%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU623^2 : 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 : n011.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 09:35:41 AM UTC 2026
% Result : Theorem 0.33s 1.43s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 606 ( 166 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 591 ( 74 ~; 52 |; 46 &; 380 @)
% ( 6 <=>; 33 =>; 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 : 23 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 118 ( 0 ^; 85 !; 33 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
binunion: $i > $i > $i ).
thf(f87,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f86,f55]) ).
thf(f55,plain,
( ( in @ sK11 @ sK9 )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( powersetsubset = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( singletoninpowerset = $true )
& ( $true
!= ( in @ ( setadjoin @ sK11 @ emptyset ) @ ( powerset @ ( binunion @ sK9 @ sK10 ) ) ) )
& ( ( in @ sK11 @ sK9 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f40,f41]) ).
thf(f41,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( $true
!= ( in @ ( setadjoin @ sK11 @ emptyset ) @ ( powerset @ ( binunion @ sK9 @ sK10 ) ) ) )
& ( ( in @ sK11 @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( powersetsubset = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( singletoninpowerset = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( powersetsubset = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( singletoninpowerset = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( singletoninpowerset = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( subsetE = $true )
=> ( ( powersetsubset = $true )
=> ( ( binunionLsub = $true )
=> ( ( singletoninpowerset = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',singletoninpowunion) ).
thf(f86,plain,
( ( in @ sK11 @ sK9 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true != $true )
| ( ( in @ sK11 @ sK9 )
!= $true ) ),
inference(superposition,[status(thm)],[f82,f76]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f48,f59]) ).
thf(f59,plain,
binunionLsub = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ( $true
!= ( subset @ sK4 @ ( binunion @ sK4 @ sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f30]) ).
thf(f30,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) )
=> ( $true
!= ( subset @ sK4 @ ( binunion @ sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
<=> ( binunionLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( binunionLsub
= ( ! [X1: $i,X0: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',binunionLsub) ).
thf(f82,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ ( binunion @ sK9 @ sK10 ) ) )
| ( $true
!= ( in @ sK11 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ ( binunion @ sK9 @ sK10 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK11 @ X0 ) ) ),
inference(superposition,[status(thm)],[f80,f73]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f46,f58]) ).
thf(f58,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
!= ( in @ sK0 @ sK2 ) )
& ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( subset @ sK1 @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f26]) ).
thf(f26,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
& ( $true
= ( in @ X3 @ X4 ) )
& ( ( subset @ X4 @ X5 )
= $true ) )
=> ( ( $true
!= ( in @ sK0 @ sK2 ) )
& ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( subset @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
& ( $true
= ( in @ X3 @ X4 ) )
& ( ( subset @ X4 @ X5 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( $true
= ( in @ X0 @ X2 ) ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetE
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',subsetE) ).
thf(f80,plain,
( $true
!= ( in @ sK11 @ ( binunion @ sK9 @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true
!= ( in @ sK11 @ ( binunion @ sK9 @ sK10 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f56,f75]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f51,f57]) ).
thf(f57,plain,
singletoninpowerset = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) )
| ( singletoninpowerset != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) )
| ( singletoninpowerset != $true ) )
& ( ( singletoninpowerset = $true )
| ( ( ( in @ sK5 @ sK6 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK5 @ emptyset ) @ ( powerset @ sK6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f33,f34]) ).
thf(f34,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X3 ) )
& ( $true
!= ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X3 ) ) ) )
=> ( ( ( in @ sK5 @ sK6 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK5 @ emptyset ) @ ( powerset @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) )
| ( singletoninpowerset != $true ) )
& ( ( singletoninpowerset = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X3 ) )
& ( $true
!= ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) )
| ( singletoninpowerset != $true ) )
& ( ( singletoninpowerset = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) )
<=> ( singletoninpowerset = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( singletoninpowerset = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) )
= singletoninpowerset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X0 ) ) )
= singletoninpowerset ),
file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',singletoninpowerset) ).
thf(f56,plain,
( $true
!= ( in @ ( setadjoin @ sK11 @ emptyset ) @ ( powerset @ ( binunion @ sK9 @ sK10 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU623^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:28:17 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SEU623^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.49 % Domain : Set Theory
% 0.32/0.49 % Problem : Ordered Pairs - Cartesian Products
% 0.32/0.49 % Version : Especial > Reduced > Especial.
% 0.32/0.49 % English : (! A:i.! B:i.! x:i.in x A -> in (setadjoin x emptyset) (powerset
% 0.32/0.49 % (binunion A B)))
% 0.32/0.49
% 0.32/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.49 % Source : [Bro08]
% 0.32/0.49 % Names : ZFC125l [Bro08]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.32/0.49 % Syntax : Number of formulae : 15 ( 4 unt; 10 typ; 4 def)
% 0.32/0.49 % Number of atoms : 22 ( 4 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 6 ( 4 avg)
% 0.32/0.49 % Number of connectives : 41 ( 0 ~; 0 |; 0 &; 32 @)
% 0.32/0.49 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 13 ( 3 avg)
% 0.32/0.49 % Number of types : 2 ( 0 usr)
% 0.32/0.49 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 11 ( 10 usr; 5 con; 0-2 aty)
% 0.32/0.49 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.32/0.49 % SPC : TH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : http://mathgate.info/detsetitem.php?id=180
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(in_type,type,
% 0.32/0.49 in: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(emptyset_type,type,
% 0.32/0.49 emptyset: $i ).
% 0.32/0.49
% 0.32/0.49 thf(setadjoin_type,type,
% 0.32/0.49 setadjoin: $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(powerset_type,type,
% 0.32/0.49 powerset: $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(subset_type,type,
% 0.32/0.49 subset: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(subsetE_type,type,
% 0.32/0.49 subsetE: $o ).
% 0.32/0.49
% 0.32/0.49 thf(subsetE,definition,
% 0.32/0.49 ( subsetE
% 0.32/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.49 ( ( subset @ A @ B )
% 0.32/0.49 => ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetsubset_type,type,
% 0.32/0.49 powersetsubset: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetsubset,definition,
% 0.32/0.49 ( powersetsubset
% 0.32/0.49 = ( ! [A: $i,B: $i] :
% 0.32/0.49 ( ( subset @ A @ B )
% 0.32/0.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunion_type,type,
% 0.32/0.49 binunion: $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(binunionLsub_type,type,
% 0.32/0.49 binunionLsub: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionLsub,definition,
% 0.32/0.49 ( binunionLsub
% 0.32/0.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(singletoninpowerset_type,type,
% 0.32/0.49 singletoninpowerset: $o ).
% 0.32/0.49
% 0.32/0.49 thf(singletoninpowerset,definition,
% 0.32/0.49 ( singletoninpowerset
% 0.32/0.49 = ( ! [A: $i,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(singletoninpowunion,conjecture,
% 0.32/0.49 ( subsetE
% 0.32/0.49 => ( powersetsubset
% 0.32/0.49 => ( binunionLsub
% 0.32/0.49 => ( singletoninpowerset
% 0.32/0.49 => ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 0.33/1.40 ---- Embedded in THF ---
% 0.33/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.40 %%% Generated on Tue Feb 24 12:28:18 EST 2026
% 0.33/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.40 %%% Logic specification used:
% 0.33/1.40 %%% thf(spec, logic, $$dhol).
% 0.33/1.40
% 0.33/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2DTF11092.p
% See solution above
% 0.33/1.40 ------------------------
% 0.33/1.41 ---- Cleaned THF ---
% 0.33/1.41 thf(in_type,type,
% 0.33/1.41 in: $i > $i > $o ).
% 0.33/1.41
% 0.33/1.41 thf(emptyset_type,type,
% 0.33/1.41 emptyset: $i ).
% 0.33/1.41
% 0.33/1.41 thf(setadjoin_type,type,
% 0.33/1.41 setadjoin: $i > $i > $i ).
% 0.33/1.41
% 0.33/1.41 thf(powerset_type,type,
% 0.33/1.41 powerset: $i > $i ).
% 0.33/1.41
% 0.33/1.41 thf(subset_type,type,
% 0.33/1.41 subset: $i > $i > $o ).
% 0.33/1.41
% 0.33/1.41 thf(subsetE_type,type,
% 0.33/1.41 subsetE: $o ).
% 0.33/1.41
% 0.33/1.41 thf(subsetE,definition,
% 0.33/1.41 ( subsetE
% 0.33/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.41 ( ( subset @ A @ B )
% 0.33/1.41 => ( ( in @ Xx @ A )
% 0.33/1.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/1.41
% 0.33/1.41 thf(powersetsubset_type,type,
% 0.33/1.41 powersetsubset: $o ).
% 0.33/1.41
% 0.33/1.41 thf(powersetsubset,definition,
% 0.33/1.41 ( powersetsubset
% 0.33/1.41 = ( ! [A: $i,B: $i] :
% 0.33/1.41 ( ( subset @ A @ B )
% 0.33/1.41 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.33/1.41
% 0.33/1.41 thf(binunion_type,type,
% 0.33/1.41 binunion: $i > $i > $i ).
% 0.33/1.41
% 0.33/1.41 thf(binunionLsub_type,type,
% 0.33/1.41 binunionLsub: $o ).
% 0.33/1.41
% 0.33/1.41 thf(binunionLsub,definition,
% 0.33/1.41 ( binunionLsub
% 0.33/1.41 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/1.41
% 0.33/1.41 thf(singletoninpowerset_type,type,
% 0.33/1.41 singletoninpowerset: $o ).
% 0.33/1.41
% 0.33/1.41 thf(singletoninpowerset,definition,
% 0.33/1.41 ( singletoninpowerset
% 0.33/1.41 = ( ! [A: $i,Xx: $i] :
% 0.33/1.41 ( ( in @ Xx @ A )
% 0.33/1.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.33/1.41
% 0.33/1.41 thf(singletoninpowunion,conjecture,
% 0.33/1.41 ( subsetE
% 0.33/1.41 => ( powersetsubset
% 0.33/1.41 => ( binunionLsub
% 0.33/1.41 => ( singletoninpowerset
% 0.33/1.41 => ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.41 ( ( in @ Xx @ A )
% 0.33/1.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.33/1.41 ------------------------
% 0.33/1.43 % (11197)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_11092 for (2999ds/4Mi)
% 0.33/1.43 % (11196)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11092 for (2999ds/183Mi)
% 0.33/1.43 % (11199)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11092 for (2999ds/2Mi)
% 0.33/1.43 % (11198)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_11092 for (2999ds/27Mi)
% 0.33/1.43 % (11200)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_11092 for (2999ds/2Mi)
% 0.33/1.43 % (11201)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_11092 for (2999ds/275Mi)
% 0.33/1.43 % (11202)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11092 for (2999ds/18Mi)
% 0.33/1.43 % (11199)Instruction limit reached!
% 0.33/1.43 % (11199)------------------------------
% 0.33/1.43 % (11199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.43 % (11199)Termination reason: Unknown
% 0.33/1.43 % (11200)Instruction limit reached!
% 0.33/1.43 % (11200)------------------------------
% 0.33/1.43 % (11200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.43 % (11199)Termination phase: Saturation
% 0.33/1.43
% 0.33/1.43 % (11199)Memory used [KB]: 5500
% 0.33/1.43 % (11199)Time elapsed: 0.003 s
% 0.33/1.43 % (11199)Instructions burned: 3 (million)
% 0.33/1.43 % (11199)------------------------------
% 0.33/1.43 % (11199)------------------------------
% 0.33/1.43 % (11200)Termination reason: Unknown
% 0.33/1.43 % (11200)Termination phase: Saturation
% 0.33/1.43
% 0.33/1.43 % (11200)Memory used [KB]: 1023
% 0.33/1.43 % (11200)Time elapsed: 0.003 s
% 0.33/1.43 % (11200)Instructions burned: 3 (million)
% 0.33/1.43 % (11200)------------------------------
% 0.33/1.43 % (11200)------------------------------
% 0.33/1.43 % (11197)Instruction limit reached!
% 0.33/1.43 % (11197)------------------------------
% 0.33/1.43 % (11197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.43 % (11197)Termination reason: Unknown
% 0.33/1.43 % (11197)Termination phase: Saturation
% 0.33/1.43
% 0.33/1.43 % (11197)Memory used [KB]: 5500
% 0.33/1.43 % (11197)Time elapsed: 0.005 s
% 0.33/1.43 % (11197)Instructions burned: 5 (million)
% 0.33/1.43 % (11197)------------------------------
% 0.33/1.43 % (11197)------------------------------
% 0.33/1.43 % (11201)First to succeed.
% 0.33/1.43 % (11196)Also succeeded, but the first one will report.
% 0.33/1.43 % (11198)Also succeeded, but the first one will report.
% 0.33/1.43 % (11201)Refutation found. Thanks to Tanya!
% 0.33/1.43 % SZS status Theorem for DTF2THF_11092
% 0.33/1.43 % SZS output start Proof for DTF2THF_11092
% 0.33/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 0.33/1.43 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.33/1.43 thf(func_def_3, type, powerset: $i > $i).
% 0.33/1.43 thf(func_def_4, type, subset: $i > $i > $o).
% 0.33/1.43 thf(func_def_8, type, binunion: $i > $i > $i).
% 0.33/1.43 thf(f87,plain,(
% 0.33/1.43 $false),
% 0.33/1.43 inference(subsumption_resolution,[status(thm)],[f86,f55])).
% 0.33/1.43 thf(f55,plain,(
% 0.33/1.43 ((in @ sK11 @ sK9) = $true)),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.43 thf(f42,plain,(
% 0.33/1.43 (powersetsubset = $true) & (binunionLsub = $true) & (subsetE = $true) & (singletoninpowerset = $true) & (($true != (in @ (setadjoin @ sK11 @ emptyset) @ (powerset @ (binunion @ sK9 @ sK10)))) & ((in @ sK11 @ sK9) = $true))),
% 0.33/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f40,f41])).
% 0.33/1.43 thf(f41,plain,(
% 0.33/1.43 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1))) != $true) & ((in @ X2 @ X0) = $true)) => (($true != (in @ (setadjoin @ sK11 @ emptyset) @ (powerset @ (binunion @ sK9 @ sK10)))) & ((in @ sK11 @ sK9) = $true))),
% 0.33/1.43 introduced(definition,[],[choice_axiom])).
% 0.33/1.43 thf(f40,plain,(
% 0.33/1.43 (powersetsubset = $true) & (binunionLsub = $true) & (subsetE = $true) & (singletoninpowerset = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1))) != $true) & ((in @ X2 @ X0) = $true))),
% 0.33/1.43 inference(rectify,[status(thm)],[f21])).
% 0.33/1.43 thf(f21,plain,(
% 0.33/1.43 (powersetsubset = $true) & (binunionLsub = $true) & (subsetE = $true) & (singletoninpowerset = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ (binunion @ X2 @ X1)))) & ($true = (in @ X0 @ X2)))),
% 0.33/1.43 inference(flattening,[status(thm)],[f20])).
% 0.33/1.43 thf(f20,plain,(
% 0.33/1.43 (((? [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ (binunion @ X2 @ X1)))) & ($true = (in @ X0 @ X2))) & (singletoninpowerset = $true)) & (binunionLsub = $true)) & (powersetsubset = $true)) & (subsetE = $true)),
% 0.33/1.43 inference(ennf_transformation,[status(thm)],[f9])).
% 0.33/1.43 thf(f9,plain,(
% 0.33/1.43 ~((subsetE = $true) => ((powersetsubset = $true) => ((binunionLsub = $true) => ((singletoninpowerset = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X0 @ X2)) => ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ (binunion @ X2 @ X1)))))))))),
% 0.33/1.43 inference(fool_elimination,[status(thm)],[f8])).
% 0.33/1.43 thf(f8,plain,(
% 0.33/1.43 ~(subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ (binunion @ X2 @ X1))))))))),
% 0.33/1.43 inference(rectify,[status(thm)],[f6])).
% 0.33/1.43 thf(f6,negated_conjecture,(
% 0.33/1.43 ~(subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1))))))))),
% 0.33/1.43 inference(negated_conjecture,[status(cth)],[f5])).
% 0.33/1.43 thf(f5,conjecture,(
% 0.33/1.43 subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.33/1.43 file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',singletoninpowunion)).
% 0.33/1.43 thf(f86,plain,(
% 0.33/1.43 ((in @ sK11 @ sK9) != $true)),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 0.33/1.43 thf(f85,plain,(
% 0.33/1.43 ($true != $true) | ((in @ sK11 @ sK9) != $true)),
% 0.33/1.43 inference(superposition,[status(thm)],[f82,f76])).
% 0.33/1.43 thf(f76,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0)))) )),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 0.33/1.43 thf(f65,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | ($true != $true)) )),
% 0.33/1.43 inference(definition_unfolding,[status(thm)],[f48,f59])).
% 0.33/1.43 thf(f59,plain,(
% 0.33/1.43 (binunionLsub = $true)),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.43 thf(f48,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) )),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f31])).
% 0.33/1.43 thf(f31,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ($true != (subset @ sK4 @ (binunion @ sK4 @ sK3))))),
% 0.33/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f30])).
% 0.33/1.43 thf(f30,plain,(
% 0.33/1.43 ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))) => ($true != (subset @ sK4 @ (binunion @ sK4 @ sK3)))),
% 0.33/1.43 introduced(definition,[],[choice_axiom])).
% 0.33/1.43 thf(f29,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))))),
% 0.33/1.43 inference(rectify,[status(thm)],[f28])).
% 0.33/1.43 thf(f28,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X1 @ X0))))),
% 0.33/1.43 inference(nnf_transformation,[status(thm)],[f17])).
% 0.33/1.43 thf(f17,plain,(
% 0.33/1.43 ! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) <=> (binunionLsub = $true)),
% 0.33/1.43 inference(fool_elimination,[status(thm)],[f16])).
% 0.33/1.43 thf(f16,plain,(
% 0.33/1.43 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)))),
% 0.33/1.43 inference(rectify,[status(thm)],[f3])).
% 0.33/1.43 thf(f3,axiom,(
% 0.33/1.43 (binunionLsub = ! [X1 : $i,X0 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 0.33/1.43 file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',binunionLsub)).
% 0.33/1.43 thf(f82,plain,(
% 0.33/1.43 ( ! [X0 : $i] : (($true != (subset @ X0 @ (binunion @ sK9 @ sK10))) | ($true != (in @ sK11 @ X0))) )),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.33/1.43 thf(f81,plain,(
% 0.33/1.43 ( ! [X0 : $i] : (($true != (subset @ X0 @ (binunion @ sK9 @ sK10))) | ($true != $true) | ($true != (in @ sK11 @ X0))) )),
% 0.33/1.43 inference(superposition,[status(thm)],[f80,f73])).
% 0.33/1.43 thf(f73,plain,(
% 0.33/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) )),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 0.33/1.43 thf(f61,plain,(
% 0.33/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) )),
% 0.33/1.43 inference(definition_unfolding,[status(thm)],[f46,f58])).
% 0.33/1.43 thf(f58,plain,(
% 0.33/1.43 (subsetE = $true)),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.43 thf(f46,plain,(
% 0.33/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2)) | (subsetE != $true)) )),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f27])).
% 0.33/1.43 thf(f27,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | (($true != (in @ sK0 @ sK2)) & ($true = (in @ sK0 @ sK1)) & ($true = (subset @ sK1 @ sK2))))),
% 0.33/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f26])).
% 0.33/1.43 thf(f26,plain,(
% 0.33/1.43 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) & ($true = (in @ X3 @ X4)) & ((subset @ X4 @ X5) = $true)) => (($true != (in @ sK0 @ sK2)) & ($true = (in @ sK0 @ sK1)) & ($true = (subset @ sK1 @ sK2)))),
% 0.33/1.43 introduced(definition,[],[choice_axiom])).
% 0.33/1.43 thf(f25,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) & ($true = (in @ X3 @ X4)) & ((subset @ X4 @ X5) = $true)))),
% 0.33/1.43 inference(rectify,[status(thm)],[f24])).
% 0.33/1.43 thf(f24,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ((in @ X0 @ X1) = $true) & ($true = (subset @ X1 @ X2))))),
% 0.33/1.43 inference(nnf_transformation,[status(thm)],[f23])).
% 0.33/1.43 thf(f23,plain,(
% 0.33/1.43 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X2))) <=> (subsetE = $true)),
% 0.33/1.43 inference(flattening,[status(thm)],[f22])).
% 0.33/1.43 thf(f22,plain,(
% 0.33/1.43 ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true)) | ($true != (subset @ X1 @ X2))) <=> (subsetE = $true)),
% 0.33/1.43 inference(ennf_transformation,[status(thm)],[f15])).
% 0.33/1.43 thf(f15,plain,(
% 0.33/1.43 ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) => (((in @ X0 @ X1) = $true) => ($true = (in @ X0 @ X2)))) <=> (subsetE = $true)),
% 0.33/1.43 inference(fool_elimination,[status(thm)],[f14])).
% 0.33/1.43 thf(f14,plain,(
% 0.33/1.43 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 0.33/1.43 inference(rectify,[status(thm)],[f1])).
% 0.33/1.43 thf(f1,axiom,(
% 0.33/1.43 (subsetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.33/1.43 file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',subsetE)).
% 0.33/1.43 thf(f80,plain,(
% 0.33/1.43 ($true != (in @ sK11 @ (binunion @ sK9 @ sK10)))),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 0.33/1.43 thf(f79,plain,(
% 0.33/1.43 ($true != (in @ sK11 @ (binunion @ sK9 @ sK10))) | ($true != $true)),
% 0.33/1.43 inference(superposition,[status(thm)],[f56,f75])).
% 0.33/1.43 thf(f75,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))) | ((in @ X0 @ X1) != $true)) )),
% 0.33/1.43 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 0.33/1.43 thf(f67,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))) | ($true != $true)) )),
% 0.33/1.43 inference(definition_unfolding,[status(thm)],[f51,f57])).
% 0.33/1.43 thf(f57,plain,(
% 0.33/1.43 (singletoninpowerset = $true)),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.43 thf(f51,plain,(
% 0.33/1.43 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))) | (singletoninpowerset != $true)) )),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f35])).
% 0.33/1.43 thf(f35,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | (((in @ sK5 @ sK6) = $true) & ($true != (in @ (setadjoin @ sK5 @ emptyset) @ (powerset @ sK6)))))),
% 0.33/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f33,f34])).
% 0.33/1.43 thf(f34,plain,(
% 0.33/1.43 ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ X3)) & ($true != (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X3)))) => (((in @ sK5 @ sK6) = $true) & ($true != (in @ (setadjoin @ sK5 @ emptyset) @ (powerset @ sK6))))),
% 0.33/1.43 introduced(definition,[],[choice_axiom])).
% 0.33/1.43 thf(f33,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ X3)) & ($true != (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X3)))))),
% 0.33/1.43 inference(rectify,[status(thm)],[f32])).
% 0.33/1.43 thf(f32,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ($true != (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))))),
% 0.33/1.43 inference(nnf_transformation,[status(thm)],[f18])).
% 0.33/1.43 thf(f18,plain,(
% 0.33/1.43 ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))) <=> (singletoninpowerset = $true)),
% 0.33/1.43 inference(ennf_transformation,[status(thm)],[f11])).
% 0.33/1.43 thf(f11,plain,(
% 0.33/1.43 (singletoninpowerset = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) => ($true = (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))))),
% 0.33/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 0.33/1.43 thf(f10,plain,(
% 0.33/1.43 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))) = singletoninpowerset)),
% 0.33/1.43 inference(rectify,[status(thm)],[f4])).
% 0.33/1.43 thf(f4,axiom,(
% 0.33/1.43 (! [X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X0))) = singletoninpowerset)),
% 0.33/1.43 file('/export/starexec/sandbox/tmp/tmp.zCFPuIK9PE/DTF2THF_11092.p',singletoninpowerset)).
% 0.33/1.43 thf(f56,plain,(
% 0.33/1.43 ($true != (in @ (setadjoin @ sK11 @ emptyset) @ (powerset @ (binunion @ sK9 @ sK10))))),
% 0.33/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.43 % SZS output end Proof for DTF2THF_11092
% 0.33/1.43 % (11201)------------------------------
% 0.33/1.43 % (11201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.43 % (11201)Termination reason: Refutation
% 0.33/1.43
% 0.33/1.43 % (11201)Memory used [KB]: 5500
% 0.33/1.43 % (11201)Time elapsed: 0.007 s
% 0.33/1.43 % (11201)Instructions burned: 6 (million)
% 0.33/1.43 % (11201)------------------------------
% 0.33/1.43 % (11201)------------------------------
% 0.33/1.43 % (11195)Success in time 0.021 s
%------------------------------------------------------------------------------