%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU587^2 : 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 : n016.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 09:35:26 AM UTC 2026
% Result : Theorem 1.62s 1.30s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 437 ( 124 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 441 ( 55 ~; 43 |; 28 &; 290 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 101 ( 0 ^; 76 !; 25 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
sK0: $i > $i > $i ).
thf(f55,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f53,f36]) ).
thf(f36,plain,
( ( subset @ sK6 @ ( binunion @ sK6 @ sK7 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( subset @ sK6 @ ( binunion @ sK6 @ sK7 ) )
!= $true )
& ( subsetI2 = $true )
& ( binunionIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f15,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
!= $true )
=> ( ( subset @ sK6 @ ( binunion @ sK6 @ sK7 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
!= $true )
& ( subsetI2 = $true )
& ( binunionIL = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
!= $true )
& ( binunionIL = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( subsetI2 = $true )
=> ( ( binunionIL = $true )
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( subsetI2
=> ( binunionIL
=> ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetI2
=> ( binunionIL
=> ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetI2
=> ( binunionIL
=> ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',binunionLsub) ).
thf(f53,plain,
( ( subset @ sK6 @ ( binunion @ sK6 @ sK7 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( ( subset @ sK6 @ ( binunion @ sK6 @ sK7 ) )
= $true ) ),
inference(superposition,[status(thm)],[f45,f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( in @ ( sK0 @ sK6 @ ( binunion @ sK6 @ sK7 ) ) @ ( binunion @ sK6 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( sK0 @ sK6 @ ( binunion @ sK6 @ sK7 ) ) @ ( binunion @ sK6 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f44,f48]) ).
thf(f48,plain,
( ( in @ ( sK0 @ sK6 @ ( binunion @ sK6 @ sK7 ) ) @ sK6 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true != $true )
| ( ( in @ ( sK0 @ sK6 @ ( binunion @ sK6 @ sK7 ) ) @ sK6 )
= $true ) ),
inference(superposition,[status(thm)],[f36,f46]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f30,f35]) ).
thf(f35,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f30,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK2 ) )
| ( ( in @ X5 @ sK1 )
= $true ) )
& ( $true
!= ( subset @ sK2 @ sK1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X4 @ X3 )
!= $true ) )
=> ( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK2 ) )
| ( ( in @ X5 @ sK1 )
= $true ) )
& ( $true
!= ( subset @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',subsetI2) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f34]) ).
thf(f34,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f33,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( ( in @ sK5 @ sK3 )
= $true )
& ( ( in @ sK5 @ ( binunion @ sK3 @ sK4 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ ( binunion @ X3 @ X4 ) )
!= $true ) )
=> ( ( ( in @ sK5 @ sK3 )
= $true )
& ( ( in @ sK5 @ ( binunion @ sK3 @ sK4 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ ( binunion @ X3 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binunionIL
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',binunionIL) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f35]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU587^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:28:06 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEU587^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Set Theory
% 0.26/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.26/0.47 % Version : Especial > Reduced > Especial.
% 0.26/0.47 % English : (! A:i.! B:i.subset A (binunion A B))
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.47 % Source : [Bro08]
% 0.26/0.47 % Names : ZFC089l [Bro08]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % 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
% 0.26/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.26/0.47 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 3 ( 4 avg)
% 0.26/0.47 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.26/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.26/0.47 % Number of types : 2 ( 0 usr)
% 0.26/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : http://mathgate.info/detsetitem.php?id=163
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(in_type,type,
% 0.26/0.47 in: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(subset_type,type,
% 0.26/0.47 subset: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI2_type,type,
% 0.26/0.47 subsetI2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI2,definition,
% 0.26/0.47 ( subsetI2
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunion_type,type,
% 0.26/0.47 binunion: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIL_type,type,
% 0.26/0.47 binunionIL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIL,definition,
% 0.26/0.47 ( binunionIL
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionLsub,conjecture,
% 0.26/0.47 ( subsetI2
% 0.26/0.47 => ( binunionIL
% 0.26/0.47 => ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:28:07 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2DTF10588.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(in_type,type,
% 1.46/1.27 in: $i > $i > $o ).
% 1.46/1.27
% 1.46/1.27 thf(subset_type,type,
% 1.46/1.27 subset: $i > $i > $o ).
% 1.46/1.27
% 1.46/1.27 thf(subsetI2_type,type,
% 1.46/1.27 subsetI2: $o ).
% 1.46/1.27
% 1.46/1.27 thf(subsetI2,definition,
% 1.46/1.27 ( subsetI2
% 1.46/1.27 = ( ! [A: $i,B: $i] :
% 1.46/1.27 ( ! [Xx: $i] :
% 1.46/1.27 ( ( in @ Xx @ A )
% 1.46/1.27 => ( in @ Xx @ B ) )
% 1.46/1.27 => ( subset @ A @ B ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(binunion_type,type,
% 1.46/1.27 binunion: $i > $i > $i ).
% 1.46/1.27
% 1.46/1.27 thf(binunionIL_type,type,
% 1.46/1.27 binunionIL: $o ).
% 1.46/1.27
% 1.46/1.27 thf(binunionIL,definition,
% 1.46/1.27 ( binunionIL
% 1.46/1.27 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.46/1.27 ( ( in @ Xx @ A )
% 1.46/1.27 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(binunionLsub,conjecture,
% 1.46/1.27 ( subsetI2
% 1.46/1.27 => ( binunionIL
% 1.46/1.27 => ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (10913)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_10588 for (3000ds/4Mi)
% 1.46/1.29 % (10913)Instruction limit reached!
% 1.46/1.29 % (10913)------------------------------
% 1.46/1.29 % (10913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (10913)Termination reason: Unknown
% 1.46/1.29 % (10913)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (10913)Memory used [KB]: 5500
% 1.46/1.29 % (10913)Time elapsed: 0.003 s
% 1.46/1.29 % (10913)Instructions burned: 4 (million)
% 1.46/1.29 % (10913)------------------------------
% 1.46/1.29 % (10913)------------------------------
% 1.46/1.30 % (10912)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10588 for (3000ds/183Mi)
% 1.46/1.30 % (10915)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10588 for (3000ds/2Mi)
% 1.46/1.30 % (10914)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_10588 for (3000ds/27Mi)
% 1.46/1.30 % (10916)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_10588 for (3000ds/2Mi)
% 1.46/1.30 % (10918)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10588 for (3000ds/18Mi)
% 1.46/1.30 % (10917)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_10588 for (3000ds/275Mi)
% 1.46/1.30 % (10915)Instruction limit reached!
% 1.46/1.30 % (10915)------------------------------
% 1.46/1.30 % (10915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (10915)Termination reason: Unknown
% 1.46/1.30 % (10915)Termination phase: Naming
% 1.46/1.30
% 1.46/1.30 % (10915)Memory used [KB]: 895
% 1.46/1.30 % (10915)Time elapsed: 0.003 s
% 1.46/1.30 % (10915)Instructions burned: 2 (million)
% 1.46/1.30 % (10915)------------------------------
% 1.46/1.30 % (10915)------------------------------
% 1.46/1.30 % (10916)Instruction limit reached!
% 1.46/1.30 % (10916)------------------------------
% 1.46/1.30 % (10916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (10916)Termination reason: Unknown
% 1.46/1.30 % (10916)Termination phase: Property scanning
% 1.46/1.30
% 1.46/1.30 % (10916)Memory used [KB]: 895
% 1.46/1.30 % (10916)Time elapsed: 0.003 s
% 1.46/1.30 % (10916)Instructions burned: 2 (million)
% 1.46/1.30 % (10916)------------------------------
% 1.46/1.30 % (10916)------------------------------
% 1.62/1.30 % (10919)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10588 for (2999ds/3Mi)
% 1.62/1.30 % (10918)First to succeed.
% 1.62/1.30 % (10919)Refutation not found, incomplete strategy
% 1.62/1.30 % (10919)------------------------------
% 1.62/1.30 % (10919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (10919)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (10919)Memory used [KB]: 5500
% 1.62/1.30 % (10919)Time elapsed: 0.002 s
% 1.62/1.30 % (10919)Instructions burned: 2 (million)
% 1.62/1.30 % (10919)------------------------------
% 1.62/1.30 % (10919)------------------------------
% 1.62/1.30 % (10912)Also succeeded, but the first one will report.
% 1.62/1.30 % (10914)Also succeeded, but the first one will report.
% 1.62/1.30 % (10918)Refutation found. Thanks to Tanya!
% 1.62/1.30 % SZS status Theorem for DTF2THF_10588
% 1.62/1.30 % SZS output start Proof for DTF2THF_10588
% 1.62/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.62/1.30 thf(func_def_1, type, subset: $i > $i > $o).
% 1.62/1.30 thf(func_def_4, type, binunion: $i > $i > $i).
% 1.62/1.30 thf(func_def_8, type, sK0: $i > $i > $i).
% 1.62/1.30 thf(f55,plain,(
% 1.62/1.30 $false),
% 1.62/1.30 inference(subsumption_resolution,[status(thm)],[f53,f36])).
% 1.62/1.30 thf(f36,plain,(
% 1.62/1.30 ((subset @ sK6 @ (binunion @ sK6 @ sK7)) != $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.30 thf(f26,plain,(
% 1.62/1.30 ((subset @ sK6 @ (binunion @ sK6 @ sK7)) != $true) & (subsetI2 = $true) & (binunionIL = $true)),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f15,f25])).
% 1.62/1.30 thf(f25,plain,(
% 1.62/1.30 ? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X0 @ X1)) != $true) => ((subset @ sK6 @ (binunion @ sK6 @ sK7)) != $true)),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f15,plain,(
% 1.62/1.30 ? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X0 @ X1)) != $true) & (subsetI2 = $true) & (binunionIL = $true)),
% 1.62/1.30 inference(flattening,[status(thm)],[f14])).
% 1.62/1.30 thf(f14,plain,(
% 1.62/1.30 (? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X0 @ X1)) != $true) & (binunionIL = $true)) & (subsetI2 = $true)),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f7])).
% 1.62/1.30 thf(f7,plain,(
% 1.62/1.30 ~((subsetI2 = $true) => ((binunionIL = $true) => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X0 @ X1)) = $true)))),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.62/1.30 thf(f6,plain,(
% 1.62/1.30 ~(subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1))))),
% 1.62/1.30 inference(rectify,[status(thm)],[f4])).
% 1.62/1.30 thf(f4,negated_conjecture,(
% 1.62/1.30 ~(subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1))))),
% 1.62/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.62/1.30 thf(f3,conjecture,(
% 1.62/1.30 subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 1.62/1.30 file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',binunionLsub)).
% 1.62/1.30 thf(f53,plain,(
% 1.62/1.30 ((subset @ sK6 @ (binunion @ sK6 @ sK7)) = $true)),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.62/1.30 thf(f51,plain,(
% 1.62/1.30 ($true != $true) | ((subset @ sK6 @ (binunion @ sK6 @ sK7)) = $true)),
% 1.62/1.30 inference(superposition,[status(thm)],[f45,f50])).
% 1.62/1.30 thf(f50,plain,(
% 1.62/1.30 ( ! [X0 : $i] : (((in @ (sK0 @ sK6 @ (binunion @ sK6 @ sK7)) @ (binunion @ sK6 @ X0)) = $true)) )),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.62/1.30 thf(f49,plain,(
% 1.62/1.30 ( ! [X0 : $i] : (($true != $true) | ((in @ (sK0 @ sK6 @ (binunion @ sK6 @ sK7)) @ (binunion @ sK6 @ X0)) = $true)) )),
% 1.62/1.30 inference(superposition,[status(thm)],[f44,f48])).
% 1.62/1.30 thf(f48,plain,(
% 1.62/1.30 ((in @ (sK0 @ sK6 @ (binunion @ sK6 @ sK7)) @ sK6) = $true)),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.62/1.30 thf(f47,plain,(
% 1.62/1.30 ($true != $true) | ((in @ (sK0 @ sK6 @ (binunion @ sK6 @ sK7)) @ sK6) = $true)),
% 1.62/1.30 inference(superposition,[status(thm)],[f36,f46])).
% 1.62/1.30 thf(f46,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ (sK0 @ X1 @ X0) @ X1) = $true)) )),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.62/1.30 thf(f37,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X0) = $true) | ($true != $true)) )),
% 1.62/1.30 inference(definition_unfolding,[status(thm)],[f30,f35])).
% 1.62/1.30 thf(f35,plain,(
% 1.62/1.30 (subsetI2 = $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.30 thf(f30,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X0) = $true) | (subsetI2 != $true)) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.62/1.30 thf(f20,plain,(
% 1.62/1.30 (! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1) = $true) & ((in @ (sK0 @ X1 @ X0) @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : (($true != (in @ X5 @ sK2)) | ((in @ X5 @ sK1) = $true)) & ($true != (subset @ sK2 @ sK1))))),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18])).
% 1.62/1.30 thf(f18,plain,(
% 1.62/1.30 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (((in @ (sK0 @ X1 @ X0) @ X1) = $true) & ((in @ (sK0 @ X1 @ X0) @ X0) != $true)))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f19,plain,(
% 1.62/1.30 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((subset @ X4 @ X3) != $true)) => (! [X5 : $i] : (($true != (in @ X5 @ sK2)) | ((in @ X5 @ sK1) = $true)) & ($true != (subset @ sK2 @ sK1)))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f17,plain,(
% 1.62/1.30 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((subset @ X4 @ X3) != $true)))),
% 1.62/1.30 inference(rectify,[status(thm)],[f16])).
% 1.62/1.30 thf(f16,plain,(
% 1.62/1.30 (! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) & ((subset @ X0 @ X1) != $true)))),
% 1.62/1.30 inference(nnf_transformation,[status(thm)],[f12])).
% 1.62/1.30 thf(f12,plain,(
% 1.62/1.30 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f11,plain,(
% 1.62/1.30 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.62/1.30 thf(f10,plain,(
% 1.62/1.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.62/1.30 inference(rectify,[status(thm)],[f1])).
% 1.62/1.30 thf(f1,axiom,(
% 1.62/1.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.62/1.30 file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',subsetI2)).
% 1.62/1.30 thf(f44,plain,(
% 1.62/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (binunion @ X0 @ X1)) = $true)) )),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.62/1.30 thf(f41,plain,(
% 1.62/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ($true != $true) | ((in @ X2 @ (binunion @ X0 @ X1)) = $true)) )),
% 1.62/1.30 inference(definition_unfolding,[status(thm)],[f33,f34])).
% 1.62/1.30 thf(f34,plain,(
% 1.62/1.30 (binunionIL = $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.30 thf(f33,plain,(
% 1.62/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (binunion @ X0 @ X1)) = $true) | (binunionIL != $true)) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.62/1.30 thf(f24,plain,(
% 1.62/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (binunion @ X0 @ X1)) = $true)) | (binunionIL != $true)) & ((binunionIL = $true) | (((in @ sK5 @ sK3) = $true) & ((in @ sK5 @ (binunion @ sK3 @ sK4)) != $true)))),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f22,f23])).
% 1.62/1.30 thf(f23,plain,(
% 1.62/1.30 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X3)) & ((in @ X5 @ (binunion @ X3 @ X4)) != $true)) => (((in @ sK5 @ sK3) = $true) & ((in @ sK5 @ (binunion @ sK3 @ sK4)) != $true))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f22,plain,(
% 1.62/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (binunion @ X0 @ X1)) = $true)) | (binunionIL != $true)) & ((binunionIL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X3)) & ((in @ X5 @ (binunion @ X3 @ X4)) != $true)))),
% 1.62/1.30 inference(rectify,[status(thm)],[f21])).
% 1.62/1.30 thf(f21,plain,(
% 1.62/1.30 (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (binunion @ X2 @ X0)) = $true)) | (binunionIL != $true)) & ((binunionIL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (binunion @ X2 @ X0)) != $true)))),
% 1.62/1.30 inference(nnf_transformation,[status(thm)],[f13])).
% 1.62/1.30 thf(f13,plain,(
% 1.62/1.30 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (binunion @ X2 @ X0)) = $true)) <=> (binunionIL = $true)),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f9])).
% 1.62/1.30 thf(f9,plain,(
% 1.62/1.30 ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) => ((in @ X1 @ (binunion @ X2 @ X0)) = $true)) <=> (binunionIL = $true)),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.62/1.30 thf(f8,plain,(
% 1.62/1.30 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 1.62/1.30 inference(rectify,[status(thm)],[f2])).
% 1.62/1.30 thf(f2,axiom,(
% 1.62/1.30 (binunionIL = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 1.62/1.30 file('/export/starexec/sandbox/tmp/tmp.aesoAKtl8i/DTF2THF_10588.p',binunionIL)).
% 1.62/1.30 thf(f45,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.62/1.30 thf(f38,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK0 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.62/1.30 inference(definition_unfolding,[status(thm)],[f29,f35])).
% 1.62/1.30 thf(f29,plain,(
% 1.62/1.30 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true) | (subsetI2 != $true)) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.62/1.30 % SZS output end Proof for DTF2THF_10588
% 1.62/1.30 % (10918)------------------------------
% 1.62/1.30 % (10918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (10918)Termination reason: Refutation
% 1.62/1.30
% 1.62/1.30 % (10918)Memory used [KB]: 5500
% 1.62/1.30 % (10918)Time elapsed: 0.007 s
% 1.62/1.30 % (10918)Instructions burned: 4 (million)
% 1.62/1.30 % (10918)------------------------------
% 1.62/1.30 % (10918)------------------------------
% 1.62/1.30 % (10911)Success in time 0.022 s
%------------------------------------------------------------------------------