%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU588^2 : 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 : n013.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 09:35:27 AM UTC 2026
% Result : Theorem 1.40s 1.29s
% Output : Refutation 1.40s
% 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_10,type,
sK2: $i > $i > $i ).
thf(f55,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f54,f27]) ).
thf(f27,plain,
( ( subset @ sK0 @ ( binunion @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( binunionIR = $true )
& ( subsetI2 = $true )
& ( ( subset @ sK0 @ ( binunion @ sK1 @ sK0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X1 @ X0 ) )
!= $true )
=> ( ( subset @ sK0 @ ( binunion @ sK1 @ sK0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( binunionIR = $true )
& ( subsetI2 = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X1 @ X0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( binunionIR = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( subsetI2 = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( subsetI2
=> ( binunionIR
=> ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetI2
=> ( binunionIR
=> ! [X1: $i,X0: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetI2
=> ( binunionIR
=> ! [X1: $i,X0: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',binunionRsub) ).
thf(f54,plain,
( ( subset @ sK0 @ ( binunion @ sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( subset @ sK0 @ ( binunion @ sK1 @ sK0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f46,f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( in @ ( sK2 @ ( binunion @ sK1 @ sK0 ) @ sK0 ) @ ( binunion @ X0 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( sK2 @ ( binunion @ sK1 @ sK0 ) @ sK0 ) @ ( binunion @ X0 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f45,f48]) ).
thf(f48,plain,
( ( in @ ( sK2 @ ( binunion @ sK1 @ sK0 ) @ sK0 ) @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( in @ ( sK2 @ ( binunion @ sK1 @ sK0 ) @ sK0 ) @ sK0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f27,f44]) ).
thf(f44,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f28]) ).
thf(f28,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK3 @ sK4 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK4 )
= $true )
| ( $true
!= ( in @ X5 @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f19,f21,f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) ) ) )
=> ( ( $true
!= ( subset @ sK3 @ sK4 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK4 )
= $true )
| ( $true
!= ( in @ X5 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,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)],[f6]) ).
thf(f6,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',subsetI2) ).
thf(f45,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( binunion @ X4 @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( binunion @ X4 @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f29]) ).
thf(f29,plain,
binunionIR = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f34,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( binunion @ X4 @ X3 ) )
= $true )
| ( binunionIR != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( binunionIR = $true )
| ( ( ( in @ sK7 @ sK5 )
= $true )
& ( ( in @ sK7 @ ( binunion @ sK6 @ sK5 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( binunion @ X4 @ X3 ) )
= $true ) )
| ( binunionIR != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) )
=> ( ( ( in @ sK7 @ sK5 )
= $true )
& ( ( in @ sK7 @ ( binunion @ sK6 @ sK5 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ( binunionIR = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( binunion @ X4 @ X3 ) )
= $true ) )
| ( binunionIR != $true ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( binunionIR = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
| ( binunionIR != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( binunionIR = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( binunionIR = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binunionIR
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binunionIR
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',binunionIR) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f28]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU588^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n013.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:27:38 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU588^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! B:i.subset B (binunion A B))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC090l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.18/0.38 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 3 ( 4 avg)
% 0.18/0.38 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.18/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 8 ( 3 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=164
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subset_type,type,
% 0.18/0.38 subset: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI2_type,type,
% 0.18/0.38 subsetI2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI2,definition,
% 0.18/0.38 ( subsetI2
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunion_type,type,
% 0.18/0.38 binunion: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIR_type,type,
% 0.18/0.38 binunionIR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIR,definition,
% 0.18/0.38 ( binunionIR
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionRsub,conjecture,
% 0.18/0.38 ( subsetI2
% 0.18/0.38 => ( binunionIR
% 0.18/0.38 => ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.40/1.25 ---- Embedded in THF ---
% 1.40/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.26 %%% Generated on Tue Feb 24 12:27:39 EST 2026
% 1.40/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.26 %%% Logic specification used:
% 1.40/1.26 %%% thf(spec, logic, $$dhol).
% 1.40/1.26
% 1.40/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2DTF18311.p
% See solution above
% 1.40/1.26 ------------------------
% 1.40/1.26 ---- Cleaned THF ---
% 1.40/1.26 thf(in_type,type,
% 1.40/1.26 in: $i > $i > $o ).
% 1.40/1.26
% 1.40/1.26 thf(subset_type,type,
% 1.40/1.26 subset: $i > $i > $o ).
% 1.40/1.26
% 1.40/1.26 thf(subsetI2_type,type,
% 1.40/1.26 subsetI2: $o ).
% 1.40/1.26
% 1.40/1.26 thf(subsetI2,definition,
% 1.40/1.26 ( subsetI2
% 1.40/1.26 = ( ! [A: $i,B: $i] :
% 1.40/1.26 ( ! [Xx: $i] :
% 1.40/1.26 ( ( in @ Xx @ A )
% 1.40/1.26 => ( in @ Xx @ B ) )
% 1.40/1.26 => ( subset @ A @ B ) ) ) ) ).
% 1.40/1.26
% 1.40/1.26 thf(binunion_type,type,
% 1.40/1.26 binunion: $i > $i > $i ).
% 1.40/1.26
% 1.40/1.26 thf(binunionIR_type,type,
% 1.40/1.26 binunionIR: $o ).
% 1.40/1.26
% 1.40/1.26 thf(binunionIR,definition,
% 1.40/1.26 ( binunionIR
% 1.40/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.40/1.26 ( ( in @ Xx @ B )
% 1.40/1.26 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.40/1.26
% 1.40/1.26 thf(binunionRsub,conjecture,
% 1.40/1.26 ( subsetI2
% 1.40/1.26 => ( binunionIR
% 1.40/1.26 => ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 1.40/1.27 ------------------------
% 1.40/1.28 % (18410)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18311 for (2999ds/183Mi)
% 1.40/1.28 % (18414)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_18311 for (2999ds/2Mi)
% 1.40/1.28 % (18415)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_18311 for (2999ds/275Mi)
% 1.40/1.28 % (18416)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18311 for (2999ds/18Mi)
% 1.40/1.28 % (18412)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_18311 for (2999ds/27Mi)
% 1.40/1.28 % (18413)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18311 for (2999ds/2Mi)
% 1.40/1.28 % (18411)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_18311 for (2999ds/4Mi)
% 1.40/1.29 % (18413)Instruction limit reached!
% 1.40/1.29 % (18413)------------------------------
% 1.40/1.29 % (18413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (18413)Termination reason: Unknown
% 1.40/1.29 % (18413)Termination phase: Saturation
% 1.40/1.29
% 1.40/1.29 % (18413)Memory used [KB]: 5373
% 1.40/1.29 % (18413)Time elapsed: 0.003 s
% 1.40/1.29 % (18413)Instructions burned: 2 (million)
% 1.40/1.29 % (18413)------------------------------
% 1.40/1.29 % (18413)------------------------------
% 1.40/1.29 % (18414)Instruction limit reached!
% 1.40/1.29 % (18414)------------------------------
% 1.40/1.29 % (18414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (18414)Termination reason: Unknown
% 1.40/1.29 % (18414)Termination phase: Saturation
% 1.40/1.29
% 1.40/1.29 % (18414)Memory used [KB]: 5373
% 1.40/1.29 % (18414)Time elapsed: 0.003 s
% 1.40/1.29 % (18414)Instructions burned: 2 (million)
% 1.40/1.29 % (18414)------------------------------
% 1.40/1.29 % (18414)------------------------------
% 1.40/1.29 % (18411)Instruction limit reached!
% 1.40/1.29 % (18411)------------------------------
% 1.40/1.29 % (18411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (18411)Termination reason: Unknown
% 1.40/1.29 % (18411)Termination phase: Saturation
% 1.40/1.29
% 1.40/1.29 % (18411)Memory used [KB]: 5500
% 1.40/1.29 % (18411)Time elapsed: 0.004 s
% 1.40/1.29 % (18411)Instructions burned: 4 (million)
% 1.40/1.29 % (18411)------------------------------
% 1.40/1.29 % (18411)------------------------------
% 1.40/1.29 % (18416)First to succeed.
% 1.40/1.29 % (18410)Also succeeded, but the first one will report.
% 1.40/1.29 % (18415)Also succeeded, but the first one will report.
% 1.40/1.29 % (18416)Refutation found. Thanks to Tanya!
% 1.40/1.29 % SZS status Theorem for DTF2THF_18311
% 1.40/1.29 % SZS output start Proof for DTF2THF_18311
% 1.40/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.40/1.29 thf(func_def_1, type, subset: $i > $i > $o).
% 1.40/1.29 thf(func_def_4, type, binunion: $i > $i > $i).
% 1.40/1.29 thf(func_def_10, type, sK2: $i > $i > $i).
% 1.40/1.29 thf(f55,plain,(
% 1.40/1.29 $false),
% 1.40/1.29 inference(subsumption_resolution,[status(thm)],[f54,f27])).
% 1.40/1.29 thf(f27,plain,(
% 1.40/1.29 ((subset @ sK0 @ (binunion @ sK1 @ sK0)) != $true)),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.29 thf(f17,plain,(
% 1.40/1.29 (binunionIR = $true) & (subsetI2 = $true) & ((subset @ sK0 @ (binunion @ sK1 @ sK0)) != $true)),
% 1.40/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16])).
% 1.40/1.29 thf(f16,plain,(
% 1.40/1.29 ? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X1 @ X0)) != $true) => ((subset @ sK0 @ (binunion @ sK1 @ sK0)) != $true)),
% 1.40/1.29 introduced(definition,[],[choice_axiom])).
% 1.40/1.29 thf(f13,plain,(
% 1.40/1.29 (binunionIR = $true) & (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X1 @ X0)) != $true)),
% 1.40/1.29 inference(flattening,[status(thm)],[f12])).
% 1.40/1.29 thf(f12,plain,(
% 1.40/1.29 (? [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X1 @ X0)) != $true) & (binunionIR = $true)) & (subsetI2 = $true)),
% 1.40/1.29 inference(ennf_transformation,[status(thm)],[f11])).
% 1.40/1.29 thf(f11,plain,(
% 1.40/1.29 ~((subsetI2 = $true) => ((binunionIR = $true) => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ (binunion @ X1 @ X0)) = $true)))),
% 1.40/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.40/1.29 thf(f10,plain,(
% 1.40/1.29 ~(subsetI2 => (binunionIR => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X1 @ X0))))),
% 1.40/1.29 inference(rectify,[status(thm)],[f4])).
% 1.40/1.29 thf(f4,negated_conjecture,(
% 1.40/1.29 ~(subsetI2 => (binunionIR => ! [X1 : $i,X0 : $i] : (subset @ X1 @ (binunion @ X0 @ X1))))),
% 1.40/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.40/1.29 thf(f3,conjecture,(
% 1.40/1.29 subsetI2 => (binunionIR => ! [X1 : $i,X0 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 1.40/1.29 file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',binunionRsub)).
% 1.40/1.29 thf(f54,plain,(
% 1.40/1.29 ((subset @ sK0 @ (binunion @ sK1 @ sK0)) = $true)),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.40/1.29 thf(f51,plain,(
% 1.40/1.29 ((subset @ sK0 @ (binunion @ sK1 @ sK0)) = $true) | ($true != $true)),
% 1.40/1.29 inference(superposition,[status(thm)],[f46,f50])).
% 1.40/1.29 thf(f50,plain,(
% 1.40/1.29 ( ! [X0 : $i] : (((in @ (sK2 @ (binunion @ sK1 @ sK0) @ sK0) @ (binunion @ X0 @ sK0)) = $true)) )),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.40/1.29 thf(f49,plain,(
% 1.40/1.29 ( ! [X0 : $i] : (($true != $true) | ((in @ (sK2 @ (binunion @ sK1 @ sK0) @ sK0) @ (binunion @ X0 @ sK0)) = $true)) )),
% 1.40/1.29 inference(superposition,[status(thm)],[f45,f48])).
% 1.40/1.29 thf(f48,plain,(
% 1.40/1.29 ((in @ (sK2 @ (binunion @ sK1 @ sK0) @ sK0) @ sK0) = $true)),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.40/1.29 thf(f47,plain,(
% 1.40/1.29 ((in @ (sK2 @ (binunion @ sK1 @ sK0) @ sK0) @ sK0) = $true) | ($true != $true)),
% 1.40/1.29 inference(superposition,[status(thm)],[f27,f44])).
% 1.40/1.29 thf(f44,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X0))) )),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.40/1.29 thf(f38,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X0)) | ((subset @ X0 @ X1) = $true)) )),
% 1.40/1.29 inference(definition_unfolding,[status(thm)],[f32,f28])).
% 1.40/1.29 thf(f28,plain,(
% 1.40/1.29 (subsetI2 = $true)),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.29 thf(f32,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X0)) | (subsetI2 != $true)) )),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f22])).
% 1.40/1.29 thf(f22,plain,(
% 1.40/1.29 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (((in @ (sK2 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK2 @ X1 @ X0) @ X0)))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (($true != (subset @ sK3 @ sK4)) & ! [X5 : $i] : (((in @ X5 @ sK4) = $true) | ($true != (in @ X5 @ sK3)))))),
% 1.40/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f19,f21,f20])).
% 1.40/1.29 thf(f20,plain,(
% 1.40/1.29 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK2 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK2 @ X1 @ X0) @ X0))))),
% 1.40/1.29 introduced(definition,[],[choice_axiom])).
% 1.40/1.29 thf(f21,plain,(
% 1.40/1.29 ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)))) => (($true != (subset @ sK3 @ sK4)) & ! [X5 : $i] : (((in @ X5 @ sK4) = $true) | ($true != (in @ X5 @ sK3))))),
% 1.40/1.29 introduced(definition,[],[choice_axiom])).
% 1.40/1.29 thf(f19,plain,(
% 1.40/1.29 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)))))),
% 1.40/1.29 inference(rectify,[status(thm)],[f18])).
% 1.40/1.29 thf(f18,plain,(
% 1.40/1.29 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))))),
% 1.40/1.29 inference(nnf_transformation,[status(thm)],[f14])).
% 1.40/1.29 thf(f14,plain,(
% 1.40/1.29 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) <=> (subsetI2 = $true)),
% 1.40/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.40/1.29 thf(f7,plain,(
% 1.40/1.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.40/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.40/1.29 thf(f6,plain,(
% 1.40/1.29 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.40/1.29 inference(rectify,[status(thm)],[f1])).
% 1.40/1.29 thf(f1,axiom,(
% 1.40/1.29 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.40/1.29 file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',subsetI2)).
% 1.40/1.29 thf(f45,plain,(
% 1.40/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ (binunion @ X4 @ X3)) = $true)) )),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.40/1.29 thf(f43,plain,(
% 1.40/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X5 @ X3)) | ((in @ X5 @ (binunion @ X4 @ X3)) = $true)) )),
% 1.40/1.29 inference(definition_unfolding,[status(thm)],[f34,f29])).
% 1.40/1.29 thf(f29,plain,(
% 1.40/1.29 (binunionIR = $true)),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.29 thf(f34,plain,(
% 1.40/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ (binunion @ X4 @ X3)) = $true) | (binunionIR != $true)) )),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f26])).
% 1.40/1.29 thf(f26,plain,(
% 1.40/1.29 ((binunionIR = $true) | (((in @ sK7 @ sK5) = $true) & ((in @ sK7 @ (binunion @ sK6 @ sK5)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ (binunion @ X4 @ X3)) = $true)) | (binunionIR != $true))),
% 1.40/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f25])).
% 1.40/1.29 thf(f25,plain,(
% 1.40/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (binunion @ X1 @ X0)) != $true)) => (((in @ sK7 @ sK5) = $true) & ((in @ sK7 @ (binunion @ sK6 @ sK5)) != $true))),
% 1.40/1.29 introduced(definition,[],[choice_axiom])).
% 1.40/1.29 thf(f24,plain,(
% 1.40/1.29 ((binunionIR = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (binunion @ X1 @ X0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ (binunion @ X4 @ X3)) = $true)) | (binunionIR != $true))),
% 1.40/1.29 inference(rectify,[status(thm)],[f23])).
% 1.40/1.29 thf(f23,plain,(
% 1.40/1.29 ((binunionIR = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ (binunion @ X2 @ X0)) != $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ((in @ X1 @ (binunion @ X2 @ X0)) = $true)) | (binunionIR != $true))),
% 1.40/1.29 inference(nnf_transformation,[status(thm)],[f15])).
% 1.40/1.29 thf(f15,plain,(
% 1.40/1.29 (binunionIR = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ((in @ X1 @ (binunion @ X2 @ X0)) = $true))),
% 1.40/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.40/1.29 thf(f9,plain,(
% 1.40/1.29 (binunionIR = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) => ((in @ X1 @ (binunion @ X2 @ X0)) = $true))),
% 1.40/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.40/1.29 thf(f8,plain,(
% 1.40/1.29 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 1.40/1.29 inference(rectify,[status(thm)],[f2])).
% 1.40/1.29 thf(f2,axiom,(
% 1.40/1.29 (binunionIR = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 1.40/1.29 file('/export/starexec/sandbox/tmp/tmp.Bf7R7OMvPT/DTF2THF_18311.p',binunionIR)).
% 1.40/1.29 thf(f46,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.40/1.29 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.40/1.29 thf(f37,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X0) @ X1) != $true) | ($true != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.40/1.29 inference(definition_unfolding,[status(thm)],[f33,f28])).
% 1.40/1.29 thf(f33,plain,(
% 1.40/1.29 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK2 @ X1 @ X0) @ X1) != $true) | (subsetI2 != $true)) )),
% 1.40/1.29 inference(cnf_transformation,[status(thm)],[f22])).
% 1.40/1.29 % SZS output end Proof for DTF2THF_18311
% 1.40/1.29 % (18416)------------------------------
% 1.40/1.29 % (18416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (18416)Termination reason: Refutation
% 1.40/1.29
% 1.40/1.29 % (18416)Memory used [KB]: 5500
% 1.40/1.29 % (18416)Time elapsed: 0.006 s
% 1.40/1.29 % (18416)Instructions burned: 4 (million)
% 1.40/1.29 % (18416)------------------------------
% 1.40/1.29 % (18416)------------------------------
% 1.40/1.29 % (18409)Success in time 0.021 s
%------------------------------------------------------------------------------