%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU597^2 : 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 : n026.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 09:35:30 AM UTC 2026
% Result : Theorem 1.67s 1.34s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 433 ( 130 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 452 ( 57 ~; 46 |; 30 &; 294 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 113 ( 0 ^; 86 !; 27 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_10,type,
sK2: $i > $i > $i ).
thf(f59,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
$true != $true,
inference(superposition,[status(thm)],[f34,f57]) ).
thf(f57,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f47,f49]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f45,f46]) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f28,f33]) ).
thf(f33,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
!= ( subset @ ( binintersect @ sK3 @ sK4 ) @ sK4 ) )
& ( subsetI2 = $true )
& ( binintersectER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true )
=> ( $true
!= ( subset @ ( binintersect @ sK3 @ sK4 ) @ sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true )
& ( subsetI2 = $true )
& ( binintersectER = $true ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
!= $true )
& ( subsetI2 = $true )
& ( binintersectER = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
!= $true )
& ( binintersectER = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( subsetI2 = $true )
=> ( ( binintersectER = $true )
=> ! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( subsetI2
=> ( binintersectER
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X1 @ X0 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetI2
=> ( binintersectER
=> ! [X1: $i,X0: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetI2
=> ( binintersectER
=> ! [X1: $i,X0: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2THF_6461.p',binintersectRsub) ).
thf(f28,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK1 @ sK0 ) )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK0 ) )
| ( $true
!= ( in @ X2 @ sK1 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) )
| ( subsetI2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
=> ( ( $true
!= ( subset @ sK1 @ sK0 ) )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK0 ) )
| ( $true
!= ( in @ X2 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true ) )
=> ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true ) ) )
| ( subsetI2 != $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( subsetI2 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetI2 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,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)],[f8]) ).
thf(f8,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.CTpd8ytSCc/DTF2THF_6461.p',subsetI2) ).
thf(f45,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f32]) ).
thf(f32,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f35,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( binintersectER = $true )
| ( ( $true
!= ( in @ sK7 @ sK5 ) )
& ( $true
= ( in @ sK7 @ ( binintersect @ sK6 @ sK5 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) )
=> ( ( $true
!= ( in @ sK7 @ sK5 ) )
& ( $true
= ( in @ sK7 @ ( binintersect @ sK6 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( binintersectER = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binintersectER = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( binintersectER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2THF_6461.p',binintersectER) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f33]) ).
thf(f29,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f34,plain,
( $true
!= ( subset @ ( binintersect @ sK3 @ sK4 ) @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU597^2 : 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 : n026.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 12:28:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : SEU597^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.47 % Domain : Set Theory
% 0.32/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.32/0.47 % Version : Especial > Reduced > Especial.
% 0.32/0.47 % English : (! A:i.! B:i.subset (binintersect A B) B)
% 0.32/0.47
% 0.32/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.47 % Source : [Bro08]
% 0.32/0.47 % Names : ZFC099l [Bro08]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % 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 v4.1.0, 0.00 v3.7.0
% 0.32/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.32/0.47 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 3 ( 4 avg)
% 0.32/0.47 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.32/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 9 ( 4 avg)
% 0.32/0.47 % Number of types : 2 ( 0 usr)
% 0.32/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.32/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.32/0.47 % SPC : TH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : http://mathgate.info/detsetitem.php?id=293
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf(in_type,type,
% 0.32/0.47 in: $i > $i > $o ).
% 0.32/0.47
% 0.32/0.47 thf(subset_type,type,
% 0.32/0.47 subset: $i > $i > $o ).
% 0.32/0.47
% 0.32/0.47 thf(subsetI2_type,type,
% 0.32/0.47 subsetI2: $o ).
% 0.32/0.47
% 0.32/0.47 thf(subsetI2,definition,
% 0.32/0.47 ( subsetI2
% 0.32/0.47 = ( ! [A: $i,B: $i] :
% 0.32/0.47 ( ! [Xx: $i] :
% 0.32/0.47 ( ( in @ Xx @ A )
% 0.32/0.47 => ( in @ Xx @ B ) )
% 0.32/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(binintersect_type,type,
% 0.32/0.47 binintersect: $i > $i > $i ).
% 0.32/0.47
% 0.32/0.47 thf(binintersectER_type,type,
% 0.32/0.47 binintersectER: $o ).
% 0.32/0.47
% 0.32/0.47 thf(binintersectER,definition,
% 0.32/0.47 ( binintersectER
% 0.32/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(binintersectRsub,conjecture,
% 0.32/0.47 ( subsetI2
% 0.32/0.47 => ( binintersectER
% 0.32/0.47 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.67/1.31 ---- Embedded in THF ---
% 1.67/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.31 %%% Generated on Tue Feb 24 12:28:26 EST 2026
% 1.67/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.31 %%% Logic specification used:
% 1.67/1.31 %%% thf(spec, logic, $$dhol).
% 1.67/1.31
% 1.67/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2DTF6461.p
% See solution above
% 1.67/1.31 ------------------------
% 1.67/1.32 ---- Cleaned THF ---
% 1.67/1.32 thf(in_type,type,
% 1.67/1.32 in: $i > $i > $o ).
% 1.67/1.32
% 1.67/1.32 thf(subset_type,type,
% 1.67/1.32 subset: $i > $i > $o ).
% 1.67/1.32
% 1.67/1.32 thf(subsetI2_type,type,
% 1.67/1.32 subsetI2: $o ).
% 1.67/1.32
% 1.67/1.32 thf(subsetI2,definition,
% 1.67/1.32 ( subsetI2
% 1.67/1.32 = ( ! [A: $i,B: $i] :
% 1.67/1.32 ( ! [Xx: $i] :
% 1.67/1.32 ( ( in @ Xx @ A )
% 1.67/1.32 => ( in @ Xx @ B ) )
% 1.67/1.32 => ( subset @ A @ B ) ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf(binintersect_type,type,
% 1.67/1.32 binintersect: $i > $i > $i ).
% 1.67/1.32
% 1.67/1.32 thf(binintersectER_type,type,
% 1.67/1.32 binintersectER: $o ).
% 1.67/1.32
% 1.67/1.32 thf(binintersectER,definition,
% 1.67/1.32 ( binintersectER
% 1.67/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.67/1.32 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.67/1.32 => ( in @ Xx @ B ) ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf(binintersectRsub,conjecture,
% 1.67/1.32 ( subsetI2
% 1.67/1.32 => ( binintersectER
% 1.67/1.32 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 1.67/1.32 ------------------------
% 1.67/1.34 % (6654)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_6461 for (3000ds/275Mi)
% 1.67/1.34 % (6654)First to succeed.
% 1.67/1.34 % (6652)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6461 for (3000ds/2Mi)
% 1.67/1.34 % (6652)Instruction limit reached!
% 1.67/1.34 % (6652)------------------------------
% 1.67/1.34 % (6652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (6652)Termination reason: Unknown
% 1.67/1.34 % (6652)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (6652)Memory used [KB]: 5500
% 1.67/1.34 % (6652)Time elapsed: 0.002 s
% 1.67/1.34 % (6652)Instructions burned: 3 (million)
% 1.67/1.34 % (6652)------------------------------
% 1.67/1.34 % (6652)------------------------------
% 1.67/1.34 % (6649)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6461 for (3000ds/183Mi)
% 1.67/1.34 % (6650)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_6461 for (3000ds/4Mi)
% 1.67/1.34 % (6653)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_6461 for (3000ds/2Mi)
% 1.67/1.34 % (6654)Refutation found. Thanks to Tanya!
% 1.67/1.34 % SZS status Theorem for DTF2THF_6461
% 1.67/1.34 % SZS output start Proof for DTF2THF_6461
% 1.67/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.34 thf(func_def_1, type, subset: $i > $i > $o).
% 1.67/1.34 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.67/1.34 thf(func_def_10, type, sK2: $i > $i > $i).
% 1.67/1.34 thf(f59,plain,(
% 1.67/1.34 $false),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.67/1.34 thf(f58,plain,(
% 1.67/1.34 ($true != $true)),
% 1.67/1.34 inference(superposition,[status(thm)],[f34,f57])).
% 1.67/1.34 thf(f57,plain,(
% 1.67/1.34 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1) = $true)) )),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.67/1.34 thf(f56,plain,(
% 1.67/1.34 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ (binintersect @ X0 @ X1) @ X1) = $true)) )),
% 1.67/1.34 inference(duplicate_literal_removal,[status(thm)],[f53])).
% 1.67/1.34 thf(f53,plain,(
% 1.67/1.34 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | ($true != $true)) )),
% 1.67/1.34 inference(superposition,[status(thm)],[f47,f49])).
% 1.67/1.34 thf(f49,plain,(
% 1.67/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.67/1.34 thf(f48,plain,(
% 1.67/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK2 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 1.67/1.34 inference(superposition,[status(thm)],[f45,f46])).
% 1.67/1.34 thf(f46,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.67/1.34 thf(f41,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f28,f33])).
% 1.67/1.34 thf(f33,plain,(
% 1.67/1.34 (subsetI2 = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.34 thf(f23,plain,(
% 1.67/1.34 ($true != (subset @ (binintersect @ sK3 @ sK4) @ sK4)) & (subsetI2 = $true) & (binintersectER = $true)),
% 1.67/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22])).
% 1.67/1.34 thf(f22,plain,(
% 1.67/1.34 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true) => ($true != (subset @ (binintersect @ sK3 @ sK4) @ sK4))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f21,plain,(
% 1.67/1.34 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true) & (subsetI2 = $true) & (binintersectER = $true)),
% 1.67/1.34 inference(rectify,[status(thm)],[f14])).
% 1.67/1.34 thf(f14,plain,(
% 1.67/1.34 ? [X1 : $i,X0 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) != $true) & (subsetI2 = $true) & (binintersectER = $true)),
% 1.67/1.34 inference(flattening,[status(thm)],[f13])).
% 1.67/1.34 thf(f13,plain,(
% 1.67/1.34 (? [X1 : $i,X0 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) != $true) & (binintersectER = $true)) & (subsetI2 = $true)),
% 1.67/1.34 inference(ennf_transformation,[status(thm)],[f7])).
% 1.67/1.34 thf(f7,plain,(
% 1.67/1.34 ~((subsetI2 = $true) => ((binintersectER = $true) => ! [X1 : $i,X0 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true)))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 1.67/1.34 thf(f6,plain,(
% 1.67/1.34 ~(subsetI2 => (binintersectER => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0)))),
% 1.67/1.34 inference(rectify,[status(thm)],[f4])).
% 1.67/1.34 thf(f4,negated_conjecture,(
% 1.67/1.34 ~(subsetI2 => (binintersectER => ! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1)))),
% 1.67/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 1.67/1.34 thf(f3,conjecture,(
% 1.67/1.34 subsetI2 => (binintersectER => ! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 1.67/1.34 file('/export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2THF_6461.p',binintersectRsub)).
% 1.67/1.34 thf(f28,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true) | (subsetI2 != $true)) )),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.34 thf(f20,plain,(
% 1.67/1.34 ((subsetI2 = $true) | (($true != (subset @ sK1 @ sK0)) & ! [X2 : $i] : (($true = (in @ X2 @ sK0)) | ($true != (in @ X2 @ sK1))))) & (! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true))) | (subsetI2 != $true))),
% 1.67/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18])).
% 1.67/1.34 thf(f18,plain,(
% 1.67/1.34 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true))) => (($true != (subset @ sK1 @ sK0)) & ! [X2 : $i] : (($true = (in @ X2 @ sK0)) | ($true != (in @ X2 @ sK1))))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f19,plain,(
% 1.67/1.34 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true)) => (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true)))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f17,plain,(
% 1.67/1.34 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ? [X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true))) | (subsetI2 != $true))),
% 1.67/1.34 inference(rectify,[status(thm)],[f16])).
% 1.67/1.34 thf(f16,plain,(
% 1.67/1.34 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)))) & (! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI2 != $true))),
% 1.67/1.34 inference(nnf_transformation,[status(thm)],[f15])).
% 1.67/1.34 thf(f15,plain,(
% 1.67/1.34 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)))),
% 1.67/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.34 thf(f9,plain,(
% 1.67/1.34 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.34 thf(f8,plain,(
% 1.67/1.34 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.67/1.34 inference(rectify,[status(thm)],[f1])).
% 1.67/1.34 thf(f1,axiom,(
% 1.67/1.34 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.67/1.34 file('/export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2THF_6461.p',subsetI2)).
% 1.67/1.34 thf(f45,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ((in @ X5 @ X3) = $true)) )),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.67/1.34 thf(f44,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ X3) = $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) != $true)) )),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f35,f32])).
% 1.67/1.34 thf(f32,plain,(
% 1.67/1.34 (binintersectER = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.34 thf(f35,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | (binintersectER != $true)) )),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.34 thf(f27,plain,(
% 1.67/1.34 ((binintersectER = $true) | (($true != (in @ sK7 @ sK5)) & ($true = (in @ sK7 @ (binintersect @ sK6 @ sK5))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) != $true)) | (binintersectER != $true))),
% 1.67/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f26])).
% 1.67/1.34 thf(f26,plain,(
% 1.67/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binintersect @ X1 @ X0)))) => (($true != (in @ sK7 @ sK5)) & ($true = (in @ sK7 @ (binintersect @ sK6 @ sK5))))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f25,plain,(
% 1.67/1.34 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binintersect @ X1 @ X0))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) != $true)) | (binintersectER != $true))),
% 1.67/1.34 inference(rectify,[status(thm)],[f24])).
% 1.67/1.34 thf(f24,plain,(
% 1.67/1.34 ((binintersectER = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectER != $true))),
% 1.67/1.34 inference(nnf_transformation,[status(thm)],[f12])).
% 1.67/1.34 thf(f12,plain,(
% 1.67/1.34 (binintersectER = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true))),
% 1.67/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.34 thf(f11,plain,(
% 1.67/1.34 (binintersectER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ((in @ X2 @ X1) = $true))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.34 thf(f10,plain,(
% 1.67/1.34 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 1.67/1.34 inference(rectify,[status(thm)],[f2])).
% 1.67/1.34 thf(f2,axiom,(
% 1.67/1.34 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 1.67/1.34 file('/export/starexec/sandbox/tmp/tmp.CTpd8ytSCc/DTF2THF_6461.p',binintersectER)).
% 1.67/1.34 thf(f47,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.67/1.34 thf(f40,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ($true != $true)) )),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f29,f33])).
% 1.67/1.34 thf(f29,plain,(
% 1.67/1.34 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X3) != $true) | (subsetI2 != $true)) )),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.34 thf(f34,plain,(
% 1.67/1.34 ($true != (subset @ (binintersect @ sK3 @ sK4) @ sK4))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.34 % SZS output end Proof for DTF2THF_6461
% 1.67/1.34 % (6654)------------------------------
% 1.67/1.34 % (6654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (6654)Termination reason: Refutation
% 1.67/1.34
% 1.67/1.34 % (6654)Memory used [KB]: 5500
% 1.67/1.34 % (6654)Time elapsed: 0.004 s
% 1.67/1.34 % (6654)Instructions burned: 4 (million)
% 1.67/1.34 % (6654)------------------------------
% 1.67/1.34 % (6654)------------------------------
% 1.67/1.34 % (6648)Success in time 0.002 s
%------------------------------------------------------------------------------