%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU599^2 : 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 : n019.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 09:35:31 AM UTC 2026
% Result : Theorem 1.66s 1.33s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 140 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 447 ( 56 ~; 44 |; 36 &; 278 @)
% ( 4 <=>; 29 =>; 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 : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 75 !; 25 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_18,type,
sK9: $i > $i > $i ).
thf(f75,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f74,f41]) ).
thf(f41,plain,
( ( subset @ sK4 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( in__Cong = $true )
& ( ( binintersect @ sK4 @ sK3 )
= sK4 )
& ( ( subset @ sK4 @ sK3 )
!= $true )
& ( subsetI1 = $true )
& ( binintersectER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f19,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) )
=> ( ( ( binintersect @ sK4 @ sK3 )
= sK4 )
& ( ( subset @ sK4 @ sK3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( in__Cong = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( subsetI1 = $true )
& ( binintersectER = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( in__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X1: $i,X0: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X1: $i,X0: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',binintersectSubset1) ).
thf(f74,plain,
( ( subset @ sK4 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( subset @ sK4 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f67,f72]) ).
thf(f72,plain,
( ( in @ ( sK9 @ sK3 @ sK4 ) @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( in @ ( sK9 @ sK3 @ sK4 ) @ sK3 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f68,f70]) ).
thf(f70,plain,
( $true
= ( in @ ( sK9 @ sK3 @ sK4 ) @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true
= ( in @ ( sK9 @ sK3 @ sK4 ) @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f41,f66]) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f50,f40]) ).
thf(f40,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ( ( subset @ sK10 @ sK11 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK11 ) )
| ( $true
!= ( in @ X5 @ sK10 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f32,f34,f33]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ) )
=> ( ( ( subset @ sK10 @ sK11 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK11 ) )
| ( $true
!= ( in @ X5 @ sK10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',subsetI1) ).
thf(f68,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK4 ) )
| ( ( in @ X0 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f65,f42]) ).
thf(f42,plain,
( ( binintersect @ sK4 @ sK3 )
= sK4 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f39]) ).
thf(f39,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f22]) ).
thf(f22,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
= $true )
& ( ( in @ X3 @ X5 )
!= $true ) )
=> ( ( ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
= $true )
& ( ( in @ X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( $true
!= ( in @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( binintersectER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
=> ( $true
= ( in @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( binintersectER
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',binintersectER) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f51,f40]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU599^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:28:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU599^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! B:i.binintersect A B = A -> subset A B)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC101l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.30/0.46 % Number of atoms : 20 ( 6 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.30/0.46 % Number of connectives : 30 ( 0 ~; 0 |; 0 &; 20 @)
% 0.30/0.46 % ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=362
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong_type,type,
% 0.30/0.46 in__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong,definition,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER_type,type,
% 0.30/0.46 binintersectER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER,definition,
% 0.30/0.46 ( binintersectER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1,conjecture,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 => ( subsetI1
% 0.30/0.46 => ( binintersectER
% 0.30/0.46 => ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = A )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.29 ---- Embedded in THF ---
% 1.48/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.29 %%% Generated on Tue Feb 24 12:28:10 EST 2026
% 1.48/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.29 %%% Logic specification used:
% 1.48/1.29 %%% thf(spec, logic, $$dhol).
% 1.48/1.29
% 1.48/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2DTF7941.p
% See solution above
% 1.48/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(in_type,type,
% 1.66/1.30 in: $i > $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(in__Cong_type,type,
% 1.66/1.30 in__Cong: $o ).
% 1.66/1.30
% 1.66/1.30 thf(in__Cong,definition,
% 1.66/1.30 ( in__Cong
% 1.66/1.30 = ( ! [A: $i,B: $i] :
% 1.66/1.30 ( ( A = B )
% 1.66/1.30 => ! [Xx: $i,Xy: $i] :
% 1.66/1.30 ( ( Xx = Xy )
% 1.66/1.30 => ( ( in @ Xx @ A )
% 1.66/1.30 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(subset_type,type,
% 1.66/1.30 subset: $i > $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(subsetI1_type,type,
% 1.66/1.30 subsetI1: $o ).
% 1.66/1.30
% 1.66/1.30 thf(subsetI1,definition,
% 1.66/1.30 ( subsetI1
% 1.66/1.30 = ( ! [A: $i,B: $i] :
% 1.66/1.30 ( ! [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ A )
% 1.66/1.30 => ( in @ Xx @ B ) )
% 1.66/1.30 => ( subset @ A @ B ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(binintersect_type,type,
% 1.66/1.30 binintersect: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER_type,type,
% 1.66/1.30 binintersectER: $o ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER,definition,
% 1.66/1.30 ( binintersectER
% 1.66/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.66/1.30 => ( in @ Xx @ B ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectSubset1,conjecture,
% 1.66/1.30 ( in__Cong
% 1.66/1.30 => ( subsetI1
% 1.66/1.30 => ( binintersectER
% 1.66/1.30 => ! [A: $i,B: $i] :
% 1.66/1.30 ( ( ( binintersect @ A @ B )
% 1.66/1.30 = A )
% 1.66/1.30 => ( subset @ A @ B ) ) ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.32 % (8215)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_7941 for (2999ds/4Mi)
% 1.66/1.32 % (8215)Instruction limit reached!
% 1.66/1.32 % (8215)------------------------------
% 1.66/1.32 % (8215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8215)Termination reason: Unknown
% 1.66/1.32 % (8215)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (8215)Memory used [KB]: 5500
% 1.66/1.32 % (8215)Time elapsed: 0.003 s
% 1.66/1.32 % (8215)Instructions burned: 5 (million)
% 1.66/1.32 % (8215)------------------------------
% 1.66/1.32 % (8215)------------------------------
% 1.66/1.32 % (8217)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7941 for (2999ds/2Mi)
% 1.66/1.32 % (8217)Instruction limit reached!
% 1.66/1.32 % (8217)------------------------------
% 1.66/1.32 % (8217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8217)Termination reason: Unknown
% 1.66/1.32 % (8217)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (8217)Memory used [KB]: 895
% 1.66/1.32 % (8217)Time elapsed: 0.002 s
% 1.66/1.32 % (8217)Instructions burned: 2 (million)
% 1.66/1.32 % (8217)------------------------------
% 1.66/1.32 % (8217)------------------------------
% 1.66/1.32 % (8214)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7941 for (2999ds/183Mi)
% 1.66/1.32 % (8216)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_7941 for (2999ds/27Mi)
% 1.66/1.32 % (8218)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_7941 for (2999ds/2Mi)
% 1.66/1.32 % (8219)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_7941 for (2999ds/275Mi)
% 1.66/1.32 % (8220)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7941 for (2999ds/18Mi)
% 1.66/1.32 % (8218)Instruction limit reached!
% 1.66/1.32 % (8218)------------------------------
% 1.66/1.32 % (8218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8218)Termination reason: Unknown
% 1.66/1.32 % (8218)Termination phase: Unused predicate definition removal
% 1.66/1.32
% 1.66/1.32 % (8218)Memory used [KB]: 895
% 1.66/1.32 % (8218)Time elapsed: 0.003 s
% 1.66/1.32 % (8218)Instructions burned: 2 (million)
% 1.66/1.32 % (8218)------------------------------
% 1.66/1.32 % (8218)------------------------------
% 1.66/1.33 % (8220)First to succeed.
% 1.66/1.33 % (8221)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7941 for (2999ds/3Mi)
% 1.66/1.33 % (8219)Also succeeded, but the first one will report.
% 1.66/1.33 % (8221)Instruction limit reached!
% 1.66/1.33 % (8221)------------------------------
% 1.66/1.33 % (8221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (8221)Termination reason: Unknown
% 1.66/1.33 % (8221)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (8221)Memory used [KB]: 5500
% 1.66/1.33 % (8221)Time elapsed: 0.003 s
% 1.66/1.33 % (8221)Instructions burned: 3 (million)
% 1.66/1.33 % (8221)------------------------------
% 1.66/1.33 % (8221)------------------------------
% 1.66/1.33 % (8220)Refutation found. Thanks to Tanya!
% 1.66/1.33 % SZS status Theorem for DTF2THF_7941
% 1.66/1.33 % SZS output start Proof for DTF2THF_7941
% 1.66/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.33 thf(func_def_3, type, subset: $i > $i > $o).
% 1.66/1.33 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.66/1.33 thf(func_def_18, type, sK9: $i > $i > $i).
% 1.66/1.33 thf(f75,plain,(
% 1.66/1.33 $false),
% 1.66/1.33 inference(subsumption_resolution,[status(thm)],[f74,f41])).
% 1.66/1.33 thf(f41,plain,(
% 1.66/1.33 ((subset @ sK4 @ sK3) != $true)),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.66/1.33 thf(f25,plain,(
% 1.66/1.33 (in__Cong = $true) & (((binintersect @ sK4 @ sK3) = sK4) & ((subset @ sK4 @ sK3) != $true)) & (subsetI1 = $true) & (binintersectER = $true)),
% 1.66/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f19,f24])).
% 1.66/1.33 thf(f24,plain,(
% 1.66/1.33 ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X1) & ((subset @ X1 @ X0) != $true)) => (((binintersect @ sK4 @ sK3) = sK4) & ((subset @ sK4 @ sK3) != $true))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f19,plain,(
% 1.66/1.33 (in__Cong = $true) & ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X1) & ((subset @ X1 @ X0) != $true)) & (subsetI1 = $true) & (binintersectER = $true)),
% 1.66/1.33 inference(flattening,[status(thm)],[f18])).
% 1.66/1.33 thf(f18,plain,(
% 1.66/1.33 ((? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X1) & ((subset @ X1 @ X0) != $true)) & (binintersectER = $true)) & (subsetI1 = $true)) & (in__Cong = $true)),
% 1.66/1.33 inference(ennf_transformation,[status(thm)],[f12])).
% 1.66/1.33 thf(f12,plain,(
% 1.66/1.33 ~((in__Cong = $true) => ((subsetI1 = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X1) => ((subset @ X1 @ X0) = $true)))))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.33 thf(f11,plain,(
% 1.66/1.33 ~(in__Cong => (subsetI1 => (binintersectER => ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X1) => (subset @ X1 @ X0)))))),
% 1.66/1.33 inference(rectify,[status(thm)],[f5])).
% 1.66/1.33 thf(f5,negated_conjecture,(
% 1.66/1.33 ~(in__Cong => (subsetI1 => (binintersectER => ! [X1 : $i,X0 : $i] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1)))))),
% 1.66/1.33 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.33 thf(f4,conjecture,(
% 1.66/1.33 in__Cong => (subsetI1 => (binintersectER => ! [X1 : $i,X0 : $i] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1))))),
% 1.66/1.33 file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',binintersectSubset1)).
% 1.66/1.33 thf(f74,plain,(
% 1.66/1.33 ((subset @ sK4 @ sK3) = $true)),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.66/1.33 thf(f73,plain,(
% 1.66/1.33 ((subset @ sK4 @ sK3) = $true) | ($true != $true)),
% 1.66/1.33 inference(superposition,[status(thm)],[f67,f72])).
% 1.66/1.33 thf(f72,plain,(
% 1.66/1.33 ((in @ (sK9 @ sK3 @ sK4) @ sK3) = $true)),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.66/1.33 thf(f71,plain,(
% 1.66/1.33 ((in @ (sK9 @ sK3 @ sK4) @ sK3) = $true) | ($true != $true)),
% 1.66/1.33 inference(superposition,[status(thm)],[f68,f70])).
% 1.66/1.33 thf(f70,plain,(
% 1.66/1.33 ($true = (in @ (sK9 @ sK3 @ sK4) @ sK4))),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.66/1.33 thf(f69,plain,(
% 1.66/1.33 ($true = (in @ (sK9 @ sK3 @ sK4) @ sK4)) | ($true != $true)),
% 1.66/1.33 inference(superposition,[status(thm)],[f41,f66])).
% 1.66/1.33 thf(f66,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK9 @ X1 @ X0) @ X0))) )),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.66/1.33 thf(f60,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true != $true) | ($true = (in @ (sK9 @ X1 @ X0) @ X0))) )),
% 1.66/1.33 inference(definition_unfolding,[status(thm)],[f50,f40])).
% 1.66/1.33 thf(f40,plain,(
% 1.66/1.33 (subsetI1 = $true)),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.66/1.33 thf(f50,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK9 @ X1 @ X0) @ X0)) | (subsetI1 != $true)) )),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f35])).
% 1.66/1.33 thf(f35,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (((in @ (sK9 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK9 @ X1 @ X0) @ X0)))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (((subset @ sK10 @ sK11) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ sK11)) | ($true != (in @ X5 @ sK10)))))),
% 1.66/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f32,f34,f33])).
% 1.66/1.33 thf(f33,plain,(
% 1.66/1.33 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK9 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK9 @ X1 @ X0) @ X0))))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f34,plain,(
% 1.66/1.33 ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true))) => (((subset @ sK10 @ sK11) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ sK11)) | ($true != (in @ X5 @ sK10))))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f32,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true))))),
% 1.66/1.33 inference(rectify,[status(thm)],[f31])).
% 1.66/1.33 thf(f31,plain,(
% 1.66/1.33 (! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true))))),
% 1.66/1.33 inference(nnf_transformation,[status(thm)],[f17])).
% 1.66/1.33 thf(f17,plain,(
% 1.66/1.33 ! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) <=> (subsetI1 = $true)),
% 1.66/1.33 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.33 thf(f10,plain,(
% 1.66/1.33 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.33 thf(f9,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 1.66/1.33 inference(rectify,[status(thm)],[f2])).
% 1.66/1.33 thf(f2,axiom,(
% 1.66/1.33 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.66/1.33 file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',subsetI1)).
% 1.66/1.33 thf(f68,plain,(
% 1.66/1.33 ( ! [X0 : $i] : (($true != (in @ X0 @ sK4)) | ((in @ X0 @ sK3) = $true)) )),
% 1.66/1.33 inference(superposition,[status(thm)],[f65,f42])).
% 1.66/1.33 thf(f42,plain,(
% 1.66/1.33 ((binintersect @ sK4 @ sK3) = sK4)),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.66/1.33 thf(f65,plain,(
% 1.66/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true)) )),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.66/1.33 thf(f52,plain,(
% 1.66/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ($true != $true) | ((in @ X0 @ (binintersect @ X1 @ X2)) != $true)) )),
% 1.66/1.33 inference(definition_unfolding,[status(thm)],[f38,f39])).
% 1.66/1.33 thf(f39,plain,(
% 1.66/1.33 (binintersectER = $true)),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.66/1.33 thf(f38,plain,(
% 1.66/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true) | (binintersectER != $true)) )),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.33 thf(f23,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true)) | (binintersectER != $true)) & ((binintersectER = $true) | (((in @ sK0 @ (binintersect @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK2) != $true)))),
% 1.66/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f22])).
% 1.66/1.33 thf(f22,plain,(
% 1.66/1.33 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) = $true) & ((in @ X3 @ X5) != $true)) => (((in @ sK0 @ (binintersect @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK2) != $true))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f21,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) = $true) & ((in @ X3 @ X5) != $true)))),
% 1.66/1.33 inference(rectify,[status(thm)],[f20])).
% 1.66/1.33 thf(f20,plain,(
% 1.66/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ($true = (in @ X1 @ X0))) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X1 @ (binintersect @ X2 @ X0))) & ($true != (in @ X1 @ X0))))),
% 1.66/1.33 inference(nnf_transformation,[status(thm)],[f16])).
% 1.66/1.33 thf(f16,plain,(
% 1.66/1.33 ! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ($true = (in @ X1 @ X0))) <=> (binintersectER = $true)),
% 1.66/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.33 thf(f8,plain,(
% 1.66/1.33 (binintersectER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (binintersect @ X2 @ X0))) => ($true = (in @ X1 @ X0)))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.33 thf(f7,plain,(
% 1.66/1.33 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X0)))),
% 1.66/1.33 inference(rectify,[status(thm)],[f3])).
% 1.66/1.33 thf(f3,axiom,(
% 1.66/1.33 (binintersectER = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 1.66/1.33 file('/export/starexec/sandbox/tmp/tmp.cnYMgMMYnY/DTF2THF_7941.p',binintersectER)).
% 1.66/1.33 thf(f67,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ (sK9 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.66/1.33 thf(f59,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK9 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.66/1.33 inference(definition_unfolding,[status(thm)],[f51,f40])).
% 1.66/1.33 thf(f51,plain,(
% 1.66/1.33 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK9 @ X1 @ X0) @ X1) != $true) | (subsetI1 != $true)) )),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f35])).
% 1.66/1.33 % SZS output end Proof for DTF2THF_7941
% 1.66/1.33 % (8220)------------------------------
% 1.66/1.33 % (8220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (8220)Termination reason: Refutation
% 1.66/1.33
% 1.66/1.33 % (8220)Memory used [KB]: 5500
% 1.66/1.33 % (8220)Time elapsed: 0.007 s
% 1.66/1.33 % (8220)Instructions burned: 4 (million)
% 1.66/1.33 % (8220)------------------------------
% 1.66/1.33 % (8220)------------------------------
% 1.66/1.33 % (8213)Success in time 0.024 s
%------------------------------------------------------------------------------