%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU548^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:35:12 AM UTC 2026
% Result : Theorem 1.51s 1.38s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 88 ( 11 ~; 0 |; 12 &; 48 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 16 !; 12 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( in @ sK3 @ sK0 )
!= ( in @ sK3 @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f15,f16,f14]) ).
thf(f14,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( inCongP = $true )
& ( sK2 = sK3 )
& ( ( in @ sK3 @ sK0 )
!= ( in @ sK2 @ sK1 ) )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X3 @ X0 )
!= ( in @ X2 @ X1 ) ) )
& ( X0 = X1 ) )
=> ( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( ( in @ X2 @ sK1 )
!= ( in @ X3 @ sK0 ) ) )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( ( in @ X2 @ sK1 )
!= ( in @ X3 @ sK0 ) ) )
=> ( ( sK2 = sK3 )
& ( ( in @ sK3 @ sK0 )
!= ( in @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( inCongP = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X3 @ X0 )
!= ( in @ X2 @ X1 ) ) )
& ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( inCongP = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X0 )
= ( in @ X2 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( inCongP
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X0 )
<=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( inCongP
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X1 )
<=> ( in @ X2 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( inCongP
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X1 )
<=> ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WmF96vqmI2/DTF2THF_1658.p',in__Cong) ).
thf(f16,plain,
sK2 = sK3,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( ( in @ sK3 @ sK0 )
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU548^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:26:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU548^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : A simple congruence property of in
% 0.20/0.45 % Version : Especial > Reduced > Especial.
% 0.20/0.45 % English : (forall A:i.forall B:i.A = B -> (forall x:i.forall y:i.x = y ->
% 0.20/0.45 % (in x A <-> in y B)))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC050l [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 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 v4.0.0
% 0.20/0.45 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.20/0.45 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.45 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 8 @)
% 0.20/0.45 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=1
% 0.20/0.45 % : v4.0.0 - Added in type
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(inCongP_type,type,
% 0.20/0.45 inCongP: $o ).
% 0.20/0.45
% 0.20/0.45 thf(inCongP,definition,
% 0.20/0.45 ( inCongP
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ( A = B )
% 0.20/0.45 => ! [Xx: $i,Xy: $i] :
% 0.20/0.45 ( ( Xx = Xy )
% 0.20/0.45 => ( ( in @ Xx @ A )
% 0.20/0.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(in__Cong,conjecture,
% 0.20/0.45 ( inCongP
% 0.20/0.45 => ! [A: $i,B: $i] :
% 0.20/0.45 ( ( A = B )
% 0.20/0.45 => ! [Xx: $i,Xy: $i] :
% 0.20/0.45 ( ( Xx = Xy )
% 0.20/0.45 => ( ( in @ Xx @ A )
% 0.20/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.51/1.35 ---- Embedded in THF ---
% 1.51/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.35 %%% Generated on Tue Feb 24 12:26:40 EST 2026
% 1.51/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.35 %%% Logic specification used:
% 1.51/1.35 %%% thf(spec, logic, $$dhol).
% 1.51/1.35
% 1.51/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WmF96vqmI2/DTF2DTF1658.p
% See solution above
% 1.51/1.35 ------------------------
% 1.51/1.36 ---- Cleaned THF ---
% 1.51/1.36 thf(in_type,type,
% 1.51/1.36 in: $i > $i > $o ).
% 1.51/1.36
% 1.51/1.36 thf(inCongP_type,type,
% 1.51/1.36 inCongP: $o ).
% 1.51/1.36
% 1.51/1.36 thf(inCongP,definition,
% 1.51/1.36 ( inCongP
% 1.51/1.36 = ( ! [A: $i,B: $i] :
% 1.51/1.36 ( ( A = B )
% 1.51/1.36 => ! [Xx: $i,Xy: $i] :
% 1.51/1.36 ( ( Xx = Xy )
% 1.51/1.36 => ( ( in @ Xx @ A )
% 1.51/1.36 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.51/1.36
% 1.51/1.36 thf(in__Cong,conjecture,
% 1.51/1.36 ( inCongP
% 1.51/1.36 => ! [A: $i,B: $i] :
% 1.51/1.36 ( ( A = B )
% 1.51/1.36 => ! [Xx: $i,Xy: $i] :
% 1.51/1.36 ( ( Xx = Xy )
% 1.51/1.36 => ( ( in @ Xx @ A )
% 1.51/1.36 <=> ( in @ Xy @ B ) ) ) ) ) ).
% 1.51/1.36 ------------------------
% 1.51/1.38 % (1763)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1658 for (3000ds/183Mi)
% 1.51/1.38 % (1768)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_1658 for (3000ds/275Mi)
% 1.51/1.38 % (1767)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_1658 for (3000ds/2Mi)
% 1.51/1.38 % (1769)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1658 for (3000ds/18Mi)
% 1.51/1.38 % (1764)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_1658 for (3000ds/4Mi)
% 1.51/1.38 % (1765)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_1658 for (3000ds/27Mi)
% 1.51/1.38 % (1766)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1658 for (3000ds/2Mi)
% 1.51/1.38 % (1763)First to succeed.
% 1.51/1.38 % (1767)Instruction limit reached!
% 1.51/1.38 % (1767)------------------------------
% 1.51/1.38 % (1767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.38 % (1767)Termination reason: Unknown
% 1.51/1.38 % (1767)Termination phase: Saturation
% 1.51/1.38
% 1.51/1.38 % (1767)Memory used [KB]: 5373
% 1.51/1.38 % (1767)Time elapsed: 0.003 s
% 1.51/1.38 % (1767)Instructions burned: 2 (million)
% 1.51/1.38 % (1767)------------------------------
% 1.51/1.38 % (1767)------------------------------
% 1.51/1.38 % (1766)Also succeeded, but the first one will report.
% 1.51/1.38 % (1769)Also succeeded, but the first one will report.
% 1.51/1.38 % (1763)Refutation found. Thanks to Tanya!
% 1.51/1.38 % SZS status Theorem for DTF2THF_1658
% 1.51/1.38 % SZS output start Proof for DTF2THF_1658
% 1.51/1.38 thf(func_def_0, type, in: $i > $i > $o).
% 1.51/1.38 thf(f20,plain,(
% 1.51/1.38 $false),
% 1.51/1.38 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.51/1.38 thf(f19,plain,(
% 1.51/1.38 ((in @ sK3 @ sK0) != (in @ sK3 @ sK0))),
% 1.51/1.38 inference(definition_unfolding,[status(thm)],[f15,f16,f14])).
% 1.51/1.38 thf(f14,plain,(
% 1.51/1.38 (sK1 = sK0)),
% 1.51/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.38 thf(f12,plain,(
% 1.51/1.38 (inCongP = $true) & (((sK2 = sK3) & ((in @ sK3 @ sK0) != (in @ sK2 @ sK1))) & (sK1 = sK0))),
% 1.51/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
% 1.51/1.38 thf(f10,plain,(
% 1.51/1.38 ? [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ((X2 = X3) & ((in @ X3 @ X0) != (in @ X2 @ X1))) & (X0 = X1)) => (? [X3 : $i,X2 : $i] : ((X2 = X3) & ((in @ X2 @ sK1) != (in @ X3 @ sK0))) & (sK1 = sK0))),
% 1.51/1.38 introduced(definition,[],[choice_axiom])).
% 1.51/1.38 thf(f11,plain,(
% 1.51/1.38 ? [X3 : $i,X2 : $i] : ((X2 = X3) & ((in @ X2 @ sK1) != (in @ X3 @ sK0))) => ((sK2 = sK3) & ((in @ sK3 @ sK0) != (in @ sK2 @ sK1)))),
% 1.51/1.38 introduced(definition,[],[choice_axiom])).
% 1.51/1.38 thf(f9,plain,(
% 1.51/1.38 (inCongP = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ((X2 = X3) & ((in @ X3 @ X0) != (in @ X2 @ X1))) & (X0 = X1))),
% 1.51/1.38 inference(ennf_transformation,[status(thm)],[f8])).
% 1.51/1.38 thf(f8,plain,(
% 1.51/1.38 ~((inCongP = $true) => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X0) = (in @ X2 @ X1)))))),
% 1.51/1.38 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.38 thf(f7,plain,(
% 1.51/1.38 ~(inCongP => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X0) <=> (in @ X2 @ X1)))))),
% 1.51/1.38 inference(rectify,[status(thm)],[f3])).
% 1.51/1.38 thf(f3,negated_conjecture,(
% 1.51/1.38 ~(inCongP => ! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X1) <=> (in @ X2 @ X0)))))),
% 1.51/1.38 inference(negated_conjecture,[status(cth)],[f2])).
% 1.51/1.38 thf(f2,conjecture,(
% 1.51/1.38 inCongP => ! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X1) <=> (in @ X2 @ X0))))),
% 1.51/1.38 file('/export/starexec/sandbox/tmp/tmp.WmF96vqmI2/DTF2THF_1658.p',in__Cong)).
% 1.51/1.38 thf(f16,plain,(
% 1.51/1.38 (sK2 = sK3)),
% 1.51/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.38 thf(f15,plain,(
% 1.51/1.38 ((in @ sK3 @ sK0) != (in @ sK2 @ sK1))),
% 1.51/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.38 % SZS output end Proof for DTF2THF_1658
% 1.51/1.38 % (1763)------------------------------
% 1.51/1.38 % (1763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.38 % (1763)Termination reason: Refutation
% 1.51/1.38
% 1.51/1.38 % (1763)Memory used [KB]: 5500
% 1.51/1.38 % (1763)Time elapsed: 0.003 s
% 1.51/1.38 % (1763)Instructions burned: 2 (million)
% 1.51/1.38 % (1763)------------------------------
% 1.51/1.38 % (1763)------------------------------
% 1.51/1.38 % (1762)Success in time 0.017 s
%------------------------------------------------------------------------------