%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU595^2 : 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 : n001.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 1.56s 1.32s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 229 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 260 ( 27 ~; 17 |; 14 &; 187 @)
% ( 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 : 93 ( 33 ^; 45 !; 15 ?; 93 :)
% 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_13,type,
sK3: $i > $o ).
thf(func_def_18,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f37,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f22]) ).
thf(f22,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( in @ sK0 @ ( binintersect @ sK2 @ sK1 ) ) )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) )
=> ( ( $true
= ( in @ sK0 @ ( binintersect @ sK2 @ sK1 ) ) )
& ( ( in @ sK0 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
=> ( $true
= ( in @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X2: $i,X4: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X2: $i,X4: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2THF_18122.p',binintersectER) ).
thf(f36,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ sK1 )
@ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ sK1 )
@ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK2
@ sK1 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f20]) ).
thf(f20,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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.CYaI6apNKp/DTF2THF_18122.p',binintersect) ).
thf(f23,plain,
( $true
= ( in @ sK0 @ ( binintersect @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f26,f21]) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f26,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK3 @ sK5 ) )
& ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18]) ).
thf(f18,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
& ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) )
=> ( ( $true
!= ( sK3 @ sK5 ) )
& ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
& ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2THF_18122.p',dsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU595^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n001.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 12:28:35 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SEU595^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.18/0.39 % Version : Especial > Reduced > Especial.
% 0.18/0.39 % English : (! A:i.! B:i.! x:i.in x (binintersect A B) -> in x B)
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.39 % Source : [Bro08]
% 0.18/0.39 % Names : ZFC097l [Bro08]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % 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, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.2.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.18/0.39 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 3 ( 2 avg)
% 0.18/0.39 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 16 @)
% 0.18/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 9 ( 4 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : http://mathgate.info/detsetitem.php?id=168
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(in_type,type,
% 0.18/0.39 in: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstr_type,type,
% 0.18/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrER_type,type,
% 0.18/0.39 dsetconstrER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrER,definition,
% 0.18/0.39 ( dsetconstrER
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersect_type,type,
% 0.18/0.39 binintersect: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(binintersect,definition,
% 0.18/0.39 ( binintersect
% 0.18/0.39 = ( ^ [A: $i,B: $i] :
% 0.18/0.39 ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectER,conjecture,
% 0.18/0.39 ( dsetconstrER
% 0.18/0.39 => ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.39 => ( in @ Xx @ B ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 12:28:36 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2DTF18122.p
% See solution above
% 1.36/1.29 ------------------------
% 1.36/1.30 ---- Cleaned THF ---
% 1.56/1.30 thf(in_type,type,
% 1.56/1.30 in: $i > $i > $o ).
% 1.56/1.30
% 1.56/1.30 thf(dsetconstr_type,type,
% 1.56/1.30 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.56/1.30
% 1.56/1.30 thf(dsetconstrER_type,type,
% 1.56/1.30 dsetconstrER: $o ).
% 1.56/1.30
% 1.56/1.30 thf(dsetconstrER,definition,
% 1.56/1.30 ( dsetconstrER
% 1.56/1.30 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.56/1.30 ( ( in @ Xx
% 1.56/1.30 @ ( dsetconstr @ A
% 1.56/1.30 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.56/1.30 => ( Xphi @ Xx ) ) ) ) ).
% 1.56/1.30
% 1.56/1.30 thf(binintersect_type,type,
% 1.56/1.30 binintersect: $i > $i > $i ).
% 1.56/1.30
% 1.56/1.30 thf(binintersect,definition,
% 1.56/1.30 ( binintersect
% 1.56/1.30 = ( ^ [A: $i,B: $i] :
% 1.56/1.30 ( dsetconstr @ A
% 1.56/1.30 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.56/1.30
% 1.56/1.30 thf(binintersectER,conjecture,
% 1.56/1.30 ( dsetconstrER
% 1.56/1.30 => ! [A: $i,B: $i,Xx: $i] :
% 1.56/1.30 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.56/1.30 => ( in @ Xx @ B ) ) ) ).
% 1.56/1.30 ------------------------
% 1.56/1.32 % (18225)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18122 for (2999ds/18Mi)
% 1.56/1.32 % (18221)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_18122 for (2999ds/27Mi)
% 1.56/1.32 % (18223)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_18122 for (2999ds/2Mi)
% 1.56/1.32 % (18224)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_18122 for (2999ds/275Mi)
% 1.56/1.32 % (18220)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_18122 for (2999ds/4Mi)
% 1.56/1.32 % (18222)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18122 for (2999ds/2Mi)
% 1.56/1.32 % (18219)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18122 for (2999ds/183Mi)
% 1.56/1.32 % (18222)Instruction limit reached!
% 1.56/1.32 % (18222)------------------------------
% 1.56/1.32 % (18222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (18222)Termination reason: Unknown
% 1.56/1.32 % (18222)Termination phase: Saturation
% 1.56/1.32 % (18223)Instruction limit reached!
% 1.56/1.32 % (18223)------------------------------
% 1.56/1.32 % (18223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (18223)Termination reason: Unknown
% 1.56/1.32 % (18223)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (18223)Memory used [KB]: 895
% 1.56/1.32 % (18223)Time elapsed: 0.003 s
% 1.56/1.32 % (18223)Instructions burned: 2 (million)
% 1.56/1.32 % (18223)------------------------------
% 1.56/1.32 % (18223)------------------------------
% 1.56/1.32
% 1.56/1.32 % (18222)Memory used [KB]: 895
% 1.56/1.32 % (18222)Time elapsed: 0.003 s
% 1.56/1.32 % (18222)Instructions burned: 2 (million)
% 1.56/1.32 % (18222)------------------------------
% 1.56/1.32 % (18222)------------------------------
% 1.56/1.32 % (18224)Refutation not found, incomplete strategy
% 1.56/1.32 % (18224)------------------------------
% 1.56/1.32 % (18224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (18224)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.32
% 1.56/1.32
% 1.56/1.32 % (18224)Memory used [KB]: 5500
% 1.56/1.32 % (18224)Time elapsed: 0.003 s
% 1.56/1.32 % (18224)Instructions burned: 2 (million)
% 1.56/1.32 % (18224)------------------------------
% 1.56/1.32 % (18224)------------------------------
% 1.56/1.32 % (18225)First to succeed.
% 1.56/1.32 % (18220)Instruction limit reached!
% 1.56/1.32 % (18220)------------------------------
% 1.56/1.32 % (18220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (18220)Termination reason: Unknown
% 1.56/1.32 % (18220)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (18220)Memory used [KB]: 5500
% 1.56/1.32 % (18220)Time elapsed: 0.005 s
% 1.56/1.32 % (18220)Instructions burned: 5 (million)
% 1.56/1.32 % (18220)------------------------------
% 1.56/1.32 % (18220)------------------------------
% 1.56/1.32 % (18219)Also succeeded, but the first one will report.
% 1.56/1.32 % (18225)Refutation found. Thanks to Tanya!
% 1.56/1.32 % SZS status Theorem for DTF2THF_18122
% 1.56/1.32 % SZS output start Proof for DTF2THF_18122
% 1.56/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.32 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.56/1.32 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.56/1.32 thf(func_def_13, type, sK3: $i > $o).
% 1.56/1.32 thf(func_def_18, type, ph7: !>[X0: $tType]:(X0)).
% 1.56/1.32 thf(f37,plain,(
% 1.56/1.32 $false),
% 1.56/1.32 inference(subsumption_resolution,[status(thm)],[f36,f22])).
% 1.56/1.32 thf(f22,plain,(
% 1.56/1.32 ((in @ sK0 @ sK1) != $true)),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 1.56/1.32 thf(f15,plain,(
% 1.56/1.32 (($true = (in @ sK0 @ (binintersect @ sK2 @ sK1))) & ((in @ sK0 @ sK1) != $true)) & (dsetconstrER = $true)),
% 1.56/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.56/1.32 thf(f14,plain,(
% 1.56/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) & ($true != (in @ X0 @ X1))) => (($true = (in @ sK0 @ (binintersect @ sK2 @ sK1))) & ((in @ sK0 @ sK1) != $true))),
% 1.56/1.32 introduced(definition,[],[choice_axiom])).
% 1.56/1.32 thf(f13,plain,(
% 1.56/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) & ($true != (in @ X0 @ X1))) & (dsetconstrER = $true)),
% 1.56/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.56/1.32 thf(f7,plain,(
% 1.56/1.32 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) => ($true = (in @ X0 @ X1))))),
% 1.56/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.56/1.32 thf(f6,plain,(
% 1.56/1.32 ~(dsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X1)))),
% 1.56/1.32 inference(rectify,[status(thm)],[f4])).
% 1.56/1.32 thf(f4,negated_conjecture,(
% 1.56/1.32 ~(dsetconstrER => ! [X2 : $i,X4 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X4)) => (in @ X2 @ X4)))),
% 1.56/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.56/1.32 thf(f3,conjecture,(
% 1.56/1.32 dsetconstrER => ! [X2 : $i,X4 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X4)) => (in @ X2 @ X4))),
% 1.56/1.32 file('/export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2THF_18122.p',binintersectER)).
% 1.56/1.32 thf(f36,plain,(
% 1.56/1.32 ((in @ sK0 @ sK1) = $true)),
% 1.56/1.32 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.56/1.32 thf(f35,plain,(
% 1.56/1.32 ($true = ((^[Y0 : $i]: (in @ Y0 @ sK1)) @ sK0))),
% 1.56/1.32 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.56/1.32 thf(f34,plain,(
% 1.56/1.32 ($true = ((^[Y0 : $i]: (in @ Y0 @ sK1)) @ sK0)) | ($true != $true)),
% 1.56/1.32 inference(superposition,[status(thm)],[f33,f31])).
% 1.56/1.32 thf(f31,plain,(
% 1.56/1.32 ((in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ Y0 @ sK1)))) = $true)),
% 1.56/1.32 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.56/1.32 thf(f27,plain,(
% 1.56/1.32 ((in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK2 @ sK1)) = $true)),
% 1.56/1.32 inference(definition_unfolding,[status(thm)],[f23,f20])).
% 1.56/1.32 thf(f20,plain,(
% 1.56/1.32 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.32 thf(f9,plain,(
% 1.56/1.32 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.56/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.56/1.32 thf(f8,plain,(
% 1.56/1.32 (binintersect = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))))),
% 1.56/1.32 inference(rectify,[status(thm)],[f2])).
% 1.56/1.32 thf(f2,axiom,(
% 1.56/1.32 (binintersect = (^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X4)))))),
% 1.56/1.32 file('/export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2THF_18122.p',binintersect)).
% 1.56/1.32 thf(f23,plain,(
% 1.56/1.32 ($true = (in @ sK0 @ (binintersect @ sK2 @ sK1)))),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 1.56/1.32 thf(f33,plain,(
% 1.56/1.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X0)) != $true) | ((X0 @ X2) = $true)) )),
% 1.56/1.32 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.56/1.32 thf(f32,plain,(
% 1.56/1.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) )),
% 1.56/1.32 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.56/1.32 thf(f28,plain,(
% 1.56/1.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true) | ($true != $true)) )),
% 1.56/1.32 inference(definition_unfolding,[status(thm)],[f26,f21])).
% 1.56/1.32 thf(f21,plain,(
% 1.56/1.32 (dsetconstrER = $true)),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 1.56/1.32 thf(f26,plain,(
% 1.56/1.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f19])).
% 1.56/1.32 thf(f19,plain,(
% 1.56/1.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (($true != (sK3 @ sK5)) & ((in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0)))) = $true)))),
% 1.56/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18])).
% 1.56/1.32 thf(f18,plain,(
% 1.56/1.32 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X5)) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)) => (($true != (sK3 @ sK5)) & ((in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0)))) = $true))),
% 1.56/1.32 introduced(definition,[],[choice_axiom])).
% 1.56/1.32 thf(f17,plain,(
% 1.56/1.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X5)) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)))),
% 1.56/1.32 inference(rectify,[status(thm)],[f16])).
% 1.56/1.32 thf(f16,plain,(
% 1.56/1.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)))),
% 1.56/1.32 inference(nnf_transformation,[status(thm)],[f12])).
% 1.56/1.32 thf(f12,plain,(
% 1.56/1.32 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 1.56/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.56/1.32 thf(f11,plain,(
% 1.56/1.32 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ((X0 @ X2) = $true)) <=> (dsetconstrER = $true)),
% 1.56/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.56/1.32 thf(f10,plain,(
% 1.56/1.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 1.56/1.32 inference(rectify,[status(thm)],[f1])).
% 1.56/1.32 thf(f1,axiom,(
% 1.56/1.32 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.56/1.32 file('/export/starexec/sandbox/tmp/tmp.CYaI6apNKp/DTF2THF_18122.p',dsetconstrER)).
% 1.56/1.32 % SZS output end Proof for DTF2THF_18122
% 1.56/1.32 % (18225)------------------------------
% 1.56/1.32 % (18225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (18225)Termination reason: Refutation
% 1.56/1.32
% 1.56/1.32 % (18225)Memory used [KB]: 5500
% 1.56/1.32 % (18225)Time elapsed: 0.005 s
% 1.56/1.32 % (18225)Instructions burned: 2 (million)
% 1.56/1.32 % (18225)------------------------------
% 1.56/1.32 % (18225)------------------------------
% 1.56/1.32 % (18218)Success in time 0.016 s
%------------------------------------------------------------------------------