%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU661^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 09:36:01 AM UTC 2026
% Result : Theorem 0.84s 0.86s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 26 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 121 ( 11 ~; 0 |; 12 &; 88 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 16 !; 14 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(f14,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( kpair @ sK0 @ sK3 )
!= ( kpair @ sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( in @ sK0 @ sK1 )
= $true )
& ( ( kpair @ sK0 @ sK3 )
!= ( kpair @ sK0 @ sK3 ) )
& ( $true
= ( in @ sK3 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( ( kpair @ X0 @ X3 )
!= ( kpair @ X0 @ X3 ) )
& ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ( ( in @ sK0 @ sK1 )
= $true )
& ? [X3: $i] :
( ( ( kpair @ sK0 @ X3 )
!= ( kpair @ sK0 @ X3 ) )
& ( $true
= ( in @ X3 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: $i] :
( ( ( kpair @ sK0 @ X3 )
!= ( kpair @ sK0 @ X3 ) )
& ( $true
= ( in @ X3 @ sK2 ) ) )
=> ( ( ( kpair @ sK0 @ sK3 )
!= ( kpair @ sK0 @ sK3 ) )
& ( $true
= ( in @ sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( ( kpair @ X0 @ X3 )
!= ( kpair @ X0 @ X3 ) )
& ( ( in @ X3 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( kpair @ X2 @ X3 )
!= ( kpair @ X2 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.prpGVEd576/DTF2THF_27461.p',cartprodmempaircEq) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU661^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 07:29:40 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEU661^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.31 % Domain : Set Theory
% 0.07/0.31 % Problem : Ordered Pairs - Properties of Pairs
% 0.07/0.31 % Version : Especial > Reduced > Especial.
% 0.07/0.31 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B ->
% 0.07/0.31 % kpair x y = kpair x y))
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.31 % Source : [Bro08]
% 0.07/0.31 % Names : ZFC163l [Bro08]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % 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 v3.7.0
% 0.07/0.31 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.07/0.31 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 3 ( 3 avg)
% 0.07/0.31 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 8 @)
% 0.07/0.31 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 9 ( 9 avg)
% 0.07/0.31 % Number of types : 2 ( 0 usr)
% 0.07/0.31 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.07/0.31 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : http://mathgate.info/detsetitem.php?id=215
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(in,type,
% 0.07/0.31 in: $i > $i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(kpair,type,
% 0.07/0.31 kpair: $i > $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(cartprodmempaircEq,conjecture,
% 0.07/0.31 ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.31 ( ( in @ Xx @ A )
% 0.07/0.31 => ! [Xy: $i] :
% 0.07/0.31 ( ( in @ Xy @ B )
% 0.07/0.31 => ( ( kpair @ Xx @ Xy )
% 0.07/0.31 = ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.84/0.84 ---- Embedded in THF ---
% 0.84/0.84 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.84 %%% Generated on Tue Feb 24 07:29:41 EST 2026
% 0.84/0.84 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.84 %%% Logic specification used:
% 0.84/0.84 %%% thf(spec, logic, $$dhol).
% 0.84/0.84
% 0.84/0.84 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.prpGVEd576/DTF2DTF27461.p
% See solution above
% 0.84/0.84 ------------------------
% 0.84/0.85 ---- Cleaned THF ---
% 0.84/0.85 thf(in,type,
% 0.84/0.85 in: $i > $i > $o ).
% 0.84/0.85
% 0.84/0.85 thf(kpair,type,
% 0.84/0.85 kpair: $i > $i > $i ).
% 0.84/0.85
% 0.84/0.85 thf(cartprodmempaircEq,conjecture,
% 0.84/0.85 ! [A: $i,B: $i,Xx: $i] :
% 0.84/0.85 ( ( in @ Xx @ A )
% 0.84/0.85 => ! [Xy: $i] :
% 0.84/0.85 ( ( in @ Xy @ B )
% 0.84/0.85 => ( ( kpair @ Xx @ Xy )
% 0.84/0.85 = ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.84/0.85 ------------------------
% 0.84/0.86 % (27661)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27461 for (3000ds/183Mi)
% 0.84/0.86 % (27662)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_27461 for (3000ds/4Mi)
% 0.84/0.86 % (27664)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27461 for (3000ds/2Mi)
% 0.84/0.86 % (27663)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_27461 for (3000ds/27Mi)
% 0.84/0.86 % (27665)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_27461 for (3000ds/2Mi)
% 0.84/0.86 % (27666)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_27461 for (3000ds/275Mi)
% 0.84/0.86 % (27667)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27461 for (3000ds/18Mi)
% 0.84/0.86 % (27661)First to succeed.
% 0.84/0.86 % (27665)Instruction limit reached!
% 0.84/0.86 % (27665)------------------------------
% 0.84/0.86 % (27665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.86 % (27665)Termination reason: Unknown
% 0.84/0.86 % (27665)Termination phase: Saturation
% 0.84/0.86
% 0.84/0.86 % (27665)Memory used [KB]: 5373
% 0.84/0.86 % (27665)Time elapsed: 0.002 s
% 0.84/0.86 % (27665)Instructions burned: 2 (million)
% 0.84/0.86 % (27665)------------------------------
% 0.84/0.86 % (27665)------------------------------
% 0.84/0.86 % (27662)Also succeeded, but the first one will report.
% 0.84/0.86 % (27666)Also succeeded, but the first one will report.
% 0.84/0.86 % (27661)Refutation found. Thanks to Tanya!
% 0.84/0.86 % SZS status Theorem for DTF2THF_27461
% 0.84/0.86 % SZS output start Proof for DTF2THF_27461
% 0.84/0.86 thf(func_def_0, type, in: $i > $i > $o).
% 0.84/0.86 thf(func_def_1, type, kpair: $i > $i > $i).
% 0.84/0.86 thf(f14,plain,(
% 0.84/0.86 $false),
% 0.84/0.86 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 0.84/0.86 thf(f12,plain,(
% 0.84/0.86 ((kpair @ sK0 @ sK3) != (kpair @ sK0 @ sK3))),
% 0.84/0.86 inference(cnf_transformation,[status(thm)],[f10])).
% 0.84/0.86 thf(f10,plain,(
% 0.84/0.86 ((in @ sK0 @ sK1) = $true) & (((kpair @ sK0 @ sK3) != (kpair @ sK0 @ sK3)) & ($true = (in @ sK3 @ sK2)))),
% 0.84/0.86 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f9,f8])).
% 0.84/0.86 thf(f8,plain,(
% 0.84/0.86 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ? [X3 : $i] : (((kpair @ X0 @ X3) != (kpair @ X0 @ X3)) & ((in @ X3 @ X2) = $true))) => (((in @ sK0 @ sK1) = $true) & ? [X3 : $i] : (((kpair @ sK0 @ X3) != (kpair @ sK0 @ X3)) & ($true = (in @ X3 @ sK2))))),
% 0.84/0.86 introduced(definition,[],[choice_axiom])).
% 0.84/0.86 thf(f9,plain,(
% 0.84/0.86 ? [X3 : $i] : (((kpair @ sK0 @ X3) != (kpair @ sK0 @ X3)) & ($true = (in @ X3 @ sK2))) => (((kpair @ sK0 @ sK3) != (kpair @ sK0 @ sK3)) & ($true = (in @ sK3 @ sK2)))),
% 0.84/0.86 introduced(definition,[],[choice_axiom])).
% 0.84/0.86 thf(f7,plain,(
% 0.84/0.86 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ? [X3 : $i] : (((kpair @ X0 @ X3) != (kpair @ X0 @ X3)) & ((in @ X3 @ X2) = $true)))),
% 0.84/0.86 inference(rectify,[status(thm)],[f6])).
% 0.84/0.86 thf(f6,plain,(
% 0.84/0.86 ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((kpair @ X2 @ X3) != (kpair @ X2 @ X3)) & ((in @ X3 @ X1) = $true)))),
% 0.84/0.86 inference(ennf_transformation,[status(thm)],[f5])).
% 0.84/0.86 thf(f5,plain,(
% 0.84/0.86 ~! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((kpair @ X2 @ X3) = (kpair @ X2 @ X3))))),
% 0.84/0.86 inference(fool_elimination,[status(thm)],[f4])).
% 0.84/0.86 thf(f4,plain,(
% 0.84/0.86 ~! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ((kpair @ X2 @ X3) = (kpair @ X2 @ X3))))),
% 0.84/0.86 inference(rectify,[status(thm)],[f2])).
% 0.84/0.86 thf(f2,negated_conjecture,(
% 0.84/0.86 ~! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ((kpair @ X2 @ X3) = (kpair @ X2 @ X3))))),
% 0.84/0.86 inference(negated_conjecture,[status(cth)],[f1])).
% 0.84/0.86 thf(f1,conjecture,(
% 0.84/0.86 ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ((kpair @ X2 @ X3) = (kpair @ X2 @ X3))))),
% 0.84/0.86 file('/export/starexec/sandbox2/tmp/tmp.prpGVEd576/DTF2THF_27461.p',cartprodmempaircEq)).
% 0.84/0.86 % SZS output end Proof for DTF2THF_27461
% 0.84/0.86 % (27661)------------------------------
% 0.84/0.86 % (27661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.86 % (27661)Termination reason: Refutation
% 0.84/0.86
% 0.84/0.86 % (27661)Memory used [KB]: 5373
% 0.84/0.86 % (27661)Time elapsed: 0.002 s
% 0.84/0.86 % (27661)Instructions burned: 1 (million)
% 0.84/0.86 % (27661)------------------------------
% 0.84/0.86 % (27661)------------------------------
% 0.84/0.86 % (27660)Success in time 0.01 s
%------------------------------------------------------------------------------