%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU602^2 : 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 : n011.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 09:35:32 AM UTC 2026
% Result : Theorem 1.53s 1.37s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 278 ( 33 ~; 17 |; 14 &; 199 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 91 ( 31 ^; 45 !; 15 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_12,type,
sK1: $i > $o ).
thf(func_def_18,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f24]) ).
thf(f24,plain,
( ( in @ sK5 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( dsetconstrEL = $true )
& ( ( in @ sK5 @ sK3 )
!= $true )
& ( ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f12,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
=> ( ( ( in @ sK5 @ sK3 )
!= $true )
& ( ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ! [X0: $i,X4: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrEL
=> ! [X0: $i,X4: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2THF_9196.p',setminusEL) ).
thf(f35,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( in @ sK5 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f32,f33]) ).
thf(f33,plain,
( ( in @ sK5
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK4 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( in @ sK5
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK3
@ sK4 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f26]) ).
thf(f26,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,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.QKFqU0znro/DTF2THF_9196.p',setminus) ).
thf(f23,plain,
( ( in @ sK5 @ ( setminus @ sK3 @ sK4 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f32,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true != $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f20,f25]) ).
thf(f25,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f20,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( dsetconstrEL = $true )
| ( ( ( in @ sK0 @ sK2 )
!= $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
=> ( ( ( in @ sK0 @ sK2 )
!= $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2THF_9196.p',dsetconstrEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU602^2 : 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 : n011.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 12:27:47 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.41 ---- Original DTF file ---
% 0.20/0.41 thf(spec,logic,$$dhol).
% 0.20/0.41 %------------------------------------------------------------------------------
% 0.20/0.41 % File : SEU602^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.41 % Domain : Set Theory
% 0.20/0.41 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.20/0.41 % Version : Especial > Reduced > Especial.
% 0.20/0.41 % English : (! A:i.! B:i.! x:i.in x (setminus A B) -> in x A)
% 0.20/0.41
% 0.20/0.41 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.41 % Source : [Bro08]
% 0.20/0.41 % Names : ZFC104l [Bro08]
% 0.20/0.41
% 0.20/0.41 % Status : Theorem
% 0.20/0.41 % 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, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 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 v4.0.0, 0.33 v3.7.0
% 0.20/0.41 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.20/0.41 % Number of atoms : 9 ( 2 equ; 0 cnn)
% 0.20/0.41 % Maximal formula atoms : 3 ( 3 avg)
% 0.20/0.41 % Number of connectives : 21 ( 1 ~; 0 |; 0 &; 17 @)
% 0.20/0.41 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.41 % Maximal formula depth : 9 ( 4 avg)
% 0.20/0.41 % Number of types : 2 ( 0 usr)
% 0.20/0.41 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.41 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.20/0.41 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.20/0.41 % SPC : TH0_THM_EQU_NAR
% 0.20/0.41
% 0.20/0.41 % Comments : http://mathgate.info/detsetitem.php?id=270
% 0.20/0.41 %------------------------------------------------------------------------------
% 0.20/0.41 thf(in_type,type,
% 0.20/0.41 in: $i > $i > $o ).
% 0.20/0.41
% 0.20/0.41 thf(dsetconstr_type,type,
% 0.20/0.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.41
% 0.20/0.41 thf(dsetconstrEL_type,type,
% 0.20/0.41 dsetconstrEL: $o ).
% 0.20/0.41
% 0.20/0.41 thf(dsetconstrEL,definition,
% 0.20/0.41 ( dsetconstrEL
% 0.20/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.41 ( ( in @ Xx
% 0.20/0.41 @ ( dsetconstr @ A
% 0.20/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.41 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.41
% 0.20/0.41 thf(setminus_type,type,
% 0.20/0.41 setminus: $i > $i > $i ).
% 0.20/0.41
% 0.20/0.41 thf(setminus,definition,
% 0.20/0.41 ( setminus
% 0.20/0.41 = ( ^ [A: $i,B: $i] :
% 0.20/0.41 ( dsetconstr @ A
% 0.20/0.41 @ ^ [Xx: $i] :
% 0.20/0.41 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.41
% 0.20/0.41 thf(setminusEL,conjecture,
% 0.20/0.41 ( dsetconstrEL
% 0.20/0.41 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.41 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.41 => ( in @ Xx @ A ) ) ) ).
% 0.20/0.41
% 0.20/0.41 %------------------------------------------------------------------------------
% 0.20/0.41 ------------------------
% 1.53/1.33 ---- Embedded in THF ---
% 1.53/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.33 %%% Generated on Tue Feb 24 12:27:48 EST 2026
% 1.53/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.33 %%% Logic specification used:
% 1.53/1.33 %%% thf(spec, logic, $$dhol).
% 1.53/1.33
% 1.53/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2DTF9196.p
% See solution above
% 1.53/1.33 ------------------------
% 1.53/1.34 ---- Cleaned THF ---
% 1.53/1.34 thf(in_type,type,
% 1.53/1.34 in: $i > $i > $o ).
% 1.53/1.34
% 1.53/1.34 thf(dsetconstr_type,type,
% 1.53/1.34 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.53/1.34
% 1.53/1.34 thf(dsetconstrEL_type,type,
% 1.53/1.34 dsetconstrEL: $o ).
% 1.53/1.34
% 1.53/1.34 thf(dsetconstrEL,definition,
% 1.53/1.34 ( dsetconstrEL
% 1.53/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.53/1.34 ( ( in @ Xx
% 1.53/1.34 @ ( dsetconstr @ A
% 1.53/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.53/1.34 => ( in @ Xx @ A ) ) ) ) ).
% 1.53/1.34
% 1.53/1.34 thf(setminus_type,type,
% 1.53/1.34 setminus: $i > $i > $i ).
% 1.53/1.34
% 1.53/1.34 thf(setminus,definition,
% 1.53/1.34 ( setminus
% 1.53/1.34 = ( ^ [A: $i,B: $i] :
% 1.53/1.34 ( dsetconstr @ A
% 1.53/1.34 @ ^ [Xx: $i] :
% 1.53/1.34 ~ ( in @ Xx @ B ) ) ) ) ).
% 1.53/1.34
% 1.53/1.34 thf(setminusEL,conjecture,
% 1.53/1.34 ( dsetconstrEL
% 1.53/1.34 => ! [A: $i,B: $i,Xx: $i] :
% 1.53/1.34 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.53/1.34 => ( in @ Xx @ A ) ) ) ).
% 1.53/1.34 ------------------------
% 1.53/1.36 % (9295)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_9196 for (2999ds/27Mi)
% 1.53/1.36 % (9293)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9196 for (2999ds/183Mi)
% 1.53/1.36 % (9297)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_9196 for (2999ds/2Mi)
% 1.53/1.36 % (9299)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9196 for (2999ds/18Mi)
% 1.53/1.36 % (9296)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9196 for (2999ds/2Mi)
% 1.53/1.36 % (9294)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_9196 for (2999ds/4Mi)
% 1.53/1.36 % (9298)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_9196 for (2999ds/275Mi)
% 1.53/1.36 % (9296)Instruction limit reached!
% 1.53/1.36 % (9296)------------------------------
% 1.53/1.36 % (9296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (9296)Termination reason: Unknown
% 1.53/1.36 % (9296)Termination phase: Saturation
% 1.53/1.36 % (9297)Instruction limit reached!
% 1.53/1.36 % (9297)------------------------------
% 1.53/1.36 % (9297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (9297)Termination reason: Unknown
% 1.53/1.36 % (9297)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (9297)Memory used [KB]: 895
% 1.53/1.36 % (9297)Time elapsed: 0.003 s
% 1.53/1.36 % (9297)Instructions burned: 2 (million)
% 1.53/1.36 % (9297)------------------------------
% 1.53/1.36 % (9297)------------------------------
% 1.53/1.36
% 1.53/1.36 % (9296)Memory used [KB]: 895
% 1.53/1.36 % (9296)Time elapsed: 0.003 s
% 1.53/1.36 % (9296)Instructions burned: 2 (million)
% 1.53/1.36 % (9296)------------------------------
% 1.53/1.36 % (9296)------------------------------
% 1.53/1.36 % (9298)Refutation not found, incomplete strategy
% 1.53/1.36 % (9298)------------------------------
% 1.53/1.36 % (9298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (9298)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.36
% 1.53/1.36
% 1.53/1.36 % (9298)Memory used [KB]: 5500
% 1.53/1.36 % (9298)Time elapsed: 0.003 s
% 1.53/1.36 % (9298)Instructions burned: 2 (million)
% 1.53/1.36 % (9298)------------------------------
% 1.53/1.36 % (9298)------------------------------
% 1.53/1.36 % (9299)First to succeed.
% 1.53/1.37 % (9293)Also succeeded, but the first one will report.
% 1.53/1.37 % (9294)Also succeeded, but the first one will report.
% 1.53/1.37 % (9299)Refutation found. Thanks to Tanya!
% 1.53/1.37 % SZS status Theorem for DTF2THF_9196
% 1.53/1.37 % SZS output start Proof for DTF2THF_9196
% 1.53/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.53/1.37 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.53/1.37 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.53/1.37 thf(func_def_12, type, sK1: $i > $o).
% 1.53/1.37 thf(func_def_18, type, ph7: !>[X0: $tType]:(X0)).
% 1.53/1.37 thf(f36,plain,(
% 1.53/1.37 $false),
% 1.53/1.37 inference(subsumption_resolution,[status(thm)],[f35,f24])).
% 1.53/1.37 thf(f24,plain,(
% 1.53/1.37 ((in @ sK5 @ sK3) != $true)),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.53/1.37 thf(f19,plain,(
% 1.53/1.37 (dsetconstrEL = $true) & (((in @ sK5 @ sK3) != $true) & ((in @ sK5 @ (setminus @ sK3 @ sK4)) = $true))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f12,f18])).
% 1.53/1.37 thf(f18,plain,(
% 1.53/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true)) => (((in @ sK5 @ sK3) != $true) & ((in @ sK5 @ (setminus @ sK3 @ sK4)) = $true))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f12,plain,(
% 1.53/1.37 (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f9])).
% 1.53/1.37 thf(f9,plain,(
% 1.53/1.37 ~((dsetconstrEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) => ((in @ X2 @ X0) = $true)))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f8])).
% 1.53/1.37 thf(f8,plain,(
% 1.53/1.37 ~(dsetconstrEL => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.53/1.37 inference(rectify,[status(thm)],[f4])).
% 1.53/1.37 thf(f4,negated_conjecture,(
% 1.53/1.37 ~(dsetconstrEL => ! [X0 : $i,X4 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ X0)))),
% 1.53/1.37 inference(negated_conjecture,[status(cth)],[f3])).
% 1.53/1.37 thf(f3,conjecture,(
% 1.53/1.37 dsetconstrEL => ! [X0 : $i,X4 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ X0))),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2THF_9196.p',setminusEL)).
% 1.53/1.37 thf(f35,plain,(
% 1.53/1.37 ((in @ sK5 @ sK3) = $true)),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.53/1.37 thf(f34,plain,(
% 1.53/1.37 ($true != $true) | ((in @ sK5 @ sK3) = $true)),
% 1.53/1.37 inference(superposition,[status(thm)],[f32,f33])).
% 1.53/1.37 thf(f33,plain,(
% 1.53/1.37 ((in @ sK5 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (~ (in @ Y0 @ sK4))))) = $true)),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.53/1.37 thf(f30,plain,(
% 1.53/1.37 ((in @ sK5 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))) @ sK3 @ sK4)) = $true)),
% 1.53/1.37 inference(definition_unfolding,[status(thm)],[f23,f26])).
% 1.53/1.37 thf(f26,plain,(
% 1.53/1.37 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.37 thf(f7,plain,(
% 1.53/1.37 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f6])).
% 1.53/1.37 thf(f6,plain,(
% 1.53/1.37 (setminus = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X1))))))),
% 1.53/1.37 inference(rectify,[status(thm)],[f2])).
% 1.53/1.37 thf(f2,axiom,(
% 1.53/1.37 (setminus = (^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X4))))))),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2THF_9196.p',setminus)).
% 1.53/1.37 thf(f23,plain,(
% 1.53/1.37 ((in @ sK5 @ (setminus @ sK3 @ sK4)) = $true)),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.53/1.37 thf(f32,plain,(
% 1.53/1.37 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ (dsetconstr @ X5 @ X4)) != $true) | ((in @ X3 @ X5) = $true)) )),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.53/1.37 thf(f31,plain,(
% 1.53/1.37 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) )),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.53/1.37 thf(f29,plain,(
% 1.53/1.37 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) )),
% 1.53/1.37 inference(definition_unfolding,[status(thm)],[f20,f25])).
% 1.53/1.37 thf(f25,plain,(
% 1.53/1.37 (dsetconstrEL = $true)),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.53/1.37 thf(f20,plain,(
% 1.53/1.37 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | (dsetconstrEL != $true)) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f17])).
% 1.53/1.37 thf(f17,plain,(
% 1.53/1.37 ((dsetconstrEL = $true) | (((in @ sK0 @ sK2) != $true) & ((in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK1 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16])).
% 1.53/1.37 thf(f16,plain,(
% 1.53/1.37 ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)) => (((in @ sK0 @ sK2) != $true) & ((in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK1 @ Y0)))) = $true))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f15,plain,(
% 1.53/1.37 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 1.53/1.37 inference(rectify,[status(thm)],[f14])).
% 1.53/1.37 thf(f14,plain,(
% 1.53/1.37 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 1.53/1.37 inference(nnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f13,plain,(
% 1.53/1.37 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f11])).
% 1.53/1.37 thf(f11,plain,(
% 1.53/1.37 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((in @ X0 @ X2) = $true)) <=> (dsetconstrEL = $true)),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f10])).
% 1.53/1.37 thf(f10,plain,(
% 1.53/1.37 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)) = dsetconstrEL)),
% 1.53/1.37 inference(rectify,[status(thm)],[f1])).
% 1.53/1.37 thf(f1,axiom,(
% 1.53/1.37 (! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.QKFqU0znro/DTF2THF_9196.p',dsetconstrEL)).
% 1.53/1.37 % SZS output end Proof for DTF2THF_9196
% 1.53/1.37 % (9299)------------------------------
% 1.53/1.37 % (9299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (9299)Termination reason: Refutation
% 1.53/1.37
% 1.53/1.37 % (9299)Memory used [KB]: 5500
% 1.53/1.37 % (9299)Time elapsed: 0.004 s
% 1.53/1.37 % (9299)Instructions burned: 2 (million)
% 1.53/1.37 % (9299)------------------------------
% 1.53/1.37 % (9299)------------------------------
% 1.53/1.37 % (9292)Success in time 0.019 s
%------------------------------------------------------------------------------