%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU591^2 : 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 : n008.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 09:35:28 AM UTC 2026
% Result : Theorem 1.52s 1.27s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 272 ( 27 ~; 17 |; 14 &; 199 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 91 ( 31 ^; 45 !; 15 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_15,type,
sK5: $i > $o ).
thf(func_def_18,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f21]) ).
thf(f21,plain,
( $true
!= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( dsetconstrEL = $true )
& ( $true
= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ! [X0: $i,X4: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrEL
=> ! [X0: $i,X4: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',binintersectEL) ).
thf(f35,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f20]) ).
thf(f20,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersect
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',binintersect) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true != $true )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f23]) ).
thf(f23,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f26,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true )
& ( ( in @ sK4 @ sK3 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18]) ).
thf(f18,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
& ( ( in @ X4 @ X3 )
!= $true ) )
=> ( ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true )
& ( ( in @ sK4 @ sK3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
& ( ( in @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( $true
= ( in @ X1 @ X0 ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',dsetconstrEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU591^2 : 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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:27:54 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SEU591^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.45 % Domain : Set Theory
% 0.31/0.45 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.31/0.45 % Version : Especial > Reduced > Especial.
% 0.31/0.45 % English : (! A:i.! B:i.! x:i.in x (binintersect A B) -> in x A)
% 0.31/0.45
% 0.31/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.45 % Source : [Bro08]
% 0.31/0.45 % Names : ZFC093l [Bro08]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 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
% 0.31/0.45 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.31/0.45 % Number of atoms : 9 ( 2 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.31/0.45 % Number of connectives : 20 ( 0 ~; 0 |; 0 &; 17 @)
% 0.31/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 9 ( 4 avg)
% 0.31/0.45 % Number of types : 2 ( 0 usr)
% 0.31/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.31/0.45 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : http://mathgate.info/detsetitem.php?id=167
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(in_type,type,
% 0.31/0.45 in: $i > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(dsetconstr_type,type,
% 0.31/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.45
% 0.31/0.45 thf(dsetconstrEL_type,type,
% 0.31/0.45 dsetconstrEL: $o ).
% 0.31/0.45
% 0.31/0.45 thf(dsetconstrEL,definition,
% 0.31/0.45 ( dsetconstrEL
% 0.31/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.45 ( ( in @ Xx
% 0.31/0.45 @ ( dsetconstr @ A
% 0.31/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(binintersect_type,type,
% 0.31/0.45 binintersect: $i > $i > $i ).
% 0.31/0.45
% 0.31/0.45 thf(binintersect,definition,
% 0.31/0.45 ( binintersect
% 0.31/0.45 = ( ^ [A: $i,B: $i] :
% 0.31/0.45 ( dsetconstr @ A
% 0.31/0.45 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(binintersectEL,conjecture,
% 0.31/0.45 ( dsetconstrEL
% 0.31/0.45 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/0.45 => ( in @ Xx @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.52/1.23 ---- Embedded in THF ---
% 1.52/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.24 %%% Generated on Tue Feb 24 12:27:55 EST 2026
% 1.52/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.24 %%% Logic specification used:
% 1.52/1.24 %%% thf(spec, logic, $$dhol).
% 1.52/1.24
% 1.52/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2DTF24203.p
% See solution above
% 1.52/1.24 ------------------------
% 1.52/1.25 ---- Cleaned THF ---
% 1.52/1.25 thf(in_type,type,
% 1.52/1.25 in: $i > $i > $o ).
% 1.52/1.25
% 1.52/1.25 thf(dsetconstr_type,type,
% 1.52/1.25 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.52/1.25
% 1.52/1.25 thf(dsetconstrEL_type,type,
% 1.52/1.25 dsetconstrEL: $o ).
% 1.52/1.25
% 1.52/1.25 thf(dsetconstrEL,definition,
% 1.52/1.25 ( dsetconstrEL
% 1.52/1.25 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.52/1.25 ( ( in @ Xx
% 1.52/1.25 @ ( dsetconstr @ A
% 1.52/1.25 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.52/1.25 => ( in @ Xx @ A ) ) ) ) ).
% 1.52/1.25
% 1.52/1.25 thf(binintersect_type,type,
% 1.52/1.25 binintersect: $i > $i > $i ).
% 1.52/1.25
% 1.52/1.25 thf(binintersect,definition,
% 1.52/1.25 ( binintersect
% 1.52/1.25 = ( ^ [A: $i,B: $i] :
% 1.52/1.25 ( dsetconstr @ A
% 1.52/1.25 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.52/1.25
% 1.52/1.25 thf(binintersectEL,conjecture,
% 1.52/1.25 ( dsetconstrEL
% 1.52/1.25 => ! [A: $i,B: $i,Xx: $i] :
% 1.52/1.25 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.52/1.25 => ( in @ Xx @ A ) ) ) ).
% 1.52/1.25 ------------------------
% 1.52/1.26 % (24394)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_24203 for (2999ds/4Mi)
% 1.52/1.26 % (24394)Instruction limit reached!
% 1.52/1.26 % (24394)------------------------------
% 1.52/1.26 % (24394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (24394)Termination reason: Unknown
% 1.52/1.26 % (24394)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (24394)Memory used [KB]: 5500
% 1.52/1.26 % (24394)Time elapsed: 0.003 s
% 1.52/1.26 % (24394)Instructions burned: 4 (million)
% 1.52/1.26 % (24394)------------------------------
% 1.52/1.26 % (24394)------------------------------
% 1.52/1.27 % (24399)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24203 for (2999ds/18Mi)
% 1.52/1.27 % (24397)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_24203 for (2999ds/2Mi)
% 1.52/1.27 % (24393)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24203 for (2999ds/183Mi)
% 1.52/1.27 % (24396)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24203 for (2999ds/2Mi)
% 1.52/1.27 % (24397)Instruction limit reached!
% 1.52/1.27 % (24397)------------------------------
% 1.52/1.27 % (24397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (24397)Termination reason: Unknown
% 1.52/1.27 % (24397)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (24397)Memory used [KB]: 895
% 1.52/1.27 % (24397)Time elapsed: 0.003 s
% 1.52/1.27 % (24397)Instructions burned: 2 (million)
% 1.52/1.27 % (24397)------------------------------
% 1.52/1.27 % (24397)------------------------------
% 1.52/1.27 % (24399)First to succeed.
% 1.52/1.27 % (24396)Instruction limit reached!
% 1.52/1.27 % (24396)------------------------------
% 1.52/1.27 % (24396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (24396)Termination reason: Unknown
% 1.52/1.27 % (24396)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (24396)Memory used [KB]: 5500
% 1.52/1.27 % (24396)Time elapsed: 0.004 s
% 1.52/1.27 % (24396)Instructions burned: 2 (million)
% 1.52/1.27 % (24396)------------------------------
% 1.52/1.27 % (24396)------------------------------
% 1.52/1.27 % (24393)Also succeeded, but the first one will report.
% 1.52/1.27 % (24395)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_24203 for (2999ds/27Mi)
% 1.52/1.27 % (24399)Refutation found. Thanks to Tanya!
% 1.52/1.27 % SZS status Theorem for DTF2THF_24203
% 1.52/1.27 % SZS output start Proof for DTF2THF_24203
% 1.52/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.52/1.27 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.52/1.27 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.52/1.27 thf(func_def_15, type, sK5: $i > $o).
% 1.52/1.27 thf(func_def_18, type, ph7: !>[X0: $tType]:(X0)).
% 1.52/1.27 thf(f36,plain,(
% 1.52/1.27 $false),
% 1.52/1.27 inference(subsumption_resolution,[status(thm)],[f35,f21])).
% 1.52/1.27 thf(f21,plain,(
% 1.52/1.27 ($true != (in @ sK2 @ sK0))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.27 thf(f15,plain,(
% 1.52/1.27 (dsetconstrEL = $true) & (($true = (in @ sK2 @ (binintersect @ sK0 @ sK1))) & ($true != (in @ sK2 @ sK0)))),
% 1.52/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.52/1.27 thf(f14,plain,(
% 1.52/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) & ((in @ X2 @ X0) != $true)) => (($true = (in @ sK2 @ (binintersect @ sK0 @ sK1))) & ($true != (in @ sK2 @ sK0)))),
% 1.52/1.27 introduced(definition,[],[choice_axiom])).
% 1.52/1.27 thf(f13,plain,(
% 1.52/1.27 (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) & ((in @ X2 @ X0) != $true))),
% 1.52/1.27 inference(ennf_transformation,[status(thm)],[f9])).
% 1.52/1.27 thf(f9,plain,(
% 1.52/1.27 ~((dsetconstrEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ((in @ X2 @ X0) = $true)))),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f8])).
% 1.52/1.27 thf(f8,plain,(
% 1.52/1.27 ~(dsetconstrEL => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.52/1.27 inference(rectify,[status(thm)],[f4])).
% 1.52/1.27 thf(f4,negated_conjecture,(
% 1.52/1.27 ~(dsetconstrEL => ! [X0 : $i,X4 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X4)) => (in @ X2 @ X0)))),
% 1.52/1.27 inference(negated_conjecture,[status(cth)],[f3])).
% 1.52/1.27 thf(f3,conjecture,(
% 1.52/1.27 dsetconstrEL => ! [X0 : $i,X4 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X4)) => (in @ X2 @ X0))),
% 1.52/1.27 file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',binintersectEL)).
% 1.52/1.27 thf(f35,plain,(
% 1.52/1.27 ($true = (in @ sK2 @ sK0))),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.52/1.27 thf(f34,plain,(
% 1.52/1.27 ($true = (in @ sK2 @ sK0)) | ($true != $true)),
% 1.52/1.27 inference(superposition,[status(thm)],[f33,f31])).
% 1.52/1.27 thf(f31,plain,(
% 1.52/1.27 ($true = (in @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1)))))),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.52/1.27 thf(f27,plain,(
% 1.52/1.27 ((in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK0 @ sK1)) = $true)),
% 1.52/1.27 inference(definition_unfolding,[status(thm)],[f22,f20])).
% 1.52/1.27 thf(f20,plain,(
% 1.52/1.27 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.27 thf(f7,plain,(
% 1.52/1.27 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f6])).
% 1.52/1.27 thf(f6,plain,(
% 1.52/1.27 (binintersect = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))))),
% 1.52/1.27 inference(rectify,[status(thm)],[f2])).
% 1.52/1.27 thf(f2,axiom,(
% 1.52/1.27 (binintersect = (^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X4)))))),
% 1.52/1.27 file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',binintersect)).
% 1.52/1.27 thf(f22,plain,(
% 1.52/1.27 ($true = (in @ sK2 @ (binintersect @ sK0 @ sK1)))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.27 thf(f33,plain,(
% 1.52/1.27 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ X2)) != $true) | ($true = (in @ X1 @ X0))) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.52/1.27 thf(f32,plain,(
% 1.52/1.27 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0))) )),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.52/1.27 thf(f28,plain,(
% 1.52/1.27 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true != $true) | ($true = (in @ X1 @ X0))) )),
% 1.52/1.27 inference(definition_unfolding,[status(thm)],[f26,f23])).
% 1.52/1.27 thf(f23,plain,(
% 1.52/1.27 (dsetconstrEL = $true)),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.27 thf(f26,plain,(
% 1.52/1.27 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0)) | (dsetconstrEL != $true)) )),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f19])).
% 1.52/1.27 thf(f19,plain,(
% 1.52/1.27 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true) & ((in @ sK4 @ sK3) != $true)))),
% 1.52/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18])).
% 1.52/1.27 thf(f18,plain,(
% 1.52/1.27 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) & ((in @ X4 @ X3) != $true)) => (((in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true) & ((in @ sK4 @ sK3) != $true))),
% 1.52/1.27 introduced(definition,[],[choice_axiom])).
% 1.52/1.27 thf(f17,plain,(
% 1.52/1.27 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) & ((in @ X4 @ X3) != $true)))),
% 1.52/1.27 inference(rectify,[status(thm)],[f16])).
% 1.52/1.27 thf(f16,plain,(
% 1.52/1.27 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) & ($true != (in @ X1 @ X0))))),
% 1.52/1.27 inference(nnf_transformation,[status(thm)],[f12])).
% 1.52/1.27 thf(f12,plain,(
% 1.52/1.27 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | ($true = (in @ X1 @ X0))) <=> (dsetconstrEL = $true)),
% 1.52/1.27 inference(ennf_transformation,[status(thm)],[f11])).
% 1.52/1.27 thf(f11,plain,(
% 1.52/1.27 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ($true = (in @ X1 @ X0))) <=> (dsetconstrEL = $true)),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f10])).
% 1.52/1.27 thf(f10,plain,(
% 1.52/1.27 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)) = dsetconstrEL)),
% 1.52/1.27 inference(rectify,[status(thm)],[f1])).
% 1.52/1.27 thf(f1,axiom,(
% 1.52/1.27 (! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.52/1.27 file('/export/starexec/sandbox/tmp/tmp.wMjIVLMlY1/DTF2THF_24203.p',dsetconstrEL)).
% 1.52/1.27 % SZS output end Proof for DTF2THF_24203
% 1.52/1.27 % (24399)------------------------------
% 1.52/1.27 % (24399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (24399)Termination reason: Refutation
% 1.52/1.27
% 1.52/1.27 % (24399)Memory used [KB]: 5500
% 1.52/1.27 % (24399)Time elapsed: 0.005 s
% 1.52/1.27 % (24399)Instructions burned: 2 (million)
% 1.52/1.27 % (24399)------------------------------
% 1.52/1.27 % (24399)------------------------------
% 1.52/1.27 % (24392)Success in time 0.021 s
%------------------------------------------------------------------------------