%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU525^2 : 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 : n007.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 09:35:05 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 92 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 221 ( 26 ~; 24 |; 22 &; 109 @)
% ( 5 <=>; 23 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 6 con; 0-2 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 74 ( 30 ^; 29 !; 15 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_15,type,
sK1: $i > $i ).
thf(f59,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( sK3 != sK3 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f54,f34]) ).
thf(f34,plain,
( ( sK0 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK0 @ sK3 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f18]) ).
thf(f18,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1qSkGFMI77/DTF2THF_22173.p',exu) ).
thf(f22,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X1: $i] :
( ( ( $true
!= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
!= X1 ) )
& ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
= X1 ) ) )
& ( exuE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
? [X2: $i] :
( ( ( ( X0 @ X2 )
!= $true )
| ( X1 != X2 ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 = X2 ) ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X1: $i] :
? [X2: $i] :
( ( ( ( sK0 @ X2 )
!= $true )
| ( X1 != X2 ) )
& ( ( ( sK0 @ X2 )
= $true )
| ( X1 = X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( ( ( sK0 @ X2 )
!= $true )
| ( X1 != X2 ) )
& ( ( ( sK0 @ X2 )
= $true )
| ( X1 = X2 ) ) )
=> ( ( ( $true
!= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
!= X1 ) )
& ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
= X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
? [X2: $i] :
( ( ( ( X0 @ X2 )
!= $true )
| ( X1 != X2 ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 = X2 ) ) ) )
& ( exuE1 = $true ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
? [X2: $i] :
( ( X1 = X2 )
<~> ( ( X0 @ X2 )
= $true ) ) )
& ( exuE1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( exuE1 = $true )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( exuE1 = $true )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
<=> ( X2 = X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X0 @ X3 )
<=> ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1qSkGFMI77/DTF2THF_22173.p',exuE2) ).
thf(f54,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
!= $true )
| ( sK3 != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( X0 != X0 )
| ( sK3 != X0 )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f21,f46]) ).
thf(f46,plain,
! [X0: $i] :
( ( ( sK1 @ X0 )
= X0 )
| ( sK3 != X0 ) ),
inference(equality_factoring,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i] :
( ( ( sK1 @ X0 )
= sK3 )
| ( ( sK1 @ X0 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( sK1 @ X0 )
= sK3 )
| ( ( sK1 @ X0 )
= X0 ) ),
inference(superposition,[status(thm)],[f20,f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK3 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK3 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f20,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
= X1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f21,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU525^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n007.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 12:25:08 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEU525^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Set Theory
% 0.26/0.47 % Problem : Preliminary Notions - Equality Laws
% 0.26/0.47 % Version : Especial > Reduced > Especial.
% 0.26/0.47 % English : (! phi:i>o.exu (^ x:i.phi x) -> (? x:i.! y:i.phi y <-> y = x))
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.47 % Source : [Bro08]
% 0.26/0.47 % Names : ZFC027l [Bro08]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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
% 0.26/0.47 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.26/0.47 % Number of atoms : 10 ( 5 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.26/0.47 % Number of connectives : 17 ( 0 ~; 0 |; 2 &; 9 @)
% 0.26/0.47 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.26/0.47 % Number of types : 2 ( 0 usr)
% 0.26/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 11 ( 3 ^; 5 !; 3 ?; 11 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : http://mathgate.info/detsetitem.php?id=405
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(exu_type,type,
% 0.26/0.47 exu: ( $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(exu,definition,
% 0.26/0.47 ( exu
% 0.26/0.47 = ( ^ [Xphi: $i > $o] :
% 0.26/0.47 ? [Xx: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 & ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE1_type,type,
% 0.26/0.47 exuE1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuE1,definition,
% 0.26/0.47 ( exuE1
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 & ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE2,conjecture,
% 0.26/0.47 ( exuE1
% 0.26/0.47 => ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 <=> ( Xy = Xx ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:25:09 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1qSkGFMI77/DTF2DTF22173.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(exu_type,type,
% 1.49/1.26 exu: ( $i > $o ) > $o ).
% 1.49/1.26
% 1.49/1.26 thf(exu,definition,
% 1.49/1.26 ( exu
% 1.49/1.26 = ( ^ [Xphi: $i > $o] :
% 1.49/1.26 ? [Xx: $i] :
% 1.49/1.26 ( ( Xphi @ Xx )
% 1.49/1.26 & ! [Xy: $i] :
% 1.49/1.26 ( ( Xphi @ Xy )
% 1.49/1.26 => ( Xx = Xy ) ) ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf(exuE1_type,type,
% 1.49/1.26 exuE1: $o ).
% 1.49/1.26
% 1.49/1.26 thf(exuE1,definition,
% 1.49/1.26 ( exuE1
% 1.49/1.26 = ( ! [Xphi: $i > $o] :
% 1.49/1.26 ( ( exu
% 1.49/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.49/1.26 => ? [Xx: $i] :
% 1.49/1.26 ( ( Xphi @ Xx )
% 1.49/1.26 & ! [Xy: $i] :
% 1.49/1.26 ( ( Xphi @ Xy )
% 1.49/1.26 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf(exuE2,conjecture,
% 1.49/1.26 ( exuE1
% 1.49/1.26 => ! [Xphi: $i > $o] :
% 1.49/1.26 ( ( exu
% 1.49/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.49/1.26 => ? [Xx: $i] :
% 1.49/1.26 ! [Xy: $i] :
% 1.49/1.26 ( ( Xphi @ Xy )
% 1.49/1.26 <=> ( Xy = Xx ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (22294)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22173 for (3000ds/18Mi)
% 1.49/1.27 % (22288)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22173 for (3000ds/183Mi)
% 1.49/1.27 % (22289)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_22173 for (3000ds/4Mi)
% 1.49/1.27 % (22289)Instruction limit reached!
% 1.49/1.27 % (22289)------------------------------
% 1.49/1.27 % (22289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (22289)Termination reason: Unknown
% 1.49/1.27 % (22289)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (22289)Memory used [KB]: 5500
% 1.49/1.27 % (22289)Time elapsed: 0.003 s
% 1.49/1.27 % (22289)Instructions burned: 5 (million)
% 1.49/1.27 % (22289)------------------------------
% 1.49/1.27 % (22289)------------------------------
% 1.49/1.27 % (22288)First to succeed.
% 1.49/1.28 % (22294)Also succeeded, but the first one will report.
% 1.49/1.28 % (22288)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_22173
% 1.49/1.28 % SZS output start Proof for DTF2THF_22173
% 1.49/1.28 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.49/1.28 thf(func_def_14, type, sK0: $i > $o).
% 1.49/1.28 thf(func_def_15, type, sK1: $i > $i).
% 1.49/1.28 thf(f59,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.49/1.28 thf(f56,plain,(
% 1.49/1.28 (sK3 != sK3) | ($true != $true)),
% 1.49/1.28 inference(superposition,[status(thm)],[f54,f34])).
% 1.49/1.28 thf(f34,plain,(
% 1.49/1.28 ((sK0 @ sK3) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.49/1.28 thf(f32,plain,(
% 1.49/1.28 (((sK0 @ sK3) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0))))) = $true)),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.49/1.28 thf(f31,plain,(
% 1.49/1.28 (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK3) = $true)),
% 1.49/1.28 inference(sigma_clausification,[status(thm)],[f30])).
% 1.49/1.28 thf(f30,plain,(
% 1.49/1.28 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $true)),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.49/1.28 thf(f24,plain,(
% 1.49/1.28 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.49/1.28 inference(definition_unfolding,[status(thm)],[f22,f18])).
% 1.49/1.28 thf(f18,plain,(
% 1.49/1.28 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f1])).
% 1.49/1.28 thf(f1,axiom,(
% 1.49/1.28 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.1qSkGFMI77/DTF2THF_22173.p',exu)).
% 1.49/1.28 thf(f22,plain,(
% 1.49/1.28 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f17])).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 (($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X1 : $i] : ((($true != (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) != X1)) & (($true = (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) = X1)))) & (exuE1 = $true)),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f16,f15])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2) != $true) | (X1 != X2)) & (((X0 @ X2) = $true) | (X1 = X2)))) => (($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X1 : $i] : ? [X2 : $i] : ((((sK0 @ X2) != $true) | (X1 != X2)) & (((sK0 @ X2) = $true) | (X1 = X2))))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ! [X1 : $i] : (? [X2 : $i] : ((((sK0 @ X2) != $true) | (X1 != X2)) & (((sK0 @ X2) = $true) | (X1 = X2))) => ((($true != (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) != X1)) & (($true = (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) = X1))))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2) != $true) | (X1 != X2)) & (((X0 @ X2) = $true) | (X1 = X2)))) & (exuE1 = $true)),
% 1.49/1.28 inference(nnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ? [X2 : $i] : ((X1 = X2) <~> ((X0 @ X2) = $true))) & (exuE1 = $true)),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ~((exuE1 = $true) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f11])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ~((exuE1 = $true) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : ! [X3 : $i] : (((X0 @ X3) = $true) <=> (X2 = X3))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ~(exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : ! [X3 : $i] : ((X0 @ X3) <=> (X2 = X3))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,negated_conjecture,(
% 1.49/1.28 ~(exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2))))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f3])).
% 1.49/1.28 thf(f3,conjecture,(
% 1.49/1.28 exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.1qSkGFMI77/DTF2THF_22173.p',exuE2)).
% 1.49/1.28 thf(f54,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((sK0 @ X0) != $true) | (sK3 != X0)) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.49/1.28 thf(f50,plain,(
% 1.49/1.28 ( ! [X0 : $i] : ((X0 != X0) | (sK3 != X0) | ((sK0 @ X0) != $true)) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f21,f46])).
% 1.49/1.28 thf(f46,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((sK1 @ X0) = X0) | (sK3 != X0)) )),
% 1.49/1.28 inference(equality_factoring,[status(thm)],[f44])).
% 1.49/1.28 thf(f44,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((sK1 @ X0) = sK3) | ((sK1 @ X0) = X0)) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.49/1.28 thf(f41,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (($false = $true) | ((sK1 @ X0) = sK3) | ((sK1 @ X0) = X0)) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f20,f38])).
% 1.49/1.28 thf(f38,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | (sK3 = X1)) )),
% 1.49/1.28 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.49/1.28 thf(f37,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((sK3 = X1) = $true)) )),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.49/1.28 thf(f36,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (($true = ((sK0 @ X1) => (sK3 = X1)))) )),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.49/1.28 thf(f35,plain,(
% 1.49/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0))) @ X1) = $true)) )),
% 1.49/1.28 inference(pi_clausification,[status(thm)],[f33])).
% 1.49/1.28 thf(f33,plain,(
% 1.49/1.28 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0)))) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.49/1.28 thf(f20,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (($true = (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) = X1)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f17])).
% 1.49/1.28 thf(f21,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (($true != (sK0 @ (sK1 @ X1))) | ((sK1 @ X1) != X1)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f17])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_22173
% 1.49/1.28 % (22288)------------------------------
% 1.49/1.28 % (22288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (22288)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (22288)Memory used [KB]: 5500
% 1.49/1.28 % (22288)Time elapsed: 0.004 s
% 1.49/1.28 % (22288)Instructions burned: 4 (million)
% 1.49/1.28 % (22288)------------------------------
% 1.49/1.28 % (22288)------------------------------
% 1.49/1.28 % (22287)Success in time 0.013 s
%------------------------------------------------------------------------------