%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU608^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:35:35 AM UTC 2026
% Result : Theorem 1.54s 1.36s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 252 ( 35 ~; 16 |; 16 &; 166 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 48 !; 18 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setminus: $i > $i > $i ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f25]) ).
thf(f25,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK5 @ ( setminus @ sK4 @ sK3 ) )
= $true )
& ( setminusER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK5 @ ( setminus @ sK4 @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
& ( setminusER = $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) )
& ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setminusER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( setminusER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( setminusER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setminusER
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setminusER
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7WycTDbgDs/DTF2THF_1914.p',setminusIRneg) ).
thf(f31,plain,
( $true
!= ( in @ sK5 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK5 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f29,f24]) ).
thf(f24,plain,
( ( in @ sK5 @ ( setminus @ sK4 @ sK3 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f29,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f23]) ).
thf(f23,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f22,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( ( in @ X5 @ X3 )
= $true ) )
=> ( ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( ( in @ X5 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( $true
= ( in @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) )
= setminusER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/tmp/tmp.7WycTDbgDs/DTF2THF_1914.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU608^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n005.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:28:14 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SEU608^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.18/0.39 % Version : Especial > Reduced > Especial.
% 0.18/0.39 % English : (! A:i.! B:i.! x:i.in x B -> ~(in x (setminus A 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 : ZFC110l [Bro08]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.18/0.39 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.39 % Number of connectives : 17 ( 2 ~; 0 |; 0 &; 12 @)
% 0.18/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 10 ( 6 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : http://mathgate.info/detsetitem.php?id=463
% 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(setminus_type,type,
% 0.18/0.39 setminus: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER_type,type,
% 0.18/0.39 setminusER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER,definition,
% 0.18/0.39 ( setminusER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusIRneg,conjecture,
% 0.18/0.39 ( setminusER
% 0.18/0.39 => ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.54/1.32 ---- Embedded in THF ---
% 1.54/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.33 %%% Generated on Tue Feb 24 12:28:15 EST 2026
% 1.54/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.33 %%% Logic specification used:
% 1.54/1.33 %%% thf(spec, logic, $$dhol).
% 1.54/1.33
% 1.54/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7WycTDbgDs/DTF2DTF1914.p
% See solution above
% 1.54/1.33 ------------------------
% 1.54/1.33 ---- Cleaned THF ---
% 1.54/1.34 thf(in_type,type,
% 1.54/1.34 in: $i > $i > $o ).
% 1.54/1.34
% 1.54/1.34 thf(setminus_type,type,
% 1.54/1.34 setminus: $i > $i > $i ).
% 1.54/1.34
% 1.54/1.34 thf(setminusER_type,type,
% 1.54/1.34 setminusER: $o ).
% 1.54/1.34
% 1.54/1.34 thf(setminusER,definition,
% 1.54/1.34 ( setminusER
% 1.54/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.34 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.54/1.34 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.54/1.34
% 1.54/1.34 thf(setminusIRneg,conjecture,
% 1.54/1.34 ( setminusER
% 1.54/1.34 => ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.34 ( ( in @ Xx @ B )
% 1.54/1.34 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ).
% 1.54/1.34 ------------------------
% 1.54/1.36 % (2020)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_1914 for (3000ds/2Mi)
% 1.54/1.36 % (2016)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1914 for (3000ds/183Mi)
% 1.54/1.36 % (2022)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1914 for (3000ds/18Mi)
% 1.54/1.36 % (2019)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1914 for (3000ds/2Mi)
% 1.54/1.36 % (2017)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_1914 for (3000ds/4Mi)
% 1.54/1.36 % (2018)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_1914 for (3000ds/27Mi)
% 1.54/1.36 % (2021)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_1914 for (3000ds/275Mi)
% 1.54/1.36 % (2019)Instruction limit reached!
% 1.54/1.36 % (2019)------------------------------
% 1.54/1.36 % (2019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (2019)Termination reason: Unknown
% 1.54/1.36 % (2020)Instruction limit reached!
% 1.54/1.36 % (2020)------------------------------
% 1.54/1.36 % (2020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (2020)Termination reason: Unknown
% 1.54/1.36 % (2020)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (2019)Termination phase: Saturation
% 1.54/1.36 % (2020)Memory used [KB]: 5373
% 1.54/1.36
% 1.54/1.36 % (2020)Time elapsed: 0.003 s
% 1.54/1.36 % (2020)Instructions burned: 2 (million)
% 1.54/1.36 % (2019)Memory used [KB]: 5373
% 1.54/1.36 % (2020)------------------------------
% 1.54/1.36 % (2020)------------------------------
% 1.54/1.36 % (2019)Time elapsed: 0.003 s
% 1.54/1.36 % (2019)Instructions burned: 2 (million)
% 1.54/1.36 % (2019)------------------------------
% 1.54/1.36 % (2019)------------------------------
% 1.54/1.36 % (2021)First to succeed.
% 1.54/1.36 % (2016)Also succeeded, but the first one will report.
% 1.54/1.36 % (2017)Also succeeded, but the first one will report.
% 1.54/1.36 % (2021)Refutation found. Thanks to Tanya!
% 1.54/1.36 % SZS status Theorem for DTF2THF_1914
% 1.54/1.36 % SZS output start Proof for DTF2THF_1914
% 1.54/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.36 thf(func_def_1, type, setminus: $i > $i > $i).
% 1.54/1.36 thf(f32,plain,(
% 1.54/1.36 $false),
% 1.54/1.36 inference(subsumption_resolution,[status(thm)],[f31,f25])).
% 1.54/1.36 thf(f25,plain,(
% 1.54/1.36 ($true = (in @ sK5 @ sK3))),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.36 thf(f19,plain,(
% 1.54/1.36 (($true = (in @ sK5 @ sK3)) & ((in @ sK5 @ (setminus @ sK4 @ sK3)) = $true)) & (setminusER = $true)),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18])).
% 1.54/1.36 thf(f18,plain,(
% 1.54/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) => (($true = (in @ sK5 @ sK3)) & ((in @ sK5 @ (setminus @ sK4 @ sK3)) = $true))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f17,plain,(
% 1.54/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) & (setminusER = $true)),
% 1.54/1.36 inference(rectify,[status(thm)],[f11])).
% 1.54/1.36 thf(f11,plain,(
% 1.54/1.36 ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ (setminus @ X2 @ X0)) = $true)) & (setminusER = $true)),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f9])).
% 1.54/1.36 thf(f9,plain,(
% 1.54/1.36 ~((setminusER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => ((in @ X1 @ (setminus @ X2 @ X0)) != $true)))),
% 1.54/1.36 inference(flattening,[status(thm)],[f6])).
% 1.54/1.36 thf(f6,plain,(
% 1.54/1.36 ~((setminusER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => ~((in @ X1 @ (setminus @ X2 @ X0)) = $true)))),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f5])).
% 1.54/1.36 thf(f5,plain,(
% 1.54/1.36 ~(setminusER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ~(in @ X1 @ (setminus @ X2 @ X0))))),
% 1.54/1.36 inference(rectify,[status(thm)],[f3])).
% 1.54/1.36 thf(f3,negated_conjecture,(
% 1.54/1.36 ~(setminusER => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 1.54/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 1.54/1.36 thf(f2,conjecture,(
% 1.54/1.36 setminusER => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1)))),
% 1.54/1.36 file('/export/starexec/sandbox2/tmp/tmp.7WycTDbgDs/DTF2THF_1914.p',setminusIRneg)).
% 1.54/1.36 thf(f31,plain,(
% 1.54/1.36 ($true != (in @ sK5 @ sK3))),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.54/1.36 thf(f30,plain,(
% 1.54/1.36 ($true != $true) | ($true != (in @ sK5 @ sK3))),
% 1.54/1.36 inference(superposition,[status(thm)],[f29,f24])).
% 1.54/1.36 thf(f24,plain,(
% 1.54/1.36 ((in @ sK5 @ (setminus @ sK4 @ sK3)) = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.36 thf(f29,plain,(
% 1.54/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ($true != (in @ X2 @ X0))) )),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.54/1.36 thf(f26,plain,(
% 1.54/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X2 @ X0)) | ($true != (in @ X2 @ (setminus @ X1 @ X0)))) )),
% 1.54/1.36 inference(definition_unfolding,[status(thm)],[f22,f23])).
% 1.54/1.36 thf(f23,plain,(
% 1.54/1.36 (setminusER = $true)),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.36 thf(f22,plain,(
% 1.54/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ($true != (in @ X2 @ X0)) | (setminusER != $true)) )),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 1.54/1.36 thf(f16,plain,(
% 1.54/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ($true != (in @ X2 @ X0))) | (setminusER != $true)) & ((setminusER = $true) | (($true = (in @ sK2 @ (setminus @ sK1 @ sK0))) & ($true = (in @ sK2 @ sK0))))),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.54/1.36 thf(f15,plain,(
% 1.54/1.36 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (setminus @ X4 @ X3))) & ((in @ X5 @ X3) = $true)) => (($true = (in @ sK2 @ (setminus @ sK1 @ sK0))) & ($true = (in @ sK2 @ sK0)))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f14,plain,(
% 1.54/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ($true != (in @ X2 @ X0))) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (setminus @ X4 @ X3))) & ((in @ X5 @ X3) = $true)))),
% 1.54/1.36 inference(rectify,[status(thm)],[f13])).
% 1.54/1.36 thf(f13,plain,(
% 1.54/1.36 (! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ($true != (in @ X1 @ X0))) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) & ($true = (in @ X1 @ X0))))),
% 1.54/1.36 inference(nnf_transformation,[status(thm)],[f12])).
% 1.54/1.36 thf(f12,plain,(
% 1.54/1.36 ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ($true != (in @ X1 @ X0))) <=> (setminusER = $true)),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f10])).
% 1.54/1.36 thf(f10,plain,(
% 1.54/1.36 (setminusER = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) => ($true != (in @ X1 @ X0)))),
% 1.54/1.36 inference(flattening,[status(thm)],[f8])).
% 1.54/1.36 thf(f8,plain,(
% 1.54/1.36 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) => ~($true = (in @ X1 @ X0))) <=> (setminusER = $true)),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.54/1.36 thf(f7,plain,(
% 1.54/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)) = setminusER)),
% 1.54/1.36 inference(rectify,[status(thm)],[f1])).
% 1.54/1.36 thf(f1,axiom,(
% 1.54/1.36 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.54/1.36 file('/export/starexec/sandbox2/tmp/tmp.7WycTDbgDs/DTF2THF_1914.p',setminusER)).
% 1.54/1.36 % SZS output end Proof for DTF2THF_1914
% 1.54/1.36 % (2021)------------------------------
% 1.54/1.36 % (2021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (2021)Termination reason: Refutation
% 1.54/1.36
% 1.54/1.36 % (2021)Memory used [KB]: 5500
% 1.54/1.36 % (2021)Time elapsed: 0.004 s
% 1.54/1.36 % (2021)Instructions burned: 2 (million)
% 1.54/1.36 % (2021)------------------------------
% 1.54/1.36 % (2021)------------------------------
% 1.54/1.36 % (2015)Success in time 0.018 s
%------------------------------------------------------------------------------