%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU567^2 : 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 : n021.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 09:35:19 AM UTC 2026
% Result : Theorem 1.65s 1.46s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 92 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 279 ( 49 ~; 27 |; 22 &; 160 @)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 46 !; 16 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
sK2: $i > $i > $i ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f37,f31]) ).
thf(f31,plain,
( $true
!= ( subset @ sK4 @ sK4 ) ),
inference(definition_unfolding,[status(thm)],[f26,f25]) ).
thf(f25,plain,
sK3 = sK4,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( subset @ sK3 @ sK4 )
!= $true )
& ( sK3 = sK4 )
& ( subsetI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) )
=> ( ( ( subset @ sK3 @ sK4 )
!= $true )
& ( sK3 = sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) )
& ( subsetI1 = $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( X0 = X1 ) )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( subsetI1 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
=> ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
=> ( X0 != X1 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ~ ( subset @ X1 @ X0 )
=> ( X0 != X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( subsetI1
=> ! [X1: $i,X0: $i] :
( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( subsetI1
=> ! [X1: $i,X0: $i] :
( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yboVi8rvLd/DTF2THF_13392.p',notequalI1) ).
thf(f26,plain,
( ( subset @ sK3 @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f37,plain,
( $true
= ( subset @ sK4 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
= ( subset @ sK4 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f35]) ).
thf(f35,plain,
( ( in @ ( sK2 @ sK4 @ sK4 ) @ sK4 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( in @ ( sK2 @ sK4 @ sK4 ) @ sK4 )
= $true ) ),
inference(superposition,[status(thm)],[f31,f32]) ).
thf(f32,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f20,f24]) ).
thf(f24,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f20,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( subsetI1 = $true )
| ( ( ( subset @ sK1 @ sK0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
=> ( ( ( subset @ sK1 @ sK0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) ) )
=> ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) ) ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( subsetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subsetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( subsetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.yboVi8rvLd/DTF2THF_13392.p',subsetI1) ).
thf(f33,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f21,f24]) ).
thf(f21,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU567^2 : 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
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:27:09 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.48 ---- Original DTF file ---
% 0.18/0.48 thf(spec,logic,$$dhol).
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 % File : SEU567^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.48 % Domain : Set Theory
% 0.18/0.48 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.18/0.48 % Version : Especial > Reduced > Especial.
% 0.18/0.48 % English : (! A:i.! B:i.~(subset A B) -> ~(A = B))
% 0.18/0.48
% 0.18/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.48 % Source : [Bro08]
% 0.18/0.48 % Names : ZFC069l [Bro08]
% 0.18/0.48
% 0.18/0.48 % Status : Theorem
% 0.18/0.48 % 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
% 0.18/0.48 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.18/0.48 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.18/0.48 % Maximal formula atoms : 3 ( 4 avg)
% 0.18/0.48 % Number of connectives : 14 ( 2 ~; 0 |; 0 &; 8 @)
% 0.18/0.48 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.48 % Maximal formula depth : 8 ( 5 avg)
% 0.18/0.48 % Number of types : 2 ( 0 usr)
% 0.18/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.48 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.18/0.48 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.18/0.48 % SPC : TH0_THM_EQU_NAR
% 0.18/0.48
% 0.18/0.48 % Comments : http://mathgate.info/detsetitem.php?id=432
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 thf(in_type,type,
% 0.18/0.48 in: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(subset_type,type,
% 0.18/0.48 subset: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(subsetI1_type,type,
% 0.18/0.48 subsetI1: $o ).
% 0.18/0.48
% 0.18/0.48 thf(subsetI1,definition,
% 0.18/0.48 ( subsetI1
% 0.18/0.48 = ( ! [A: $i,B: $i] :
% 0.18/0.48 ( ! [Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ A )
% 0.18/0.48 => ( in @ Xx @ B ) )
% 0.18/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(notequalI1,conjecture,
% 0.18/0.48 ( subsetI1
% 0.18/0.48 => ! [A: $i,B: $i] :
% 0.18/0.48 ( ~ ( subset @ A @ B )
% 0.18/0.48 => ( A != B ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 ------------------------
% 1.65/1.42 ---- Embedded in THF ---
% 1.65/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.42 %%% Generated on Tue Feb 24 12:27:10 EST 2026
% 1.65/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.42 %%% Logic specification used:
% 1.65/1.42 %%% thf(spec, logic, $$dhol).
% 1.65/1.42
% 1.65/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yboVi8rvLd/DTF2DTF13392.p
% See solution above
% 1.65/1.42 ------------------------
% 1.65/1.43 ---- Cleaned THF ---
% 1.65/1.43 thf(in_type,type,
% 1.65/1.43 in: $i > $i > $o ).
% 1.65/1.43
% 1.65/1.43 thf(subset_type,type,
% 1.65/1.43 subset: $i > $i > $o ).
% 1.65/1.43
% 1.65/1.43 thf(subsetI1_type,type,
% 1.65/1.43 subsetI1: $o ).
% 1.65/1.43
% 1.65/1.43 thf(subsetI1,definition,
% 1.65/1.43 ( subsetI1
% 1.65/1.43 = ( ! [A: $i,B: $i] :
% 1.65/1.43 ( ! [Xx: $i] :
% 1.65/1.43 ( ( in @ Xx @ A )
% 1.65/1.43 => ( in @ Xx @ B ) )
% 1.65/1.43 => ( subset @ A @ B ) ) ) ) ).
% 1.65/1.43
% 1.65/1.43 thf(notequalI1,conjecture,
% 1.65/1.43 ( subsetI1
% 1.65/1.43 => ! [A: $i,B: $i] :
% 1.65/1.43 ( ~ ( subset @ A @ B )
% 1.65/1.43 => ( A != B ) ) ) ).
% 1.65/1.43 ------------------------
% 1.65/1.45 % (13526)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_13392 for (3000ds/27Mi)
% 1.65/1.45 % (13524)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13392 for (3000ds/183Mi)
% 1.65/1.45 % (13527)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13392 for (3000ds/2Mi)
% 1.65/1.45 % (13528)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_13392 for (3000ds/2Mi)
% 1.65/1.45 % (13525)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_13392 for (3000ds/4Mi)
% 1.65/1.45 % (13529)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_13392 for (3000ds/275Mi)
% 1.65/1.45 % (13530)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13392 for (3000ds/18Mi)
% 1.65/1.45 % (13529)Refutation not found, incomplete strategy
% 1.65/1.45 % (13529)------------------------------
% 1.65/1.45 % (13529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (13529)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.45
% 1.65/1.45
% 1.65/1.45 % (13529)Memory used [KB]: 5373
% 1.65/1.45 % (13529)Time elapsed: 0.002 s
% 1.65/1.45 % (13529)Instructions burned: 1 (million)
% 1.65/1.45 % (13529)------------------------------
% 1.65/1.45 % (13529)------------------------------
% 1.65/1.45 % (13527)Instruction limit reached!
% 1.65/1.45 % (13527)------------------------------
% 1.65/1.45 % (13527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (13527)Termination reason: Unknown
% 1.65/1.45 % (13527)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (13527)Memory used [KB]: 5500
% 1.65/1.45 % (13527)Time elapsed: 0.003 s
% 1.65/1.45 % (13527)Instructions burned: 2 (million)
% 1.65/1.45 % (13527)------------------------------
% 1.65/1.45 % (13527)------------------------------
% 1.65/1.45 % (13528)Instruction limit reached!
% 1.65/1.45 % (13528)------------------------------
% 1.65/1.45 % (13528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (13528)Termination reason: Unknown
% 1.65/1.45 % (13528)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (13528)Memory used [KB]: 5500
% 1.65/1.45 % (13528)Time elapsed: 0.003 s
% 1.65/1.45 % (13528)Instructions burned: 3 (million)
% 1.65/1.45 % (13528)------------------------------
% 1.65/1.45 % (13528)------------------------------
% 1.65/1.45 % (13530)First to succeed.
% 1.65/1.45 % (13525)Instruction limit reached!
% 1.65/1.45 % (13525)------------------------------
% 1.65/1.45 % (13525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (13525)Termination reason: Unknown
% 1.65/1.45 % (13525)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (13525)Memory used [KB]: 5500
% 1.65/1.45 % (13525)Time elapsed: 0.004 s
% 1.65/1.45 % (13525)Instructions burned: 4 (million)
% 1.65/1.45 % (13525)------------------------------
% 1.65/1.45 % (13525)------------------------------
% 1.65/1.46 % (13524)Also succeeded, but the first one will report.
% 1.65/1.46 % (13530)Refutation found. Thanks to Tanya!
% 1.65/1.46 % SZS status Theorem for DTF2THF_13392
% 1.65/1.46 % SZS output start Proof for DTF2THF_13392
% 1.65/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.46 thf(func_def_1, type, subset: $i > $i > $o).
% 1.65/1.46 thf(func_def_8, type, sK2: $i > $i > $i).
% 1.65/1.46 thf(f38,plain,(
% 1.65/1.46 $false),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f37,f31])).
% 1.65/1.46 thf(f31,plain,(
% 1.65/1.46 ($true != (subset @ sK4 @ sK4))),
% 1.65/1.46 inference(definition_unfolding,[status(thm)],[f26,f25])).
% 1.65/1.46 thf(f25,plain,(
% 1.65/1.46 (sK3 = sK4)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.65/1.46 thf(f19,plain,(
% 1.65/1.46 (((subset @ sK3 @ sK4) != $true) & (sK3 = sK4)) & (subsetI1 = $true)),
% 1.65/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f18])).
% 1.65/1.46 thf(f18,plain,(
% 1.65/1.46 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1)) => (((subset @ sK3 @ sK4) != $true) & (sK3 = sK4))),
% 1.65/1.46 introduced(definition,[],[choice_axiom])).
% 1.65/1.46 thf(f17,plain,(
% 1.65/1.46 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1)) & (subsetI1 = $true)),
% 1.65/1.46 inference(rectify,[status(thm)],[f11])).
% 1.65/1.46 thf(f11,plain,(
% 1.65/1.46 ? [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) & (X0 = X1)) & (subsetI1 = $true)),
% 1.65/1.46 inference(ennf_transformation,[status(thm)],[f9])).
% 1.65/1.46 thf(f9,plain,(
% 1.65/1.46 ~((subsetI1 = $true) => ! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) => (X0 != X1)))),
% 1.65/1.46 inference(flattening,[status(thm)],[f8])).
% 1.65/1.46 thf(f8,plain,(
% 1.65/1.46 ~((subsetI1 = $true) => ! [X0 : $i,X1 : $i] : (~((subset @ X1 @ X0) = $true) => (X0 != X1)))),
% 1.65/1.46 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.46 thf(f7,plain,(
% 1.65/1.46 ~(subsetI1 => ! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)))),
% 1.65/1.46 inference(rectify,[status(thm)],[f3])).
% 1.65/1.46 thf(f3,negated_conjecture,(
% 1.65/1.46 ~(subsetI1 => ! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)))),
% 1.65/1.46 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.46 thf(f2,conjecture,(
% 1.65/1.46 subsetI1 => ! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1))),
% 1.65/1.46 file('/export/starexec/sandbox/tmp/tmp.yboVi8rvLd/DTF2THF_13392.p',notequalI1)).
% 1.65/1.46 thf(f26,plain,(
% 1.65/1.46 ((subset @ sK3 @ sK4) != $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.65/1.46 thf(f37,plain,(
% 1.65/1.46 ($true = (subset @ sK4 @ sK4))),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.65/1.46 thf(f36,plain,(
% 1.65/1.46 ($true = (subset @ sK4 @ sK4)) | ($true != $true)),
% 1.65/1.46 inference(superposition,[status(thm)],[f33,f35])).
% 1.65/1.46 thf(f35,plain,(
% 1.65/1.46 ((in @ (sK2 @ sK4 @ sK4) @ sK4) = $true)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.65/1.46 thf(f34,plain,(
% 1.65/1.46 ($true != $true) | ((in @ (sK2 @ sK4 @ sK4) @ sK4) = $true)),
% 1.65/1.46 inference(superposition,[status(thm)],[f31,f32])).
% 1.65/1.46 thf(f32,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true)) )),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.65/1.46 thf(f30,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true)) )),
% 1.65/1.46 inference(definition_unfolding,[status(thm)],[f20,f24])).
% 1.65/1.46 thf(f24,plain,(
% 1.65/1.46 (subsetI1 = $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.65/1.46 thf(f20,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true) | (subsetI1 != $true)) )),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.46 thf(f16,plain,(
% 1.65/1.46 ((subsetI1 = $true) | (((subset @ sK1 @ sK0) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) = $true) | ((in @ X2 @ sK1) != $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true))) | (subsetI1 != $true))),
% 1.65/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14])).
% 1.65/1.46 thf(f14,plain,(
% 1.65/1.46 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true))) => (((subset @ sK1 @ sK0) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) = $true) | ((in @ X2 @ sK1) != $true)))),
% 1.65/1.46 introduced(definition,[],[choice_axiom])).
% 1.65/1.46 thf(f15,plain,(
% 1.65/1.46 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X3) != $true) & ($true = (in @ X5 @ X4))) => (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true)))),
% 1.65/1.46 introduced(definition,[],[choice_axiom])).
% 1.65/1.46 thf(f13,plain,(
% 1.65/1.46 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ? [X5 : $i] : (((in @ X5 @ X3) != $true) & ($true = (in @ X5 @ X4)))) | (subsetI1 != $true))),
% 1.65/1.46 inference(rectify,[status(thm)],[f12])).
% 1.65/1.46 thf(f12,plain,(
% 1.65/1.46 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)))) & (! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true))),
% 1.65/1.46 inference(nnf_transformation,[status(thm)],[f10])).
% 1.65/1.46 thf(f10,plain,(
% 1.65/1.46 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)))),
% 1.65/1.46 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.46 thf(f6,plain,(
% 1.65/1.46 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 1.65/1.46 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.46 thf(f5,plain,(
% 1.65/1.46 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.65/1.46 inference(rectify,[status(thm)],[f1])).
% 1.65/1.46 thf(f1,axiom,(
% 1.65/1.46 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.65/1.46 file('/export/starexec/sandbox/tmp/tmp.yboVi8rvLd/DTF2THF_13392.p',subsetI1)).
% 1.65/1.46 thf(f33,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.65/1.46 thf(f29,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true) | ($true != $true)) )),
% 1.65/1.46 inference(definition_unfolding,[status(thm)],[f21,f24])).
% 1.65/1.46 thf(f21,plain,(
% 1.65/1.46 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ((in @ (sK2 @ X4 @ X3) @ X3) != $true) | (subsetI1 != $true)) )),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.46 % SZS output end Proof for DTF2THF_13392
% 1.65/1.46 % (13530)------------------------------
% 1.65/1.46 % (13530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (13530)Termination reason: Refutation
% 1.65/1.46
% 1.65/1.46 % (13530)Memory used [KB]: 5500
% 1.65/1.46 % (13530)Time elapsed: 0.004 s
% 1.65/1.46 % (13530)Instructions burned: 2 (million)
% 1.65/1.46 % (13530)------------------------------
% 1.65/1.46 % (13530)------------------------------
% 1.65/1.46 % (13523)Success in time 0.018 s
%------------------------------------------------------------------------------