%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU552^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 09:35:14 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% 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 : 65 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 79 ( 11 ~; 0 |; 12 &; 48 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 12 !; 16 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
setadjoin: $i > $i > $i ).
thf(f14,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setadjoin @ sK1 @ sK2 )
!= ( setadjoin @ sK1 @ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f11,f10,f12]) ).
thf(f12,plain,
sK3 = sK2,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK3 = sK2 )
& ( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK1 @ sK3 ) )
& ( sK0 = sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X0 @ X2 )
!= ( setadjoin @ X1 @ X3 ) ) )
& ( X0 = X1 ) )
=> ( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ sK1 @ X3 )
!= ( setadjoin @ sK0 @ X2 ) ) )
& ( sK0 = sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ sK1 @ X3 )
!= ( setadjoin @ sK0 @ X2 ) ) )
=> ( ( sK3 = sK2 )
& ( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X0 @ X2 )
!= ( setadjoin @ X1 @ X3 ) ) )
& ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
? [X0: $i,X1: $i] :
( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X1 @ X2 )
!= ( setadjoin @ X0 @ X3 ) ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X1 @ X2 )
= ( setadjoin @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.R2QvIP8P8H/DTF2THF_28279.p',setadjoin__Cong) ).
thf(f10,plain,
sK0 = sK1,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU552^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n004.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 12:26:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU552^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : A simple congruence property of setadjoin
% 0.29/0.46 % Version : Especial > Reduced > Especial.
% 0.29/0.46 % English : (forall x:i.forall y:i.x = y -> (forall z:i.forall u:i.z = u ->
% 0.29/0.46 % setadjoin x z = setadjoin y u))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC054l [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.46 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.46 % Number of types : 1 ( 0 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=29
% 0.29/0.46 % : v4.0.0 - Added setadjoin type
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(setadjoin,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,conjecture,
% 0.29/0.46 ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.26 ---- 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 12:26:12 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/sandbox2/tmp/tmp.R2QvIP8P8H/DTF2DTF28279.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(setadjoin,type,
% 1.47/1.27 setadjoin: $i > $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(setadjoin__Cong,conjecture,
% 1.47/1.27 ! [Xx: $i,Xy: $i] :
% 1.47/1.27 ( ( Xx = Xy )
% 1.47/1.27 => ! [Xz: $i,Xu: $i] :
% 1.47/1.27 ( ( Xz = Xu )
% 1.47/1.27 => ( ( setadjoin @ Xx @ Xz )
% 1.47/1.27 = ( setadjoin @ Xy @ Xu ) ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (28550)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_28279 for (3000ds/4Mi)
% 1.47/1.29 % (28549)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28279 for (3000ds/183Mi)
% 1.47/1.29 % (28551)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_28279 for (3000ds/27Mi)
% 1.47/1.29 % (28552)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28279 for (3000ds/2Mi)
% 1.47/1.29 % (28553)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_28279 for (3000ds/2Mi)
% 1.47/1.29 % (28555)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28279 for (3000ds/18Mi)
% 1.47/1.29 % (28554)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_28279 for (3000ds/275Mi)
% 1.47/1.29 % (28550)First to succeed.
% 1.47/1.29 % (28549)Also succeeded, but the first one will report.
% 1.47/1.29 % (28553)Instruction limit reached!
% 1.47/1.29 % (28553)------------------------------
% 1.47/1.29 % (28553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (28553)Termination reason: Unknown
% 1.47/1.29 % (28553)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (28553)Memory used [KB]: 5500
% 1.47/1.29 % (28553)Time elapsed: 0.004 s
% 1.47/1.29 % (28553)Instructions burned: 3 (million)
% 1.47/1.29 % (28553)------------------------------
% 1.47/1.29 % (28553)------------------------------
% 1.47/1.29 % (28551)Also succeeded, but the first one will report.
% 1.47/1.29 % (28550)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_28279
% 1.47/1.29 % SZS output start Proof for DTF2THF_28279
% 1.47/1.29 thf(func_def_0, type, setadjoin: $i > $i > $i).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ((setadjoin @ sK1 @ sK2) != (setadjoin @ sK1 @ sK2))),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f11,f10,f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 (sK3 = sK2)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ((sK3 = sK2) & ((setadjoin @ sK0 @ sK2) != (setadjoin @ sK1 @ sK3))) & (sK0 = sK1)),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ((X2 = X3) & ((setadjoin @ X0 @ X2) != (setadjoin @ X1 @ X3))) & (X0 = X1)) => (? [X3 : $i,X2 : $i] : ((X2 = X3) & ((setadjoin @ sK1 @ X3) != (setadjoin @ sK0 @ X2))) & (sK0 = sK1))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ? [X3 : $i,X2 : $i] : ((X2 = X3) & ((setadjoin @ sK1 @ X3) != (setadjoin @ sK0 @ X2))) => ((sK3 = sK2) & ((setadjoin @ sK0 @ sK2) != (setadjoin @ sK1 @ sK3)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ((X2 = X3) & ((setadjoin @ X0 @ X2) != (setadjoin @ X1 @ X3))) & (X0 = X1))),
% 1.47/1.29 inference(rectify,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : (? [X3 : $i,X2 : $i] : ((X2 = X3) & ((setadjoin @ X1 @ X2) != (setadjoin @ X0 @ X3))) & (X0 = X1))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((setadjoin @ X1 @ X2) = (setadjoin @ X0 @ X3))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((setadjoin @ X0 @ X2) = (setadjoin @ X1 @ X3))))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((setadjoin @ X0 @ X2) = (setadjoin @ X1 @ X3))))),
% 1.47/1.29 file('/export/starexec/sandbox2/tmp/tmp.R2QvIP8P8H/DTF2THF_28279.p',setadjoin__Cong)).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 (sK0 = sK1)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ((setadjoin @ sK0 @ sK2) != (setadjoin @ sK1 @ sK3))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_28279
% 1.47/1.29 % (28550)------------------------------
% 1.47/1.29 % (28550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (28550)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (28550)Memory used [KB]: 5373
% 1.47/1.29 % (28550)Time elapsed: 0.003 s
% 1.47/1.29 % (28550)Instructions burned: 1 (million)
% 1.47/1.29 % (28550)------------------------------
% 1.47/1.29 % (28550)------------------------------
% 1.47/1.29 % (28548)Success in time 0.02 s
%------------------------------------------------------------------------------