%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU728^2 : 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 : n001.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 09:36:43 AM UTC 2026
% Result : Theorem 1.54s 1.36s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 577 ( 158 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 615 ( 68 ~; 43 |; 51 &; 410 @)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 113 ( 0 ^; 81 !; 32 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
setminus: $i > $i > $i ).
thf(f59,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f58,f37]) ).
thf(f37,plain,
( ( in @ sK5 @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( setminusI = $true )
& ( setminusER = $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ sK5 @ sK4 )
!= $true )
& ( ( in @ sK5 @ ( setminus @ sK3 @ ( setminus @ sK3 @ sK4 ) ) )
= $true )
& ( ( in @ sK5 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f23,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ? [X2: $i] :
( ( $true
!= ( in @ X2 @ sK4 ) )
& ( $true
= ( in @ X2 @ ( setminus @ sK3 @ ( setminus @ sK3 @ sK4 ) ) ) )
& ( ( in @ X2 @ sK3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X2: $i] :
( ( $true
!= ( in @ X2 @ sK4 ) )
& ( $true
= ( in @ X2 @ ( setminus @ sK3 @ ( setminus @ sK3 @ sK4 ) ) ) )
& ( ( in @ X2 @ sK3 )
= $true ) )
=> ( ( ( in @ sK5 @ sK4 )
!= $true )
& ( ( in @ sK5 @ ( setminus @ sK3 @ ( setminus @ sK3 @ sK4 ) ) )
= $true )
& ( ( in @ sK5 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( setminusI = $true )
& ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setminusI = $true )
& ( setminusER = $true )
& ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( $true
= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X3 ) ) )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusI
=> ( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X3 ) ) )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',doubleComplementE1) ).
thf(f58,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f57,f35]) ).
thf(f35,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f57,plain,
( ( ( in @ sK5 @ sK3 )
!= $true )
| ( ( in @ sK5 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( in @ sK5 @ sK3 )
!= $true )
| ( ( in @ sK5 @ sK4 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f54,f51]) ).
thf(f51,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f31,f40]) ).
thf(f40,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f31,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true ) )
=> ( ( $true
!= ( in @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) )
= setminusI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',setminusI) ).
thf(f54,plain,
( $true
!= ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
!= ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f52,f36]) ).
thf(f36,plain,
( ( in @ sK5 @ ( setminus @ sK3 @ ( setminus @ sK3 @ sK4 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f52,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f41,f39]) ).
thf(f39,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f41,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK8 @ sK6 ) )
& ( $true
= ( in @ sK8 @ ( setminus @ sK7 @ sK6 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f28,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( in @ sK8 @ sK6 ) )
& ( $true
= ( in @ sK8 @ ( setminus @ sK7 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setminusER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminusER
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU728^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n001.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:33:05 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SEU728^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.40 % Domain : Set Theory
% 0.17/0.40 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.17/0.40 % Version : Especial > Reduced > Especial.
% 0.17/0.40 % English : (! A:i.! X:i.in X (powerset A) -> (! x:i.in x A ->
% 0.17/0.40 % in x (setminus A (setminus A X)) -> in x X))
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.40 % Source : [Bro08]
% 0.17/0.40 % Names : ZFC230l [Bro08]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % 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, 0.25 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 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.17/0.40 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.17/0.40 % Number of atoms : 15 ( 2 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 6 ( 5 avg)
% 0.17/0.40 % Number of connectives : 37 ( 2 ~; 0 |; 0 &; 27 @)
% 0.17/0.40 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 13 ( 5 avg)
% 0.17/0.40 % Number of types : 2 ( 0 usr)
% 0.17/0.40 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : http://mathgate.info/detsetitem.php?id=288
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(in_type,type,
% 0.17/0.40 in: $i > $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(powerset_type,type,
% 0.17/0.40 powerset: $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(setminus_type,type,
% 0.17/0.40 setminus: $i > $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(setminusI_type,type,
% 0.17/0.40 setminusI: $o ).
% 0.17/0.40
% 0.17/0.40 thf(setminusI,definition,
% 0.17/0.40 ( setminusI
% 0.17/0.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.40 ( ( in @ Xx @ A )
% 0.17/0.40 => ( ~ ( in @ Xx @ B )
% 0.17/0.40 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(setminusER_type,type,
% 0.17/0.40 setminusER: $o ).
% 0.17/0.40
% 0.17/0.40 thf(setminusER,definition,
% 0.17/0.40 ( setminusER
% 0.17/0.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.40 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.40 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(doubleComplementE1,conjecture,
% 0.17/0.40 ( setminusI
% 0.17/0.40 => ( setminusER
% 0.17/0.40 => ! [A: $i,X: $i] :
% 0.17/0.40 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.40 => ! [Xx: $i] :
% 0.17/0.40 ( ( in @ Xx @ A )
% 0.17/0.40 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.17/0.40 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.54/1.32 ---- Embedded in THF ---
% 1.54/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.32 %%% Generated on Tue Feb 24 12:33:06 EST 2026
% 1.54/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.32 %%% Logic specification used:
% 1.54/1.32 %%% thf(spec, logic, $$dhol).
% 1.54/1.32
% 1.54/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2DTF7752.p
% See solution above
% 1.54/1.32 ------------------------
% 1.54/1.33 ---- Cleaned THF ---
% 1.54/1.33 thf(in_type,type,
% 1.54/1.33 in: $i > $i > $o ).
% 1.54/1.33
% 1.54/1.33 thf(powerset_type,type,
% 1.54/1.33 powerset: $i > $i ).
% 1.54/1.33
% 1.54/1.33 thf(setminus_type,type,
% 1.54/1.33 setminus: $i > $i > $i ).
% 1.54/1.33
% 1.54/1.33 thf(setminusI_type,type,
% 1.54/1.33 setminusI: $o ).
% 1.54/1.33
% 1.54/1.33 thf(setminusI,definition,
% 1.54/1.33 ( setminusI
% 1.54/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.33 ( ( in @ Xx @ A )
% 1.54/1.33 => ( ~ ( in @ Xx @ B )
% 1.54/1.33 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.54/1.33
% 1.54/1.33 thf(setminusER_type,type,
% 1.54/1.33 setminusER: $o ).
% 1.54/1.33
% 1.54/1.33 thf(setminusER,definition,
% 1.54/1.33 ( setminusER
% 1.54/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.33 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.54/1.33 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.54/1.33
% 1.54/1.33 thf(doubleComplementE1,conjecture,
% 1.54/1.33 ( setminusI
% 1.54/1.33 => ( setminusER
% 1.54/1.33 => ! [A: $i,X: $i] :
% 1.54/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.54/1.33 => ! [Xx: $i] :
% 1.54/1.33 ( ( in @ Xx @ A )
% 1.54/1.33 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 1.54/1.33 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.54/1.33 ------------------------
% 1.54/1.35 % (7851)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_7752 for (2999ds/4Mi)
% 1.54/1.35 % (7853)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7752 for (2999ds/2Mi)
% 1.54/1.35 % (7850)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7752 for (2999ds/183Mi)
% 1.54/1.35 % (7852)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_7752 for (2999ds/27Mi)
% 1.54/1.35 % (7854)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_7752 for (2999ds/2Mi)
% 1.54/1.35 % (7855)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_7752 for (2999ds/275Mi)
% 1.54/1.35 % (7853)Instruction limit reached!
% 1.54/1.35 % (7853)------------------------------
% 1.54/1.35 % (7853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (7853)Termination reason: Unknown
% 1.54/1.35 % (7853)Termination phase: Saturation
% 1.54/1.35
% 1.54/1.35 % (7853)Memory used [KB]: 5500
% 1.54/1.35 % (7853)Time elapsed: 0.003 s
% 1.54/1.35 % (7853)Instructions burned: 3 (million)
% 1.54/1.35 % (7853)------------------------------
% 1.54/1.35 % (7853)------------------------------
% 1.54/1.36 % (7851)Instruction limit reached!
% 1.54/1.36 % (7851)------------------------------
% 1.54/1.36 % (7851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (7851)Termination reason: Unknown
% 1.54/1.36 % (7851)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (7851)Memory used [KB]: 5500
% 1.54/1.36 % (7851)Time elapsed: 0.005 s
% 1.54/1.36 % (7851)Instructions burned: 5 (million)
% 1.54/1.36 % (7851)------------------------------
% 1.54/1.36 % (7851)------------------------------
% 1.54/1.36 % (7854)Instruction limit reached!
% 1.54/1.36 % (7854)------------------------------
% 1.54/1.36 % (7854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (7854)Termination reason: Unknown
% 1.54/1.36 % (7854)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (7854)Memory used [KB]: 5500
% 1.54/1.36 % (7854)Time elapsed: 0.003 s
% 1.54/1.36 % (7854)Instructions burned: 3 (million)
% 1.54/1.36 % (7854)------------------------------
% 1.54/1.36 % (7854)------------------------------
% 1.54/1.36 % (7855)First to succeed.
% 1.54/1.36 % (7856)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7752 for (2999ds/18Mi)
% 1.54/1.36 % (7850)Also succeeded, but the first one will report.
% 1.54/1.36 % (7852)Also succeeded, but the first one will report.
% 1.54/1.36 % (7855)Refutation found. Thanks to Tanya!
% 1.54/1.36 % SZS status Theorem for DTF2THF_7752
% 1.54/1.36 % SZS output start Proof for DTF2THF_7752
% 1.54/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.36 thf(func_def_1, type, powerset: $i > $i).
% 1.54/1.36 thf(func_def_2, type, setminus: $i > $i > $i).
% 1.54/1.36 thf(f59,plain,(
% 1.54/1.36 $false),
% 1.54/1.36 inference(subsumption_resolution,[status(thm)],[f58,f37])).
% 1.54/1.36 thf(f37,plain,(
% 1.54/1.36 ((in @ sK5 @ sK4) != $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.36 thf(f26,plain,(
% 1.54/1.36 (setminusI = $true) & (setminusER = $true) & (((in @ sK4 @ (powerset @ sK3)) = $true) & (((in @ sK5 @ sK4) != $true) & ((in @ sK5 @ (setminus @ sK3 @ (setminus @ sK3 @ sK4))) = $true) & ((in @ sK5 @ sK3) = $true)))),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f23,f25,f24])).
% 1.54/1.36 thf(f24,plain,(
% 1.54/1.36 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) & ((in @ X2 @ X0) = $true))) => (((in @ sK4 @ (powerset @ sK3)) = $true) & ? [X2 : $i] : (($true != (in @ X2 @ sK4)) & ($true = (in @ X2 @ (setminus @ sK3 @ (setminus @ sK3 @ sK4)))) & ((in @ X2 @ sK3) = $true)))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f25,plain,(
% 1.54/1.36 ? [X2 : $i] : (($true != (in @ X2 @ sK4)) & ($true = (in @ X2 @ (setminus @ sK3 @ (setminus @ sK3 @ sK4)))) & ((in @ X2 @ sK3) = $true)) => (((in @ sK5 @ sK4) != $true) & ((in @ sK5 @ (setminus @ sK3 @ (setminus @ sK3 @ sK4))) = $true) & ((in @ sK5 @ sK3) = $true))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f23,plain,(
% 1.54/1.36 (setminusI = $true) & (setminusER = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) & ((in @ X2 @ X0) = $true)))),
% 1.54/1.36 inference(rectify,[status(thm)],[f15])).
% 1.54/1.36 thf(f15,plain,(
% 1.54/1.36 (setminusI = $true) & (setminusER = $true) & ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) & ((in @ X2 @ X1) = $true)))),
% 1.54/1.36 inference(flattening,[status(thm)],[f14])).
% 1.54/1.36 thf(f14,plain,(
% 1.54/1.36 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))))) & ((in @ X2 @ X1) = $true)) & ($true = (in @ X0 @ (powerset @ X1)))) & (setminusER = $true)) & (setminusI = $true)),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f11])).
% 1.54/1.36 thf(f11,plain,(
% 1.54/1.36 ~((setminusI = $true) => ((setminusER = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ X1) = $true) => (($true = (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) => ((in @ X2 @ X0) = $true))))))),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f10])).
% 1.54/1.36 thf(f10,plain,(
% 1.54/1.36 ~(setminusI => (setminusER => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) => (in @ X2 @ X0))))))),
% 1.54/1.36 inference(rectify,[status(thm)],[f4])).
% 1.54/1.36 thf(f4,negated_conjecture,(
% 1.54/1.36 ~(setminusI => (setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X3))) => (in @ X2 @ X3))))))),
% 1.54/1.36 inference(negated_conjecture,[status(cth)],[f3])).
% 1.54/1.36 thf(f3,conjecture,(
% 1.54/1.36 setminusI => (setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X3))) => (in @ X2 @ X3)))))),
% 1.54/1.36 file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',doubleComplementE1)).
% 1.54/1.36 thf(f58,plain,(
% 1.54/1.36 ((in @ sK5 @ sK4) = $true)),
% 1.54/1.36 inference(subsumption_resolution,[status(thm)],[f57,f35])).
% 1.54/1.36 thf(f35,plain,(
% 1.54/1.36 ((in @ sK5 @ sK3) = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.36 thf(f57,plain,(
% 1.54/1.36 ((in @ sK5 @ sK3) != $true) | ((in @ sK5 @ sK4) = $true)),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.54/1.36 thf(f56,plain,(
% 1.54/1.36 ((in @ sK5 @ sK3) != $true) | ((in @ sK5 @ sK4) = $true) | ($true != $true)),
% 1.54/1.36 inference(superposition,[status(thm)],[f54,f51])).
% 1.54/1.36 thf(f51,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X3 @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true)) )),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.54/1.36 thf(f47,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ X5) = $true) | ((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ (setminus @ X3 @ X5)))) )),
% 1.54/1.36 inference(definition_unfolding,[status(thm)],[f31,f40])).
% 1.54/1.36 thf(f40,plain,(
% 1.54/1.36 (setminusI = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.36 thf(f31,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X3 @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true) | (setminusI != $true)) )),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f22])).
% 1.54/1.36 thf(f22,plain,(
% 1.54/1.36 ((setminusI = $true) | (($true != (in @ sK1 @ (setminus @ sK0 @ sK2))) & ($true = (in @ sK1 @ sK0)) & ((in @ sK1 @ sK2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X3 @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true)) | (setminusI != $true))),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21])).
% 1.54/1.36 thf(f21,plain,(
% 1.54/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) != $true) & ($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true)) => (($true != (in @ sK1 @ (setminus @ sK0 @ sK2))) & ($true = (in @ sK1 @ sK0)) & ((in @ sK1 @ sK2) != $true))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f20,plain,(
% 1.54/1.36 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) != $true) & ($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X3 @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true)) | (setminusI != $true))),
% 1.54/1.36 inference(rectify,[status(thm)],[f19])).
% 1.54/1.36 thf(f19,plain,(
% 1.54/1.36 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) != $true) & ($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) | ($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true)) | (setminusI != $true))),
% 1.54/1.36 inference(nnf_transformation,[status(thm)],[f17])).
% 1.54/1.36 thf(f17,plain,(
% 1.54/1.36 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) | ($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true))),
% 1.54/1.36 inference(flattening,[status(thm)],[f16])).
% 1.54/1.36 thf(f16,plain,(
% 1.54/1.36 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2)) = $true) | ((in @ X1 @ X2) = $true)) | ($true != (in @ X1 @ X0))) <=> (setminusI = $true)),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f12])).
% 1.54/1.36 thf(f12,plain,(
% 1.54/1.36 ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) != $true) => ((in @ X1 @ (setminus @ X0 @ X2)) = $true))) <=> (setminusI = $true)),
% 1.54/1.36 inference(flattening,[status(thm)],[f9])).
% 1.54/1.36 thf(f9,plain,(
% 1.54/1.36 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (~((in @ X1 @ X2) = $true) => ((in @ X1 @ (setminus @ X0 @ X2)) = $true))) <=> (setminusI = $true)),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f8])).
% 1.54/1.36 thf(f8,plain,(
% 1.54/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (in @ X1 @ (setminus @ X0 @ X2)))) = setminusI)),
% 1.54/1.36 inference(rectify,[status(thm)],[f1])).
% 1.54/1.36 thf(f1,axiom,(
% 1.54/1.36 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 1.54/1.36 file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',setminusI)).
% 1.54/1.36 thf(f54,plain,(
% 1.54/1.36 ($true != (in @ sK5 @ (setminus @ sK3 @ sK4)))),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.54/1.36 thf(f53,plain,(
% 1.54/1.36 ($true != (in @ sK5 @ (setminus @ sK3 @ sK4))) | ($true != $true)),
% 1.54/1.36 inference(superposition,[status(thm)],[f52,f36])).
% 1.54/1.36 thf(f36,plain,(
% 1.54/1.36 ((in @ sK5 @ (setminus @ sK3 @ (setminus @ sK3 @ sK4))) = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.36 thf(f52,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X4 @ X3)) != $true) | ((in @ X5 @ X3) != $true)) )),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.54/1.36 thf(f50,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ (setminus @ X4 @ X3)) != $true) | ($true != $true)) )),
% 1.54/1.36 inference(definition_unfolding,[status(thm)],[f41,f39])).
% 1.54/1.36 thf(f39,plain,(
% 1.54/1.36 (setminusER = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.36 thf(f41,plain,(
% 1.54/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ (setminus @ X4 @ X3)) != $true) | (setminusER != $true)) )),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f30])).
% 1.54/1.36 thf(f30,plain,(
% 1.54/1.36 ((setminusER = $true) | (($true = (in @ sK8 @ sK6)) & ($true = (in @ sK8 @ (setminus @ sK7 @ sK6))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ (setminus @ X4 @ X3)) != $true)) | (setminusER != $true))),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f28,f29])).
% 1.54/1.36 thf(f29,plain,(
% 1.54/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) => (($true = (in @ sK8 @ sK6)) & ($true = (in @ sK8 @ (setminus @ sK7 @ sK6))))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f28,plain,(
% 1.54/1.36 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ (setminus @ X4 @ X3)) != $true)) | (setminusER != $true))),
% 1.54/1.36 inference(rectify,[status(thm)],[f27])).
% 1.54/1.36 thf(f27,plain,(
% 1.54/1.36 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X2 @ (setminus @ X1 @ X0)))) | (setminusER != $true))),
% 1.54/1.36 inference(nnf_transformation,[status(thm)],[f18])).
% 1.54/1.36 thf(f18,plain,(
% 1.54/1.36 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X2 @ (setminus @ X1 @ X0))))),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f13])).
% 1.54/1.36 thf(f13,plain,(
% 1.54/1.36 (setminusER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ((in @ X2 @ X0) != $true))),
% 1.54/1.36 inference(flattening,[status(thm)],[f7])).
% 1.54/1.36 thf(f7,plain,(
% 1.54/1.36 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ~((in @ X2 @ X0) = $true))),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f6])).
% 1.54/1.36 thf(f6,plain,(
% 1.54/1.36 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)))),
% 1.54/1.36 inference(rectify,[status(thm)],[f2])).
% 1.54/1.36 thf(f2,axiom,(
% 1.54/1.36 (setminusER = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 1.54/1.36 file('/export/starexec/sandbox/tmp/tmp.qRjw8SMRbC/DTF2THF_7752.p',setminusER)).
% 1.54/1.36 % SZS output end Proof for DTF2THF_7752
% 1.54/1.36 % (7855)------------------------------
% 1.54/1.36 % (7855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (7855)Termination reason: Refutation
% 1.54/1.36
% 1.54/1.36 % (7855)Memory used [KB]: 5500
% 1.54/1.36 % (7855)Time elapsed: 0.006 s
% 1.54/1.36 % (7855)Instructions burned: 4 (million)
% 1.54/1.36 % (7855)------------------------------
% 1.54/1.36 % (7855)------------------------------
% 1.54/1.36 % (7849)Success in time 0.009 s
%------------------------------------------------------------------------------