%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU530^2 : 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 : n017.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 09:35:07 AM UTC 2026
% Result : Theorem 1.78s 1.50s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 378 ( 113 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 348 ( 46 ~; 31 |; 30 &; 216 @)
% ( 4 <=>; 21 =>; 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 : 14 ( 11 usr; 11 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 48 !; 20 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f51,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f50,f44]) ).
thf(f44,plain,
! [X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ emptyset ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( $true != $true ) ),
inference(equality_resolution,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f30,f33]) ).
thf(f33,plain,
eqinunit = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) )
= $true )
& ( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
!= $true )
& ( uniqinunit = $true )
& ( eqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
=> ( ( ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) )
= $true )
& ( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
& ( uniqinunit = $true )
& ( eqinunit = $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
& ( uniqinunit = $true )
& ( eqinunit = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
& ( eqinunit = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( uniqinunit = $true )
=> ( ( eqinunit = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',singletonsswitch) ).
thf(f30,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( eqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( eqinunit = $true )
| ( ( sK2 = sK3 )
& ( ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true ) )
| ( eqinunit != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
=> ( ( sK2 = sK3 )
& ( ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ( eqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true ) )
| ( eqinunit != $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( eqinunit = $true )
| ? [X1: $i,X0: $i] :
( ( X0 = X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) )
| ( eqinunit != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( eqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( eqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',eqinunit) ).
thf(f50,plain,
( ( in @ sK4 @ ( setadjoin @ sK4 @ emptyset ) )
!= $true ),
inference(superposition,[status(thm)],[f35,f48]) ).
thf(f48,plain,
sK5 = sK4,
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( sK5 = sK4 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f45,f36]) ).
thf(f36,plain,
( ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f34]) ).
thf(f34,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( sK0 != sK1 )
& ( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
thf(f18,plain,
( ? [X2: $i,X3: $i] :
( ( X2 != X3 )
& ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
= $true ) )
=> ( ( sK0 != sK1 )
& ( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( X2 != X3 )
& ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X1: $i,X0: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',uniqinunit) ).
thf(f35,plain,
( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU530^2 : 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
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:24:26 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : SEU530^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.50 % Domain : Set Theory
% 0.29/0.50 % Problem : Preliminary Notions - Equality Laws
% 0.29/0.50 % Version : Especial > Reduced > Especial.
% 0.29/0.50 % English : (! x:i.! y:i.in x (setadjoin y emptyset) -> in y
% 0.29/0.50 % (setadjoin x emptyset))
% 0.29/0.50
% 0.29/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.50 % Source : [Bro08]
% 0.29/0.50 % Names : ZFC032l [Bro08]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % 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
% 0.29/0.50 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.29/0.50 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.50 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.29/0.50 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.29/0.50 % Maximal formula depth : 9 ( 4 avg)
% 0.29/0.50 % Number of types : 2 ( 0 usr)
% 0.29/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.29/0.50 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.29/0.50 % SPC : TH0_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : http://mathgate.info/detsetitem.php?id=471
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 thf(in_type,type,
% 0.29/0.50 in: $i > $i > $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptyset_type,type,
% 0.29/0.50 emptyset: $i ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoin_type,type,
% 0.29/0.50 setadjoin: $i > $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(uniqinunit_type,type,
% 0.29/0.50 uniqinunit: $o ).
% 0.29/0.50
% 0.29/0.50 thf(uniqinunit,definition,
% 0.29/0.50 ( uniqinunit
% 0.29/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.50 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(eqinunit_type,type,
% 0.29/0.50 eqinunit: $o ).
% 0.29/0.50
% 0.29/0.50 thf(eqinunit,definition,
% 0.29/0.50 ( eqinunit
% 0.29/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.50 ( ( Xx = Xy )
% 0.29/0.50 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(singletonsswitch,conjecture,
% 0.29/0.50 ( uniqinunit
% 0.29/0.50 => ( eqinunit
% 0.29/0.50 => ! [Xx: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 1.63/1.47 ---- Embedded in THF ---
% 1.63/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.47 %%% Generated on Tue Feb 24 12:24:27 EST 2026
% 1.63/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.47 %%% Logic specification used:
% 1.63/1.47 %%% thf(spec, logic, $$dhol).
% 1.63/1.47
% 1.63/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2DTF6278.p
% See solution above
% 1.63/1.47 ------------------------
% 1.63/1.48 ---- Cleaned THF ---
% 1.63/1.48 thf(in_type,type,
% 1.63/1.48 in: $i > $i > $o ).
% 1.63/1.48
% 1.63/1.48 thf(emptyset_type,type,
% 1.63/1.48 emptyset: $i ).
% 1.63/1.48
% 1.63/1.48 thf(setadjoin_type,type,
% 1.63/1.48 setadjoin: $i > $i > $i ).
% 1.63/1.48
% 1.63/1.48 thf(uniqinunit_type,type,
% 1.63/1.48 uniqinunit: $o ).
% 1.63/1.48
% 1.63/1.48 thf(uniqinunit,definition,
% 1.63/1.48 ( uniqinunit
% 1.63/1.48 = ( ! [Xx: $i,Xy: $i] :
% 1.63/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.63/1.48 => ( Xx = Xy ) ) ) ) ).
% 1.63/1.48
% 1.63/1.48 thf(eqinunit_type,type,
% 1.63/1.48 eqinunit: $o ).
% 1.63/1.48
% 1.63/1.48 thf(eqinunit,definition,
% 1.63/1.48 ( eqinunit
% 1.63/1.48 = ( ! [Xx: $i,Xy: $i] :
% 1.63/1.48 ( ( Xx = Xy )
% 1.63/1.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.63/1.48
% 1.63/1.48 thf(singletonsswitch,conjecture,
% 1.63/1.48 ( uniqinunit
% 1.63/1.48 => ( eqinunit
% 1.63/1.48 => ! [Xx: $i,Xy: $i] :
% 1.63/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.63/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.63/1.48 ------------------------
% 1.78/1.50 % (6380)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_6278 for (2999ds/275Mi)
% 1.78/1.50 % (6376)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_6278 for (2999ds/4Mi)
% 1.78/1.50 % (6375)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6278 for (2999ds/183Mi)
% 1.78/1.50 % (6379)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_6278 for (2999ds/2Mi)
% 1.78/1.50 % (6381)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6278 for (2999ds/18Mi)
% 1.78/1.50 % (6377)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_6278 for (2999ds/27Mi)
% 1.78/1.50 % (6378)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6278 for (2999ds/2Mi)
% 1.78/1.50 % (6379)Instruction limit reached!
% 1.78/1.50 % (6379)------------------------------
% 1.78/1.50 % (6379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6379)Termination reason: Unknown
% 1.78/1.50 % (6379)Termination phase: Naming
% 1.78/1.50
% 1.78/1.50 % (6379)Memory used [KB]: 895
% 1.78/1.50 % (6379)Time elapsed: 0.003 s
% 1.78/1.50 % (6379)Instructions burned: 2 (million)
% 1.78/1.50 % (6379)------------------------------
% 1.78/1.50 % (6379)------------------------------
% 1.78/1.50 % (6378)Instruction limit reached!
% 1.78/1.50 % (6378)------------------------------
% 1.78/1.50 % (6378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6378)Termination reason: Unknown
% 1.78/1.50 % (6378)Termination phase: Saturation
% 1.78/1.50
% 1.78/1.50 % (6378)Memory used [KB]: 5500
% 1.78/1.50 % (6378)Time elapsed: 0.004 s
% 1.78/1.50 % (6378)Instructions burned: 3 (million)
% 1.78/1.50 % (6378)------------------------------
% 1.78/1.50 % (6378)------------------------------
% 1.78/1.50 % (6380)First to succeed.
% 1.78/1.50 % (6376)Instruction limit reached!
% 1.78/1.50 % (6376)------------------------------
% 1.78/1.50 % (6376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6376)Termination reason: Unknown
% 1.78/1.50 % (6376)Termination phase: Saturation
% 1.78/1.50
% 1.78/1.50 % (6376)Memory used [KB]: 5500
% 1.78/1.50 % (6376)Time elapsed: 0.004 s
% 1.78/1.50 % (6376)Instructions burned: 4 (million)
% 1.78/1.50 % (6376)------------------------------
% 1.78/1.50 % (6376)------------------------------
% 1.78/1.50 % (6375)Also succeeded, but the first one will report.
% 1.78/1.50 % (6377)Also succeeded, but the first one will report.
% 1.78/1.50 % (6380)Refutation found. Thanks to Tanya!
% 1.78/1.50 % SZS status Theorem for DTF2THF_6278
% 1.78/1.50 % SZS output start Proof for DTF2THF_6278
% 1.78/1.50 thf(func_def_0, type, in: $i > $i > $o).
% 1.78/1.50 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.78/1.50 thf(f51,plain,(
% 1.78/1.50 $false),
% 1.78/1.50 inference(subsumption_resolution,[status(thm)],[f50,f44])).
% 1.78/1.50 thf(f44,plain,(
% 1.78/1.50 ( ! [X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ emptyset)) = $true)) )),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.78/1.50 thf(f43,plain,(
% 1.78/1.50 ( ! [X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ emptyset)) = $true) | ($true != $true)) )),
% 1.78/1.50 inference(equality_resolution,[status(thm)],[f42])).
% 1.78/1.50 thf(f42,plain,(
% 1.78/1.50 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) | ($true != $true)) )),
% 1.78/1.50 inference(definition_unfolding,[status(thm)],[f30,f33])).
% 1.78/1.50 thf(f33,plain,(
% 1.78/1.50 (eqinunit = $true)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f26])).
% 1.78/1.50 thf(f26,plain,(
% 1.78/1.50 (((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true) & ((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) != $true)) & (uniqinunit = $true) & (eqinunit = $true)),
% 1.78/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f24,f25])).
% 1.78/1.50 thf(f25,plain,(
% 1.78/1.50 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) => (((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true) & ((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) != $true))),
% 1.78/1.50 introduced(definition,[],[choice_axiom])).
% 1.78/1.50 thf(f24,plain,(
% 1.78/1.50 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) & (uniqinunit = $true) & (eqinunit = $true)),
% 1.78/1.50 inference(rectify,[status(thm)],[f13])).
% 1.78/1.50 thf(f13,plain,(
% 1.78/1.50 ? [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true)) & (uniqinunit = $true) & (eqinunit = $true)),
% 1.78/1.50 inference(flattening,[status(thm)],[f12])).
% 1.78/1.50 thf(f12,plain,(
% 1.78/1.50 (? [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true)) & (eqinunit = $true)) & (uniqinunit = $true)),
% 1.78/1.50 inference(ennf_transformation,[status(thm)],[f9])).
% 1.78/1.50 thf(f9,plain,(
% 1.78/1.50 ~((uniqinunit = $true) => ((eqinunit = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true))))),
% 1.78/1.50 inference(fool_elimination,[status(thm)],[f8])).
% 1.78/1.50 thf(f8,plain,(
% 1.78/1.50 ~(uniqinunit => (eqinunit => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 1.78/1.50 inference(rectify,[status(thm)],[f4])).
% 1.78/1.50 thf(f4,negated_conjecture,(
% 1.78/1.50 ~(uniqinunit => (eqinunit => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 1.78/1.50 inference(negated_conjecture,[status(cth)],[f3])).
% 1.78/1.50 thf(f3,conjecture,(
% 1.78/1.50 uniqinunit => (eqinunit => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.78/1.50 file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',singletonsswitch)).
% 1.78/1.50 thf(f30,plain,(
% 1.78/1.50 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) | (eqinunit != $true)) )),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f23])).
% 1.78/1.50 thf(f23,plain,(
% 1.78/1.50 ((eqinunit = $true) | ((sK2 = sK3) & ((in @ sK2 @ (setadjoin @ sK3 @ emptyset)) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true)) | (eqinunit != $true))),
% 1.78/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f21,f22])).
% 1.78/1.50 thf(f22,plain,(
% 1.78/1.50 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) => ((sK2 = sK3) & ((in @ sK2 @ (setadjoin @ sK3 @ emptyset)) != $true))),
% 1.78/1.50 introduced(definition,[],[choice_axiom])).
% 1.78/1.50 thf(f21,plain,(
% 1.78/1.50 ((eqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true)) | (eqinunit != $true))),
% 1.78/1.50 inference(rectify,[status(thm)],[f20])).
% 1.78/1.50 thf(f20,plain,(
% 1.78/1.50 ((eqinunit = $true) | ? [X1 : $i,X0 : $i] : ((X0 = X1) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true))) & (! [X1 : $i,X0 : $i] : ((X0 != X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true)) | (eqinunit != $true))),
% 1.78/1.50 inference(nnf_transformation,[status(thm)],[f14])).
% 1.78/1.50 thf(f14,plain,(
% 1.78/1.50 (eqinunit = $true) <=> ! [X1 : $i,X0 : $i] : ((X0 != X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true))),
% 1.78/1.50 inference(ennf_transformation,[status(thm)],[f11])).
% 1.78/1.50 thf(f11,plain,(
% 1.78/1.50 (eqinunit = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true))),
% 1.78/1.50 inference(fool_elimination,[status(thm)],[f10])).
% 1.78/1.50 thf(f10,plain,(
% 1.78/1.50 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 1.78/1.50 inference(rectify,[status(thm)],[f2])).
% 1.78/1.50 thf(f2,axiom,(
% 1.78/1.50 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = eqinunit)),
% 1.78/1.50 file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',eqinunit)).
% 1.78/1.50 thf(f50,plain,(
% 1.78/1.50 ((in @ sK4 @ (setadjoin @ sK4 @ emptyset)) != $true)),
% 1.78/1.50 inference(superposition,[status(thm)],[f35,f48])).
% 1.78/1.50 thf(f48,plain,(
% 1.78/1.50 (sK5 = sK4)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.78/1.50 thf(f46,plain,(
% 1.78/1.50 (sK5 = sK4) | ($true != $true)),
% 1.78/1.50 inference(superposition,[status(thm)],[f45,f36])).
% 1.78/1.50 thf(f36,plain,(
% 1.78/1.50 ((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f26])).
% 1.78/1.50 thf(f45,plain,(
% 1.78/1.50 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) )),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.78/1.50 thf(f37,plain,(
% 1.78/1.50 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | ($true != $true)) )),
% 1.78/1.50 inference(definition_unfolding,[status(thm)],[f29,f34])).
% 1.78/1.50 thf(f34,plain,(
% 1.78/1.50 (uniqinunit = $true)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f26])).
% 1.78/1.50 thf(f29,plain,(
% 1.78/1.50 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (uniqinunit != $true)) )),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f19])).
% 1.78/1.50 thf(f19,plain,(
% 1.78/1.50 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ((sK0 != sK1) & ((in @ sK1 @ (setadjoin @ sK0 @ emptyset)) = $true)))),
% 1.78/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 1.78/1.50 thf(f18,plain,(
% 1.78/1.50 ? [X2 : $i,X3 : $i] : ((X2 != X3) & ((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true)) => ((sK0 != sK1) & ((in @ sK1 @ (setadjoin @ sK0 @ emptyset)) = $true))),
% 1.78/1.50 introduced(definition,[],[choice_axiom])).
% 1.78/1.50 thf(f17,plain,(
% 1.78/1.50 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : ((X2 != X3) & ((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true)))),
% 1.78/1.50 inference(rectify,[status(thm)],[f16])).
% 1.78/1.50 thf(f16,plain,(
% 1.78/1.50 (! [X1 : $i,X0 : $i] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)))),
% 1.78/1.50 inference(nnf_transformation,[status(thm)],[f15])).
% 1.78/1.50 thf(f15,plain,(
% 1.78/1.50 ! [X1 : $i,X0 : $i] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) <=> (uniqinunit = $true)),
% 1.78/1.50 inference(ennf_transformation,[status(thm)],[f7])).
% 1.78/1.50 thf(f7,plain,(
% 1.78/1.50 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 1.78/1.50 inference(fool_elimination,[status(thm)],[f6])).
% 1.78/1.50 thf(f6,plain,(
% 1.78/1.50 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.78/1.50 inference(rectify,[status(thm)],[f1])).
% 1.78/1.50 thf(f1,axiom,(
% 1.78/1.50 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.78/1.50 file('/export/starexec/sandbox/tmp/tmp.0ydVtl2a5M/DTF2THF_6278.p',uniqinunit)).
% 1.78/1.50 thf(f35,plain,(
% 1.78/1.50 ((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) != $true)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f26])).
% 1.78/1.50 % SZS output end Proof for DTF2THF_6278
% 1.78/1.50 % (6380)------------------------------
% 1.78/1.50 % (6380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6380)Termination reason: Refutation
% 1.78/1.50
% 1.78/1.50 % (6380)Memory used [KB]: 5500
% 1.78/1.50 % (6380)Time elapsed: 0.005 s
% 1.78/1.50 % (6380)Instructions burned: 3 (million)
% 1.78/1.50 % (6380)------------------------------
% 1.78/1.50 % (6380)------------------------------
% 1.78/1.50 % (6374)Success in time 0.019 s
%------------------------------------------------------------------------------