%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU620^2 : 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 : n027.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 09:35:40 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 285 ( 20 ~; 8 |; 5 &; 245 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 10 ^; 26 !; 10 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
iskpair: $i > $o ).
thf(func_def_7,type,
kpair: $i > $i > $i ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f30,f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f22,f26]) ).
thf(f26,plain,
kpairiskpair = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( kpairiskpair = $true )
& ( $true
!= ( iskpair @ ( kpair @ sK2 @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $true )
=> ( $true
!= ( iskpair @ ( kpair @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( kpairiskpair = $true )
& ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( kpairiskpair = $true )
=> ! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( kpairiskpair
=> ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( kpairiskpair
=> ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpairp) ).
thf(f22,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ( kpairiskpair != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( kpairiskpair = $true )
| ( ( iskpair @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ( kpairiskpair != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( iskpair @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ( kpairiskpair = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ( kpairiskpair != $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( kpairiskpair = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( kpairiskpair != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( kpairiskpair = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpairiskpair ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X2: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= kpairiskpair ),
file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpairiskpair) ).
thf(f30,plain,
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
!= ( iskpair
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f24]) ).
thf(f24,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpair) ).
thf(f25,plain,
( $true
!= ( iskpair @ ( kpair @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU620^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.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 12:28:52 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU620^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Kuratowski Pairs
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! x:i.! y:i.iskpair (kpair x y))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC122l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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 v4.0.0, 0.33 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.30/0.46 % Number of atoms : 11 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 43 ( 0 ~; 0 |; 2 &; 40 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 9 ( 3 ^; 4 !; 2 ?; 9 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=176
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair_type,type,
% 0.30/0.46 iskpair: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair,definition,
% 0.30/0.46 ( iskpair
% 0.30/0.46 = ( ^ [A: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.30/0.46 & ( A
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair_type,type,
% 0.30/0.46 kpairiskpair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair,definition,
% 0.30/0.46 ( kpairiskpair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpair_type,type,
% 0.30/0.46 kpair: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kpair,definition,
% 0.30/0.46 ( kpair
% 0.30/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp,conjecture,
% 0.30/0.46 ( kpairiskpair
% 0.30/0.46 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 12:28:53 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2DTF7537.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(in_type,type,
% 1.47/1.26 in: $i > $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(emptyset_type,type,
% 1.47/1.26 emptyset: $i ).
% 1.47/1.26
% 1.47/1.26 thf(setadjoin_type,type,
% 1.47/1.26 setadjoin: $i > $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(setunion_type,type,
% 1.47/1.26 setunion: $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(iskpair_type,type,
% 1.47/1.26 iskpair: $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(iskpair,definition,
% 1.47/1.26 ( iskpair
% 1.47/1.26 = ( ^ [A: $i] :
% 1.47/1.26 ? [Xx: $i] :
% 1.47/1.26 ( ( in @ Xx @ ( setunion @ A ) )
% 1.47/1.26 & ? [Xy: $i] :
% 1.47/1.26 ( ( in @ Xy @ ( setunion @ A ) )
% 1.47/1.26 & ( A
% 1.47/1.26 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(kpairiskpair_type,type,
% 1.47/1.26 kpairiskpair: $o ).
% 1.47/1.26
% 1.47/1.26 thf(kpairiskpair,definition,
% 1.47/1.26 ( kpairiskpair
% 1.47/1.26 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(kpair_type,type,
% 1.47/1.26 kpair: $i > $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(kpair,definition,
% 1.47/1.26 ( kpair
% 1.47/1.26 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(kpairp,conjecture,
% 1.47/1.26 ( kpairiskpair
% 1.47/1.26 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.28 % (7729)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_7537 for (2999ds/2Mi)
% 1.47/1.28 % (7729)Instruction limit reached!
% 1.47/1.28 % (7729)------------------------------
% 1.47/1.28 % (7729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7729)Termination reason: Unknown
% 1.47/1.28 % (7729)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (7729)Memory used [KB]: 1023
% 1.47/1.28 % (7729)Time elapsed: 0.002 s
% 1.47/1.28 % (7729)Instructions burned: 3 (million)
% 1.47/1.28 % (7729)------------------------------
% 1.47/1.28 % (7729)------------------------------
% 1.47/1.28 % (7727)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_7537 for (2999ds/27Mi)
% 1.47/1.29 % (7726)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_7537 for (2999ds/4Mi)
% 1.47/1.29 % (7728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7537 for (2999ds/2Mi)
% 1.47/1.29 % (7730)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_7537 for (2999ds/275Mi)
% 1.47/1.29 % (7731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7537 for (2999ds/18Mi)
% 1.47/1.29 % (7728)Instruction limit reached!
% 1.47/1.29 % (7728)------------------------------
% 1.47/1.29 % (7728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (7728)Termination reason: Unknown
% 1.47/1.29 % (7728)Termination phase: Unused predicate definition removal
% 1.47/1.29
% 1.47/1.29 % (7728)Memory used [KB]: 895
% 1.47/1.29 % (7728)Time elapsed: 0.003 s
% 1.47/1.29 % (7728)Instructions burned: 2 (million)
% 1.47/1.29 % (7728)------------------------------
% 1.47/1.29 % (7728)------------------------------
% 1.47/1.29 % (7730)First to succeed.
% 1.47/1.29 % (7730)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_7537
% 1.47/1.29 % SZS output start Proof for DTF2THF_7537
% 1.47/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.47/1.29 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.47/1.29 thf(func_def_3, type, setunion: $i > $i).
% 1.47/1.29 thf(func_def_4, type, iskpair: $i > $o).
% 1.47/1.29 thf(func_def_7, type, kpair: $i > $i > $i).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f30,f31])).
% 1.47/1.29 thf(f31,plain,(
% 1.47/1.29 ( ! [X2 : $i,X3 : $i] : (($true = (iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))) )),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ( ! [X2 : $i,X3 : $i] : (($true = (iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) | ($true != $true)) )),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f22,f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 (kpairiskpair = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f21])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 (kpairiskpair = $true) & ($true != (iskpair @ (kpair @ sK2 @ sK3)))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f20])).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X0 @ X1)) != $true) => ($true != (iskpair @ (kpair @ sK2 @ sK3)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 (kpairiskpair = $true) & ? [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X0 @ X1)) != $true)),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ~((kpairiskpair = $true) => ! [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X0 @ X1)) = $true))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ~(kpairiskpair => ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,negated_conjecture,(
% 1.47/1.29 ~(kpairiskpair => ! [X1 : $i,X2 : $i] : (iskpair @ (kpair @ X1 @ X2)))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.47/1.29 thf(f4,conjecture,(
% 1.47/1.29 kpairiskpair => ! [X1 : $i,X2 : $i] : (iskpair @ (kpair @ X1 @ X2))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpairp)).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ( ! [X2 : $i,X3 : $i] : (($true = (iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) | (kpairiskpair != $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ((kpairiskpair = $true) | ((iskpair @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset))) != $true)) & (! [X2 : $i,X3 : $i] : ($true = (iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) | (kpairiskpair != $true))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) => ((iskpair @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset))) != $true)),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ((kpairiskpair = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) & (! [X2 : $i,X3 : $i] : ($true = (iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) | (kpairiskpair != $true))),
% 1.47/1.29 inference(rectify,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ((kpairiskpair = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) & (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) | (kpairiskpair != $true))),
% 1.47/1.29 inference(nnf_transformation,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 (kpairiskpair = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 (! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,axiom,(
% 1.47/1.29 (! [X1 : $i,X2 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpairiskpair)).
% 1.47/1.29 thf(f30,plain,(
% 1.47/1.29 ($true != (iskpair @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.47/1.29 thf(f29,plain,(
% 1.47/1.29 ($true != (iskpair @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK2 @ sK3)))),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f25,f24])).
% 1.47/1.29 thf(f24,plain,(
% 1.47/1.29 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f3])).
% 1.47/1.29 thf(f3,axiom,(
% 1.47/1.29 (kpair = (^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.ceot303Ae6/DTF2THF_7537.p',kpair)).
% 1.47/1.29 thf(f25,plain,(
% 1.47/1.29 ($true != (iskpair @ (kpair @ sK2 @ sK3)))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f21])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_7537
% 1.47/1.29 % (7730)------------------------------
% 1.47/1.29 % (7730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (7730)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (7730)Memory used [KB]: 5500
% 1.47/1.29 % (7730)Time elapsed: 0.002 s
% 1.47/1.29 % (7730)Instructions burned: 3 (million)
% 1.47/1.29 % (7730)------------------------------
% 1.47/1.29 % (7730)------------------------------
% 1.47/1.29 % (7724)Success in time 0.012 s
%------------------------------------------------------------------------------