @ sK5 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f34]) ).
thf(f34,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f21,f25]) ).
thf(f25,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f21,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
| ( ( X0 != X1 )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ( X0 = X1 )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( sK1 != sK0 )
& ( ( in @ sK1 @ sK2 )
!= $true ) )
| ( ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) )
!= $true ) )
& ( ( sK1 = sK0 )
| ( ( in @ sK1 @ sK2 )
= $true )
| ( ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( X3 != X4 )
& ( ( in @ X4 @ X5 )
!= $true ) )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true ) )
& ( ( X3 = X4 )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true ) ) )
=> ( ( ( ( sK1 != sK0 )
& ( ( in @ sK1 @ sK2 )
!= $true ) )
| ( ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) )
!= $true ) )
& ( ( sK1 = sK0 )
| ( ( in @ sK1 @ sK2 )
= $true )
| ( ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
| ( ( X0 != X1 )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ( X0 = X1 )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( X3 != X4 )
& ( ( in @ X4 @ X5 )
!= $true ) )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true ) )
& ( ( X3 = X4 )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( X0 != X2 )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( ( X0 != X2 )
& ( $true
!= ( in @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( X0 != X2 )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( ( X0 != X2 )
& ( $true
!= ( in @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
<=> ( ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X0 @ X1 )
| ( X0 = X2 ) )
<=> ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( ( in @ X2 @ X1 )
| ( X0 = X2 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox/tmp/tmp.2HjOLh0nb5/DTF2THF_1323.p',setadjoinAx) ).
thf(f24,plain,
( $true
!= ( in @ sK5 @ ( setadjoin @ sK3 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU514^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n025.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
% 0.17/0.35 % DateTime : Tue Feb 24 12:25:27 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEU514^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.48 % Domain : Set Theory
% 0.20/0.48 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.20/0.48 % Version : Especial > Reduced > Especial.
% 0.20/0.48 % English : (! x:i.! A:i.! y:i.in y A -> in y (setadjoin x A))
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.48 % Source : [Bro08]
% 0.20/0.48 % Names : ZFC016l [Bro08]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % 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 v3.7.0
% 0.20/0.48 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.48 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 3 ( 4 avg)
% 0.20/0.48 % Number of connectives : 16 ( 0 ~; 1 |; 0 &; 12 @)
% 0.20/0.48 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 9 ( 5 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : http://mathgate.info/detsetitem.php?id=81
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(in_type,type,
% 0.20/0.48 in: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoin_type,type,
% 0.20/0.48 setadjoin: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinAx_type,type,
% 0.20/0.48 setadjoinAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinAx,definition,
% 0.20/0.48 ( setadjoinAx
% 0.20/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.48 <=> ( ( Xy = Xx )
% 0.20/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinIR,conjecture,
% 0.20/0.48 ( setadjoinAx
% 0.20/0.48 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ A )
% 0.20/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 12:25:28 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2HjOLh0nb5/DTF2DTF1323.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.41 ---- Cleaned THF ---
% 0.32/1.41 thf(in_type,type,
% 0.32/1.41 in: $i > $i > $o ).
% 0.32/1.41
% 0.32/1.41 thf(setadjoin_type,type,
% 0.32/1.41 setadjoin: $i > $i > $i ).
% 0.32/1.41
% 0.32/1.41 thf(setadjoinAx_type,type,
% 0.32/1.41 setadjoinAx: $o ).
% 0.32/1.41
% 0.32/1.41 thf(setadjoinAx,definition,
% 0.32/1.41 ( setadjoinAx
% 0.32/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.41 <=> ( ( Xy = Xx )
% 0.32/1.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.41
% 0.32/1.41 thf(setadjoinIR,conjecture,
% 0.32/1.41 ( setadjoinAx
% 0.32/1.41 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.41 ( ( in @ Xy @ A )
% 0.32/1.41 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.32/1.41 ------------------------
% 0.32/1.43 % (1421)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1323 for (3000ds/183Mi)
% 0.32/1.43 % (1424)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1323 for (3000ds/2Mi)
% 0.32/1.43 % (1422)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_1323 for (3000ds/4Mi)
% 0.32/1.43 % (1423)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_1323 for (3000ds/27Mi)
% 0.32/1.43 % (1425)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_1323 for (3000ds/2Mi)
% 0.32/1.43 % (1426)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_1323 for (3000ds/275Mi)
% 0.32/1.43 % (1427)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1323 for (3000ds/18Mi)
% 0.32/1.43 % (1424)Instruction limit reached!
% 0.32/1.43 % (1424)------------------------------
% 0.32/1.43 % (1424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (1424)Termination reason: Unknown
% 0.32/1.43 % (1424)Termination phase: Saturation
% 0.32/1.43 % (1425)Instruction limit reached!
% 0.32/1.43 % (1425)------------------------------
% 0.32/1.43 % (1425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (1425)Termination reason: Unknown
% 0.32/1.43 % (1425)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (1425)Memory used [KB]: 5500
% 0.32/1.43 % (1425)Time elapsed: 0.003 s
% 0.32/1.43 % (1425)Instructions burned: 2 (million)
% 0.32/1.43 % (1425)------------------------------
% 0.32/1.43 % (1425)------------------------------
% 0.32/1.43
% 0.32/1.43 % (1424)Memory used [KB]: 5500
% 0.32/1.43 % (1424)Time elapsed: 0.003 s
% 0.32/1.43 % (1424)Instructions burned: 2 (million)
% 0.32/1.43 % (1424)------------------------------
% 0.32/1.43 % (1424)------------------------------
% 0.32/1.43 % (1422)Instruction limit reached!
% 0.32/1.43 % (1422)------------------------------
% 0.32/1.43 % (1422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (1426)First to succeed.
% 0.32/1.43 % (1422)Termination reason: Unknown
% 0.32/1.43 % (1422)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (1422)Memory used [KB]: 5500
% 0.32/1.43 % (1422)Time elapsed: 0.004 s
% 0.32/1.43 % (1422)Instructions burned: 4 (million)
% 0.32/1.43 % (1422)------------------------------
% 0.32/1.43 % (1422)------------------------------
% 0.32/1.43 % (1421)Also succeeded, but the first one will report.
% 0.32/1.43 % (1423)Also succeeded, but the first one will report.
% 0.32/1.43 % (1426)Refutation found. Thanks to Tanya!
% 0.32/1.43 % SZS status Theorem for DTF2THF_1323
% 0.32/1.43 % SZS output start Proof for DTF2THF_1323
% 0.32/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.43 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 0.32/1.43 thf(f38,plain,(
% 0.32/1.43 $false),
% 0.32/1.43 inference(subsumption_resolution,[status(thm)],[f37,f23])).
% 0.32/1.43 thf(f23,plain,(
% 0.32/1.43 ($true = (in @ sK5 @ sK4))),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.43 thf(f16,plain,(
% 0.32/1.43 (setadjoinAx = $true) & (($true != (in @ sK5 @ (setadjoin @ sK3 @ sK4))) & ($true = (in @ sK5 @ sK4)))),
% 0.32/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f9,f15])).
% 0.32/1.43 thf(f15,plain,(
% 0.32/1.43 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ X1)) != $true) & ((in @ X2 @ X1) = $true)) => (($true != (in @ sK5 @ (setadjoin @ sK3 @ sK4))) & ($true = (in @ sK5 @ sK4)))),
% 0.32/1.43 introduced(definition,[],[choice_axiom])).
% 0.32/1.43 thf(f9,plain,(
% 0.32/1.43 (setadjoinAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ X1)) != $true) & ((in @ X2 @ X1) = $true))),
% 0.32/1.43 inference(ennf_transformation,[status(thm)],[f8])).
% 0.32/1.43 thf(f8,plain,(
% 0.32/1.43 ~((setadjoinAx = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ (setadjoin @ X0 @ X1)) = $true)))),
% 0.32/1.43 inference(fool_elimination,[status(thm)],[f7])).
% 0.32/1.43 thf(f7,plain,(
% 0.32/1.43 ~(setadjoinAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 0.32/1.43 inference(rectify,[status(thm)],[f3])).
% 0.32/1.43 thf(f3,negated_conjecture,(
% 0.32/1.43 ~(setadjoinAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 0.32/1.43 inference(negated_conjecture,[status(cth)],[f2])).
% 0.32/1.43 thf(f2,conjecture,(
% 0.32/1.43 setadjoinAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1)))),
% 0.32/1.43 file('/export/starexec/sandbox/tmp/tmp.2HjOLh0nb5/DTF2THF_1323.p',setadjoinIR)).
% 0.32/1.43 thf(f37,plain,(
% 0.32/1.43 ($true != (in @ sK5 @ sK4))),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.32/1.43 thf(f36,plain,(
% 0.32/1.43 ($true != (in @ sK5 @ sK4)) | ($true != $true)),
% 0.32/1.43 inference(superposition,[status(thm)],[f24,f34])).
% 0.32/1.43 thf(f34,plain,(
% 0.32/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) | ((in @ X1 @ X2) != $true)) )),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 0.32/1.43 thf(f27,plain,(
% 0.32/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) | ((in @ X1 @ X2) != $true)) )),
% 0.32/1.43 inference(definition_unfolding,[status(thm)],[f21,f25])).
% 0.32/1.43 thf(f25,plain,(
% 0.32/1.43 (setadjoinAx = $true)),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.43 thf(f21,plain,(
% 0.32/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) | ((in @ X1 @ X2) != $true) | (setadjoinAx != $true)) )),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.43 thf(f14,plain,(
% 0.32/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) | ((X0 != X1) & ((in @ X1 @ X2) != $true))) & ((X0 = X1) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ((((sK1 != sK0) & ((in @ sK1 @ sK2) != $true)) | ((in @ sK1 @ (setadjoin @ sK0 @ sK2)) != $true)) & ((sK1 = sK0) | ((in @ sK1 @ sK2) = $true) | ((in @ sK1 @ (setadjoin @ sK0 @ sK2)) = $true))))),
% 0.32/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13])).
% 0.32/1.43 thf(f13,plain,(
% 0.32/1.43 ? [X3 : $i,X4 : $i,X5 : $i] : ((((X3 != X4) & ((in @ X4 @ X5) != $true)) | ((in @ X4 @ (setadjoin @ X3 @ X5)) != $true)) & ((X3 = X4) | ((in @ X4 @ X5) = $true) | ((in @ X4 @ (setadjoin @ X3 @ X5)) = $true))) => ((((sK1 != sK0) & ((in @ sK1 @ sK2) != $true)) | ((in @ sK1 @ (setadjoin @ sK0 @ sK2)) != $true)) & ((sK1 = sK0) | ((in @ sK1 @ sK2) = $true) | ((in @ sK1 @ (setadjoin @ sK0 @ sK2)) = $true)))),
% 0.32/1.43 introduced(definition,[],[choice_axiom])).
% 0.32/1.43 thf(f12,plain,(
% 0.32/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) | ((X0 != X1) & ((in @ X1 @ X2) != $true))) & ((X0 = X1) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((X3 != X4) & ((in @ X4 @ X5) != $true)) | ((in @ X4 @ (setadjoin @ X3 @ X5)) != $true)) & ((X3 = X4) | ((in @ X4 @ X5) = $true) | ((in @ X4 @ (setadjoin @ X3 @ X5)) = $true))))),
% 0.32/1.43 inference(rectify,[status(thm)],[f11])).
% 0.32/1.43 thf(f11,plain,(
% 0.32/1.43 (! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | ((X0 != X2) & ($true != (in @ X0 @ X1)))) & ((X0 = X2) | ($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1))))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((X0 != X2) & ($true != (in @ X0 @ X1))) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & ((X0 = X2) | ($true = (in @ X0 @ X1)) | ($true = (in @ X0 @ (setadjoin @ X2 @ X1))))))),
% 0.32/1.43 inference(flattening,[status(thm)],[f10])).
% 0.32/1.43 thf(f10,plain,(
% 0.32/1.43 (! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | ((X0 != X2) & ($true != (in @ X0 @ X1)))) & (((X0 = X2) | ($true = (in @ X0 @ X1))) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1))))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((X0 != X2) & ($true != (in @ X0 @ X1))) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & (((X0 = X2) | ($true = (in @ X0 @ X1))) | ($true = (in @ X0 @ (setadjoin @ X2 @ X1))))))),
% 0.32/1.43 inference(nnf_transformation,[status(thm)],[f6])).
% 0.32/1.43 thf(f6,plain,(
% 0.32/1.43 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) <=> ((X0 = X2) | ($true = (in @ X0 @ X1)))) <=> (setadjoinAx = $true)),
% 0.32/1.43 inference(fool_elimination,[status(thm)],[f5])).
% 0.32/1.43 thf(f5,plain,(
% 0.32/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) | (X0 = X2)) <=> (in @ X0 @ (setadjoin @ X2 @ X1))) = setadjoinAx)),
% 0.32/1.43 inference(rectify,[status(thm)],[f1])).
% 0.32/1.43 thf(f1,axiom,(
% 0.32/1.43 (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) | (X0 = X2)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinAx)),
% 0.32/1.43 file('/export/starexec/sandbox/tmp/tmp.2HjOLh0nb5/DTF2THF_1323.p',setadjoinAx)).
% 0.32/1.43 thf(f24,plain,(
% 0.32/1.43 ($true != (in @ sK5 @ (setadjoin @ sK3 @ sK4)))),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.43 % SZS output end Proof for DTF2THF_1323
% 0.32/1.43 % (1426)------------------------------
% 0.32/1.43 % (1426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (1426)Termination reason: Refutation
% 0.32/1.43
% 0.32/1.43 % (1426)Memory used [KB]: 5500
% 0.32/1.43 % (1426)Time elapsed: 0.005 s
% 0.32/1.43 % (1426)Instructions burned: 2 (million)
% 0.32/1.43 % (1426)------------------------------
% 0.32/1.43 % (1426)------------------------------
% 0.32/1.43 % (1420)Success in time 0.018 s
%------------------------------------------------------------------------------