%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU515^2 : 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 : 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 09:35:01 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 17 unt; 0 typ; 3 def)
% Number of atoms : 342 ( 114 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 342 ( 32 ~; 45 |; 22 &; 197 @)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 11 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 18 ^; 46 !; 14 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f44,f49,f65]) ).
thf(f65,plain,
( spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| spl4_1
| spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f63,f38]) ).
thf(f38,plain,
( ( $true
!= ( in @ sK1 @ sK2 ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl4_1
<=> ( $true
= ( in @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( in @ sK1 @ sK2 ) )
| spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f56,f48]) ).
thf(f48,plain,
( ( sK1 != sK0 )
| spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl4_3
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f56,plain,
( ( sK1 = sK0 )
| ( $true
= ( in @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( sK1 = sK0 )
| ( $true = $false )
| ( $true
= ( in @ sK1 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f34,f14]) ).
thf(f14,plain,
( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setadjoinAx = $true )
& ( $true != sK3 )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( ( $true = sK3 )
| ( sK1 != sK0 ) )
& ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X2 ) ) )
& ( ( $true = X3 )
| ( X0 != X1 ) ) )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
=> ( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( ( $true = X3 )
| ( sK1 != sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( ( $true = X3 )
| ( sK1 != sK0 ) ) )
=> ( ( $true != sK3 )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( ( $true = sK3 )
| ( sK1 != sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( setadjoinAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X2 ) ) )
& ( ( $true = X3 )
| ( X0 != X1 ) ) )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X2 ) ) )
& ( ( $true = X3 )
| ( X0 != X1 ) ) )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
& ( setadjoinAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setadjoinAx = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X1 @ X2 )
=> X3 )
=> X3 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9NwOnxxYIT/DTF2THF_11910.p',setadjoinE) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
| ( X1 = X2 )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
| ( $true
= ( X2 = X1 ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ X3 )
| ( X2 = X1 ) ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
| ( X2 = X1 ) )
= ( in @ X1 @ ( setadjoin @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X3 ) )
= ( ( in @ X1 @ X3 )
| ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ Y0 ) )
= ( ( in @ X1 @ Y0 )
| ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ Y0 ) )
= ( ( in @ X1 @ Y0 )
| ( X2 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ X1 @ Y1 )
| ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ X1 @ Y1 )
| ( Y0 = X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ Y2 ) )
= ( ( in @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ Y2 ) )
= ( ( in @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f18]) ).
thf(f18,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f19,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ Y2 ) )
= ( ( in @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ Y2 ) )
= ( ( in @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
<=> ( ( X1 = X2 )
| ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinAx
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( X0 = X2 )
| ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9NwOnxxYIT/DTF2THF_11910.p',setadjoinAx) ).
thf(f49,plain,
( spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f15,f46,f40]) ).
thf(f40,definition,
( spl4_2
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f15,plain,
( ( $true = sK3 )
| ( sK1 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f44,plain,
~ spl4_2,
inference(avatar_split_clause,[status(thm)],[f17,f40]) ).
thf(f17,plain,
$true != sK3,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f43,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f16,f40,f36]) ).
thf(f16,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU515^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU515^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.29/0.45 % Version : Especial > Reduced > Especial.
% 0.29/0.45 % English : (! x:i.! A:i.! y:i.in y (setadjoin x A) -> (! phi:o.(y = x -> phi)
% 0.29/0.45 % -> (in y A -> phi) -> phi))
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.45 % Source : [Bro08]
% 0.29/0.45 % Names : ZFC017l [Bro08]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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
% 0.29/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.29/0.45 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.45 % Number of connectives : 20 ( 0 ~; 1 |; 0 &; 12 @)
% 0.29/0.45 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 12 ( 7 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : http://mathgate.info/detsetitem.php?id=82
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(in_type,type,
% 0.29/0.45 in: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin_type,type,
% 0.29/0.45 setadjoin: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx_type,type,
% 0.29/0.45 setadjoinAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx,definition,
% 0.29/0.45 ( setadjoinAx
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 <=> ( ( Xy = Xx )
% 0.29/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinE,conjecture,
% 0.29/0.45 ( setadjoinAx
% 0.29/0.45 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 => ! [Xphi: $o] :
% 0.29/0.45 ( ( ( Xy = Xx )
% 0.29/0.45 => Xphi )
% 0.29/0.45 => ( ( ( in @ Xy @ A )
% 0.29/0.45 => Xphi )
% 0.29/0.45 => Xphi ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 12:25:16 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9NwOnxxYIT/DTF2DTF11910.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(in_type,type,
% 1.47/1.29 in: $i > $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(setadjoin_type,type,
% 1.47/1.29 setadjoin: $i > $i > $i ).
% 1.47/1.29
% 1.47/1.29 thf(setadjoinAx_type,type,
% 1.47/1.29 setadjoinAx: $o ).
% 1.47/1.29
% 1.47/1.29 thf(setadjoinAx,definition,
% 1.47/1.29 ( setadjoinAx
% 1.47/1.29 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.47/1.29 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.47/1.29 <=> ( ( Xy = Xx )
% 1.47/1.29 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(setadjoinE,conjecture,
% 1.47/1.29 ( setadjoinAx
% 1.47/1.29 => ! [Xx: $i,A: $i,Xy: $i] :
% 1.47/1.29 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.47/1.29 => ! [Xphi: $o] :
% 1.47/1.29 ( ( ( Xy = Xx )
% 1.47/1.29 => Xphi )
% 1.47/1.29 => ( ( ( in @ Xy @ A )
% 1.47/1.29 => Xphi )
% 1.47/1.29 => Xphi ) ) ) ) ).
% 1.47/1.29 ------------------------
% 1.64/1.30 % (12099)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_11910 for (2999ds/4Mi)
% 1.64/1.30 % (12098)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/183Mi)
% 1.64/1.30 % (12103)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_11910 for (2999ds/275Mi)
% 1.64/1.30 % (12101)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11910 for (2999ds/2Mi)
% 1.64/1.30 % (12099)Instruction limit reached!
% 1.64/1.30 % (12099)------------------------------
% 1.64/1.30 % (12099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (12099)Termination reason: Unknown
% 1.64/1.30 % (12099)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (12099)Memory used [KB]: 5500
% 1.64/1.30 % (12099)Time elapsed: 0.003 s
% 1.64/1.30 % (12099)Instructions burned: 4 (million)
% 1.64/1.30 % (12099)------------------------------
% 1.64/1.30 % (12099)------------------------------
% 1.64/1.30 % (12101)Instruction limit reached!
% 1.64/1.30 % (12101)------------------------------
% 1.64/1.30 % (12101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (12101)Termination reason: Unknown
% 1.64/1.30 % (12101)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (12101)Memory used [KB]: 895
% 1.64/1.30 % (12101)Time elapsed: 0.002 s
% 1.64/1.30 % (12101)Instructions burned: 2 (million)
% 1.64/1.30 % (12101)------------------------------
% 1.64/1.30 % (12101)------------------------------
% 1.64/1.30 % (12098)First to succeed.
% 1.64/1.31 % (12103)Also succeeded, but the first one will report.
% 1.64/1.31 % (12098)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_11910
% 1.64/1.31 % SZS output start Proof for DTF2THF_11910
% 1.64/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.31 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.64/1.31 thf(f66,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(avatar_sat_refutation,[status(thm)],[f43,f44,f49,f65])).
% 1.64/1.31 thf(f65,plain,(
% 1.64/1.31 spl4_1 | spl4_3),
% 1.64/1.31 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.64/1.31 thf(f64,plain,(
% 1.64/1.31 $false | (spl4_1 | spl4_3)),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f63,f38])).
% 1.64/1.31 thf(f38,plain,(
% 1.64/1.31 ($true != (in @ sK1 @ sK2)) | spl4_1),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.64/1.31 thf(f36,definition,(
% 1.64/1.31 spl4_1 <=> ($true = (in @ sK1 @ sK2))),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.64/1.31 thf(f63,plain,(
% 1.64/1.31 ($true = (in @ sK1 @ sK2)) | spl4_3),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f56,f48])).
% 1.64/1.31 thf(f48,plain,(
% 1.64/1.31 (sK1 != sK0) | spl4_3),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.64/1.31 thf(f46,definition,(
% 1.64/1.31 spl4_3 <=> (sK1 = sK0)),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.64/1.31 thf(f56,plain,(
% 1.64/1.31 (sK1 = sK0) | ($true = (in @ sK1 @ sK2))),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.64/1.31 thf(f50,plain,(
% 1.64/1.31 (sK1 = sK0) | ($true = $false) | ($true = (in @ sK1 @ sK2))),
% 1.64/1.31 inference(superposition,[status(thm)],[f34,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ($true = (in @ sK1 @ (setadjoin @ sK0 @ sK2)))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 (setadjoinAx = $true) & ((($true != sK3) & (($true = sK3) | ($true != (in @ sK1 @ sK2))) & (($true = sK3) | (sK1 != sK0))) & ($true = (in @ sK1 @ (setadjoin @ sK0 @ sK2))))),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ X1 @ X2))) & (($true = X3) | (X0 != X1))) & ($true = (in @ X1 @ (setadjoin @ X0 @ X2)))) => (? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ sK1 @ sK2))) & (($true = X3) | (sK1 != sK0))) & ($true = (in @ sK1 @ (setadjoin @ sK0 @ sK2))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 ? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ sK1 @ sK2))) & (($true = X3) | (sK1 != sK0))) => (($true != sK3) & (($true = sK3) | ($true != (in @ sK1 @ sK2))) & (($true = sK3) | (sK1 != sK0)))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 (setadjoinAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ X1 @ X2))) & (($true = X3) | (X0 != X1))) & ($true = (in @ X1 @ (setadjoin @ X0 @ X2))))),
% 1.64/1.31 inference(flattening,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : ((($true != X3) & (($true = X3) | ($true != (in @ X1 @ X2)))) & (($true = X3) | (X0 != X1))) & ($true = (in @ X1 @ (setadjoin @ X0 @ X2)))) & (setadjoinAx = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 ~((setadjoinAx = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) => ! [X3 : $o] : (((X0 = X1) => ($true = X3)) => ((($true = (in @ X1 @ X2)) => ($true = X3)) => ($true = X3)))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 ~(setadjoinAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X0 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X1 @ X2) => X3) => X3))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f3])).
% 1.64/1.31 thf(f3,negated_conjecture,(
% 1.64/1.31 ~(setadjoinAx => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ! [X3 : $o] : (((X0 = X2) => X3) => (((in @ X2 @ X1) => X3) => X3))))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.31 thf(f2,conjecture,(
% 1.64/1.31 setadjoinAx => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ! [X3 : $o] : (((X0 = X2) => X3) => (((in @ X2 @ X1) => X3) => X3)))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.9NwOnxxYIT/DTF2THF_11910.p',setadjoinE)).
% 1.64/1.31 thf(f34,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (setadjoin @ X2 @ X3))) | (X1 = X2) | ($true = (in @ X1 @ X3))) )),
% 1.64/1.31 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.64/1.31 thf(f33,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (setadjoin @ X2 @ X3))) | ($true = (X2 = X1)) | ($true = (in @ X1 @ X3))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ X3) | (X2 = X1))) | ($false = (in @ X1 @ (setadjoin @ X2 @ X3)))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3) | (X2 = X1)) = (in @ X1 @ (setadjoin @ X2 @ X3)))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ X3)) = ((in @ X1 @ X3) | (X2 = X1))) = $true)) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.64/1.31 thf(f25,plain,(
% 1.64/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ X2 @ Y0)) = ((in @ X1 @ Y0) | (X2 = X1)))) @ X3))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f24])).
% 1.64/1.31 thf(f24,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ X2 @ Y0)) = ((in @ X1 @ Y0) | (X2 = X1))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.64/1.31 thf(f23,plain,(
% 1.64/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ Y1)) = ((in @ X1 @ Y1) | (Y0 = X1)))))) @ X2))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f22])).
% 1.64/1.31 thf(f22,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ Y1)) = ((in @ X1 @ Y1) | (Y0 = X1))))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.31 thf(f21,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0)))))))) @ X1))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f20])).
% 1.64/1.31 thf(f20,plain,(
% 1.64/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0))))))))))),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f19,f18])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 (setadjoinAx = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0))))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0))))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.31 thf(f5,plain,(
% 1.64/1.31 (setadjoinAx = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X0)) <=> ((X1 = X2) | (in @ X2 @ X0))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 (setadjoinAx = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) <=> ((X0 = X2) | (in @ X2 @ X1))))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.9NwOnxxYIT/DTF2THF_11910.p',setadjoinAx)).
% 1.64/1.31 thf(f49,plain,(
% 1.64/1.31 spl4_2 | ~spl4_3),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f15,f46,f40])).
% 1.64/1.31 thf(f40,definition,(
% 1.64/1.31 spl4_2 <=> ($true = sK3)),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 ($true = sK3) | (sK1 != sK0)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.31 thf(f44,plain,(
% 1.64/1.31 ~spl4_2),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f17,f40])).
% 1.64/1.31 thf(f17,plain,(
% 1.64/1.31 ($true != sK3)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.31 thf(f43,plain,(
% 1.64/1.31 ~spl4_1 | spl4_2),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f16,f40,f36])).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 ($true = sK3) | ($true != (in @ sK1 @ sK2))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_11910
% 1.64/1.31 % (12098)------------------------------
% 1.64/1.31 % (12098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (12098)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (12098)Memory used [KB]: 5500
% 1.64/1.31 % (12098)Time elapsed: 0.004 s
% 1.64/1.31 % (12098)Instructions burned: 4 (million)
% 1.64/1.31 % (12098)------------------------------
% 1.64/1.31 % (12098)------------------------------
% 1.64/1.31 % (12097)Success in time 0.013 s
%------------------------------------------------------------------------------