%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU603^2 : 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 : n009.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 09:35:33 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 276 ( 18 ~; 2 |; 6 &; 209 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-2 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 44 ^; 36 !; 6 ?; 86 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_18,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
$true = $false,
inference(superposition,[status(thm)],[f41,f18]) ).
thf(f18,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X2 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X4: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ~ ( in @ X2 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X4: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ~ ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',setminusER) ).
thf(f41,plain,
( ( in @ sK2 @ sK0 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ~ ( in @ sK2 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 )
@ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 )
@ sK2 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f23,f31]) ).
thf(f31,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
= $false )
| ( $true
= ( X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f16]) ).
thf(f16,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f19,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',dsetconstrER) ).
thf(f23,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f20]) ).
thf(f20,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminus
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',setminus) ).
thf(f17,plain,
( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU603^2 : 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
% 0.16/0.34 % Computer : n009.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 12:28:10 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU603^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! B:i.! x:i.in x (setminus A B) -> ~(in x B))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC105l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.20/0.46 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.46 % Number of connectives : 21 ( 2 ~; 0 |; 0 &; 16 @)
% 0.20/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 9 ( 4 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=278
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER_type,type,
% 0.20/0.46 dsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER,definition,
% 0.20/0.46 ( dsetconstrER
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminus_type,type,
% 0.20/0.46 setminus: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setminus,definition,
% 0.20/0.46 ( setminus
% 0.20/0.46 = ( ^ [A: $i,B: $i] :
% 0.20/0.46 ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER,conjecture,
% 0.20/0.46 ( dsetconstrER
% 0.20/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ~ ( in @ Xx @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:28:11 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2DTF13894.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.29 thf(in_type,type,
% 1.46/1.29 in: $i > $i > $o ).
% 1.46/1.29
% 1.46/1.29 thf(dsetconstr_type,type,
% 1.46/1.29 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.46/1.29
% 1.46/1.29 thf(dsetconstrER_type,type,
% 1.46/1.29 dsetconstrER: $o ).
% 1.46/1.29
% 1.46/1.29 thf(dsetconstrER,definition,
% 1.46/1.29 ( dsetconstrER
% 1.46/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.46/1.29 ( ( in @ Xx
% 1.46/1.29 @ ( dsetconstr @ A
% 1.46/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.46/1.29 => ( Xphi @ Xx ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(setminus_type,type,
% 1.46/1.29 setminus: $i > $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(setminus,definition,
% 1.46/1.29 ( setminus
% 1.46/1.29 = ( ^ [A: $i,B: $i] :
% 1.46/1.29 ( dsetconstr @ A
% 1.46/1.29 @ ^ [Xx: $i] :
% 1.46/1.29 ~ ( in @ Xx @ B ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(setminusER,conjecture,
% 1.46/1.29 ( dsetconstrER
% 1.46/1.29 => ! [A: $i,B: $i,Xx: $i] :
% 1.46/1.29 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.46/1.29 => ~ ( in @ Xx @ B ) ) ) ).
% 1.46/1.29 ------------------------
% 1.64/1.30 % (14225)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13894 for (2999ds/2Mi)
% 1.64/1.30 % (14225)Instruction limit reached!
% 1.64/1.30 % (14225)------------------------------
% 1.64/1.30 % (14225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (14225)Termination reason: Unknown
% 1.64/1.30 % (14225)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (14225)Memory used [KB]: 895
% 1.64/1.30 % (14225)Time elapsed: 0.002 s
% 1.64/1.30 % (14225)Instructions burned: 2 (million)
% 1.64/1.30 % (14225)------------------------------
% 1.64/1.30 % (14225)------------------------------
% 1.64/1.30 % (14226)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_13894 for (2999ds/2Mi)
% 1.64/1.30 % (14226)Instruction limit reached!
% 1.64/1.30 % (14226)------------------------------
% 1.64/1.30 % (14226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (14226)Termination reason: Unknown
% 1.64/1.30 % (14226)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (14226)Memory used [KB]: 5500
% 1.64/1.30 % (14226)Time elapsed: 0.002 s
% 1.64/1.30 % (14226)Instructions burned: 3 (million)
% 1.64/1.30 % (14226)------------------------------
% 1.64/1.30 % (14226)------------------------------
% 1.64/1.31 % (14222)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13894 for (2999ds/183Mi)
% 1.64/1.31 % (14223)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_13894 for (2999ds/4Mi)
% 1.64/1.31 % (14224)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_13894 for (2999ds/27Mi)
% 1.64/1.31 % (14227)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_13894 for (2999ds/275Mi)
% 1.64/1.31 % (14228)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13894 for (2999ds/18Mi)
% 1.64/1.31 % (14227)Refutation not found, incomplete strategy
% 1.64/1.31 % (14227)------------------------------
% 1.64/1.31 % (14227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14227)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (14227)Memory used [KB]: 5500
% 1.64/1.31 % (14227)Time elapsed: 0.004 s
% 1.64/1.31 % (14227)Instructions burned: 2 (million)
% 1.64/1.31 % (14227)------------------------------
% 1.64/1.31 % (14227)------------------------------
% 1.64/1.31 % (14229)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13894 for (2999ds/3Mi)
% 1.64/1.31 % (14223)Instruction limit reached!
% 1.64/1.31 % (14223)------------------------------
% 1.64/1.31 % (14223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14223)Termination reason: Unknown
% 1.64/1.31 % (14223)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (14223)Memory used [KB]: 5500
% 1.64/1.31 % (14223)Time elapsed: 0.005 s
% 1.64/1.31 % (14223)Instructions burned: 4 (million)
% 1.64/1.31 % (14223)------------------------------
% 1.64/1.31 % (14223)------------------------------
% 1.64/1.31 % (14222)First to succeed.
% 1.64/1.31 % (14229)Refutation not found, incomplete strategy
% 1.64/1.31 % (14229)------------------------------
% 1.64/1.31 % (14229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14229)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (14229)Memory used [KB]: 5500
% 1.64/1.31 % (14229)Time elapsed: 0.002 s
% 1.64/1.31 % (14229)Instructions burned: 2 (million)
% 1.64/1.31 % (14229)------------------------------
% 1.64/1.31 % (14229)------------------------------
% 1.64/1.31 % (14230)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13894 for (2999ds/37Mi)
% 1.64/1.31 % (14224)Also succeeded, but the first one will report.
% 1.64/1.31 % (14222)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_13894
% 1.64/1.31 % SZS output start Proof for DTF2THF_13894
% 1.64/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.31 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.64/1.31 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.64/1.31 thf(func_def_18, type, ph4: !>[X0: $tType]:(X0)).
% 1.64/1.31 thf(f44,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.64/1.31 thf(f42,plain,(
% 1.64/1.31 ($true = $false)),
% 1.64/1.31 inference(superposition,[status(thm)],[f41,f18])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 ($true = (in @ sK2 @ sK0))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))) & (dsetconstrER = $true)),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) => (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ sK0))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) & (dsetconstrER = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ($true != (in @ X2 @ X0))))),
% 1.64/1.31 inference(flattening,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ~($true = (in @ X2 @ X0))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 ~(dsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f4])).
% 1.64/1.31 thf(f4,negated_conjecture,(
% 1.64/1.31 ~(dsetconstrER => ! [X4 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X4)) => ~(in @ X2 @ X4)))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.31 thf(f3,conjecture,(
% 1.64/1.31 dsetconstrER => ! [X4 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X4)) => ~(in @ X2 @ X4))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',setminusER)).
% 1.64/1.31 thf(f41,plain,(
% 1.64/1.31 ((in @ sK2 @ sK0) = $false)),
% 1.64/1.31 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.64/1.31 thf(f40,plain,(
% 1.64/1.31 ((~ (in @ sK2 @ sK0)) = $true)),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.31 thf(f39,plain,(
% 1.64/1.31 ($true = ((^[Y0 : $i]: (~ (in @ Y0 @ sK0))) @ sK2))),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.64/1.31 thf(f34,plain,(
% 1.64/1.31 ($true = ((^[Y0 : $i]: (~ (in @ Y0 @ sK0))) @ sK2)) | ($true = $false)),
% 1.64/1.31 inference(superposition,[status(thm)],[f23,f31])).
% 1.64/1.31 thf(f31,plain,(
% 1.64/1.31 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X3 @ X2)) = $false) | ($true = (X2 @ X1))) )),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.31 thf(f30,plain,(
% 1.64/1.31 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X3 @ X2)) => (X2 @ X1)))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.64/1.31 thf(f29,plain,(
% 1.64/1.31 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1))) @ X3) = $true)) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f28])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1)))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1))))) @ X2))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1)))))))) )),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.64/1.31 thf(f25,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0))))))) @ X1))) )),
% 1.64/1.31 inference(pi_clausification,[status(thm)],[f24])).
% 1.64/1.31 thf(f24,plain,(
% 1.64/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))))),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.64/1.31 thf(f22,plain,(
% 1.64/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f19,f16])).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 (dsetconstrER = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',dsetconstrER)).
% 1.64/1.31 thf(f23,plain,(
% 1.64/1.31 ($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (~ (in @ Y0 @ sK0))))))),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.31 thf(f21,plain,(
% 1.64/1.31 ($true = (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))) @ sK1 @ sK0)))),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f17,f20])).
% 1.64/1.31 thf(f20,plain,(
% 1.64/1.31 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 (setminus = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X1))))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f2])).
% 1.64/1.31 thf(f2,axiom,(
% 1.64/1.31 (setminus = (^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X4))))))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.ZVOpygEXXB/DTF2THF_13894.p',setminus)).
% 1.64/1.31 thf(f17,plain,(
% 1.64/1.31 ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_13894
% 1.64/1.31 % (14222)------------------------------
% 1.64/1.31 % (14222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14222)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (14222)Memory used [KB]: 5500
% 1.64/1.31 % (14222)Time elapsed: 0.006 s
% 1.64/1.31 % (14222)Instructions burned: 4 (million)
% 1.64/1.31 % (14222)------------------------------
% 1.64/1.31 % (14222)------------------------------
% 1.64/1.31 % (14221)Success in time 0.02 s
%------------------------------------------------------------------------------