%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU719^2 : 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 : n023.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 09:36:39 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 336 ( 91 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 358 ( 35 ~; 16 |; 34 &; 243 @)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 48 !; 23 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
setminus: $i > $i > $i ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f23]) ).
thf(f23,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setminusER = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
& ( ( in @ X2 @ sK1 )
= $true )
& ( ( in @ X2 @ ( setminus @ sK0 @ sK1 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
& ( ( in @ X2 @ sK1 )
= $true )
& ( ( in @ X2 @ ( setminus @ sK0 @ sK1 ) )
= $true ) )
=> ( ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( setminusER = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setminusER = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OfQSe51IMp/DTF2THF_8772.p',complementTI1) ).
thf(f35,plain,
( ( in @ sK2 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( in @ sK2 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f33,f22]) ).
thf(f22,plain,
( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f33,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f27,f26]) ).
thf(f26,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f27,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) )
= $true )
& ( ( in @ sK5 @ sK4 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f19,f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) )
= $true )
& ( ( in @ sK5 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( setminusER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
=> ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
=> ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusER
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OfQSe51IMp/DTF2THF_8772.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU719^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.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 12:32:34 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
% 0.26/0.45 ---- Original DTF file ---
% 0.26/0.45 thf(spec,logic,$$dhol).
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % File : SEU719^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.45 % Domain : Set Theory
% 0.26/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.26/0.45 % Version : Especial > Reduced > Especial.
% 0.26/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! x:i.in x A -> in x X ->
% 0.26/0.45 % ~(in x (setminus A X))))
% 0.26/0.45
% 0.26/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.45 % Source : [Bro08]
% 0.26/0.45 % Names : ZFC221l [Bro08]
% 0.26/0.45
% 0.26/0.45 % Status : Theorem
% 0.26/0.45 % 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
% 0.26/0.45 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.26/0.45 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.26/0.45 % Maximal formula atoms : 5 ( 4 avg)
% 0.26/0.45 % Number of connectives : 24 ( 2 ~; 0 |; 0 &; 17 @)
% 0.26/0.45 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.26/0.45 % Maximal formula depth : 12 ( 7 avg)
% 0.26/0.45 % Number of types : 2 ( 0 usr)
% 0.26/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.26/0.45 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.26/0.45 % SPC : TH0_THM_EQU_NAR
% 0.26/0.45
% 0.26/0.45 % Comments : http://mathgate.info/detsetitem.php?id=279
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 thf(in_type,type,
% 0.26/0.45 in: $i > $i > $o ).
% 0.26/0.45
% 0.26/0.45 thf(powerset_type,type,
% 0.26/0.45 powerset: $i > $i ).
% 0.26/0.45
% 0.26/0.45 thf(setminus_type,type,
% 0.26/0.45 setminus: $i > $i > $i ).
% 0.26/0.45
% 0.26/0.45 thf(setminusER_type,type,
% 0.26/0.45 setminusER: $o ).
% 0.26/0.45
% 0.26/0.45 thf(setminusER,definition,
% 0.26/0.45 ( setminusER
% 0.26/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.45 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 thf(complementTI1,conjecture,
% 0.26/0.45 ( setminusER
% 0.26/0.45 => ! [A: $i,X: $i] :
% 0.26/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.45 => ! [Xx: $i] :
% 0.26/0.45 ( ( in @ Xx @ A )
% 0.26/0.45 => ( ( in @ Xx @ X )
% 0.26/0.45 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:32:35 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OfQSe51IMp/DTF2DTF8772.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(in_type,type,
% 1.47/1.27 in: $i > $i > $o ).
% 1.47/1.27
% 1.47/1.27 thf(powerset_type,type,
% 1.47/1.27 powerset: $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(setminus_type,type,
% 1.47/1.27 setminus: $i > $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(setminusER_type,type,
% 1.47/1.27 setminusER: $o ).
% 1.47/1.27
% 1.47/1.27 thf(setminusER,definition,
% 1.47/1.27 ( setminusER
% 1.47/1.27 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.27 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.47/1.27 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(complementTI1,conjecture,
% 1.47/1.27 ( setminusER
% 1.47/1.27 => ! [A: $i,X: $i] :
% 1.47/1.27 ( ( in @ X @ ( powerset @ A ) )
% 1.47/1.27 => ! [Xx: $i] :
% 1.47/1.27 ( ( in @ Xx @ A )
% 1.47/1.27 => ( ( in @ Xx @ X )
% 1.47/1.27 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (9093)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_8772 for (2999ds/2Mi)
% 1.47/1.28 % (9093)Instruction limit reached!
% 1.47/1.28 % (9093)------------------------------
% 1.47/1.28 % (9093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (9093)Termination reason: Unknown
% 1.47/1.28 % (9093)Termination phase: Property scanning
% 1.47/1.28
% 1.47/1.28 % (9093)Memory used [KB]: 895
% 1.47/1.28 % (9093)Time elapsed: 0.002 s
% 1.47/1.28 % (9093)Instructions burned: 2 (million)
% 1.47/1.28 % (9093)------------------------------
% 1.47/1.28 % (9093)------------------------------
% 1.47/1.28 % (9092)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8772 for (2999ds/2Mi)
% 1.47/1.28 % (9092)Instruction limit reached!
% 1.47/1.28 % (9092)------------------------------
% 1.47/1.28 % (9092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (9092)Termination reason: Unknown
% 1.47/1.28 % (9092)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (9092)Memory used [KB]: 5500
% 1.47/1.28 % (9092)Time elapsed: 0.002 s
% 1.47/1.28 % (9092)Instructions burned: 2 (million)
% 1.47/1.28 % (9092)------------------------------
% 1.47/1.28 % (9092)------------------------------
% 1.47/1.29 % (9089)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8772 for (2999ds/183Mi)
% 1.47/1.29 % (9090)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_8772 for (2999ds/4Mi)
% 1.47/1.29 % (9091)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_8772 for (2999ds/27Mi)
% 1.47/1.29 % (9094)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_8772 for (2999ds/275Mi)
% 1.47/1.29 % (9095)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8772 for (2999ds/18Mi)
% 1.47/1.29 % (9096)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8772 for (2999ds/3Mi)
% 1.47/1.29 % (9094)First to succeed.
% 1.47/1.29 % (9090)Instruction limit reached!
% 1.47/1.29 % (9090)------------------------------
% 1.47/1.29 % (9090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (9090)Termination reason: Unknown
% 1.47/1.29 % (9090)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (9090)Memory used [KB]: 5500
% 1.47/1.29 % (9090)Time elapsed: 0.005 s
% 1.47/1.29 % (9090)Instructions burned: 4 (million)
% 1.47/1.29 % (9090)------------------------------
% 1.47/1.29 % (9090)------------------------------
% 1.47/1.29 % (9096)Refutation not found, incomplete strategy
% 1.47/1.29 % (9096)------------------------------
% 1.47/1.29 % (9096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (9096)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (9096)Memory used [KB]: 5500
% 1.47/1.29 % (9096)Time elapsed: 0.002 s
% 1.47/1.29 % (9096)Instructions burned: 2 (million)
% 1.47/1.29 % (9096)------------------------------
% 1.47/1.29 % (9096)------------------------------
% 1.47/1.29 % (9095)Also succeeded, but the first one will report.
% 1.47/1.29 % (9097)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_8772 for (2999ds/37Mi)
% 1.47/1.29 % (9089)Also succeeded, but the first one will report.
% 1.47/1.29 % (9094)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_8772
% 1.47/1.29 % SZS output start Proof for DTF2THF_8772
% 1.47/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.47/1.29 thf(func_def_1, type, powerset: $i > $i).
% 1.47/1.29 thf(func_def_2, type, setminus: $i > $i > $i).
% 1.47/1.29 thf(f36,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f35,f23])).
% 1.47/1.29 thf(f23,plain,(
% 1.47/1.29 ((in @ sK2 @ sK1) = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 (setminusER = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & (((in @ sK2 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true) & ((in @ sK2 @ (setminus @ sK0 @ sK1)) = $true)))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f16,f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2 : $i] : (((in @ X2 @ sK0) = $true) & ((in @ X2 @ sK1) = $true) & ((in @ X2 @ (setminus @ sK0 @ sK1)) = $true)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ? [X2 : $i] : (((in @ X2 @ sK0) = $true) & ((in @ X2 @ sK1) = $true) & ((in @ X2 @ (setminus @ sK0 @ sK1)) = $true)) => (((in @ sK2 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true) & ((in @ sK2 @ (setminus @ sK0 @ sK1)) = $true))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 (setminusER = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 (setminusER = $true) & ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.47/1.29 inference(flattening,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((($true = (in @ X2 @ (setminus @ X1 @ X0))) & ((in @ X2 @ X0) = $true)) & ((in @ X2 @ X1) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (setminusER = $true)),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ~((setminusER = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ($true != (in @ X2 @ (setminus @ X1 @ X0)))))))),
% 1.47/1.29 inference(flattening,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ~((setminusER = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ~($true = (in @ X2 @ (setminus @ X1 @ X0)))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~(setminusER => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X1 @ X0))))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f3])).
% 1.47/1.29 thf(f3,negated_conjecture,(
% 1.47/1.29 ~(setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => ~(in @ X2 @ (setminus @ X0 @ X3))))))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.47/1.29 thf(f2,conjecture,(
% 1.47/1.29 setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => ~(in @ X2 @ (setminus @ X0 @ X3)))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.OfQSe51IMp/DTF2THF_8772.p',complementTI1)).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ((in @ sK2 @ sK1) != $true)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ($true != $true) | ((in @ sK2 @ sK1) != $true)),
% 1.47/1.29 inference(superposition,[status(thm)],[f33,f22])).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ((in @ sK2 @ (setminus @ sK0 @ sK1)) = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X3 @ X4)) != $true) | ((in @ X5 @ X4) != $true)) )),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ((in @ X5 @ (setminus @ X3 @ X4)) != $true) | ($true != $true)) )),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f27,f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 (setminusER = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.47/1.29 thf(f27,plain,(
% 1.47/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X3 @ X4)) != $true) | ((in @ X5 @ X4) != $true) | (setminusER != $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f21])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 ((setminusER = $true) | (((in @ sK5 @ (setminus @ sK3 @ sK4)) = $true) & ((in @ sK5 @ sK4) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X3 @ X4)) != $true) | ((in @ X5 @ X4) != $true)) | (setminusER != $true))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f19,f20])).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) & ((in @ X2 @ X1) = $true)) => (((in @ sK5 @ (setminus @ sK3 @ sK4)) = $true) & ((in @ sK5 @ sK4) = $true))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) & ((in @ X2 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X3 @ X4)) != $true) | ((in @ X5 @ X4) != $true)) | (setminusER != $true))),
% 1.47/1.29 inference(rectify,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ((setminusER = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) & ((in @ X0 @ X1) = $true))) & (! [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ X0 @ (setminus @ X2 @ X1))) | ((in @ X0 @ X1) != $true)) | (setminusER != $true))),
% 1.47/1.29 inference(nnf_transformation,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 (setminusER = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ X0 @ (setminus @ X2 @ X1))) | ((in @ X0 @ X1) != $true))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) => ((in @ X0 @ X1) != $true)) <=> (setminusER = $true)),
% 1.47/1.29 inference(flattening,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) => ~((in @ X0 @ X1) = $true))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f1])).
% 1.47/1.29 thf(f1,axiom,(
% 1.47/1.29 (setminusER = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.OfQSe51IMp/DTF2THF_8772.p',setminusER)).
% 1.47/1.29 % SZS output end Proof for DTF2THF_8772
% 1.47/1.29 % (9094)------------------------------
% 1.47/1.29 % (9094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (9094)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (9094)Memory used [KB]: 5500
% 1.47/1.29 % (9094)Time elapsed: 0.005 s
% 1.47/1.29 % (9094)Instructions burned: 2 (million)
% 1.47/1.29 % (9094)------------------------------
% 1.47/1.29 % (9094)------------------------------
% 1.47/1.29 % (9088)Success in time 0.019 s
%------------------------------------------------------------------------------