%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU499^2 : 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 : n025.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 09:34:56 AM UTC 2026
% Result : Theorem 1.45s 1.28s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 75 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 200 ( 25 ~; 13 |; 23 &; 105 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 4 usr; 5 con; 0-2 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 67 ( 29 ^; 25 !; 13 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_13,type,
sK0: $i > $o ).
thf(func_def_14,type,
sK1: $i > $i ).
thf(f43,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f22]) ).
thf(f22,plain,
( ( sK0 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) )
& ( sK0 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f17]) ).
thf(f17,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8XwMtOHCY0/DTF2THF_29278.p',exu) ).
thf(f16,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X1: $i] :
( ( ( ( sK1 @ X1 )
!= X1 )
& ( ( sK0 @ ( sK1 @ X1 ) )
= $true ) )
| ( $true
!= ( sK0 @ X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X2 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ( $true
= ( sK0 @ X2 ) ) )
| ( $true
!= ( sK0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ( $true
= ( sK0 @ X2 ) ) )
=> ( ( ( sK1 @ X1 )
!= X1 )
& ( ( sK0 @ ( sK1 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X2 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( X2 = X3 ) )
& ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8XwMtOHCY0/DTF2THF_29278.p',exuE1) ).
thf(f41,plain,
( ( sK0 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( sK3 != sK3 )
| ( ( sK0 @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f29,f38]) ).
thf(f38,plain,
! [X0: $i] :
( ( ( sK1 @ X0 )
= sK3 )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( sK1 @ X0 )
= sK3 )
| ( $false = $true )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f14,f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK3 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK3 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f14,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK1 @ X1 ) )
= $true )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f29,plain,
( ( sK1 @ sK3 )
!= sK3 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK3 )
!= sK3 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f22]) ).
thf(f15,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU499^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:24:27 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU499^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Foundation - Axioms - Logical Axioms
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (!phi:i>o.exu(^x:i.phi x)->(?x:i.phi x & (!y:i.phi y -> x = y)))
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC001l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.31/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 7 ( 2 ^; 3 !; 2 ?; 7 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=404
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(exu_type,type,
% 0.31/0.46 exu: ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(exu,definition,
% 0.31/0.46 ( exu
% 0.31/0.46 = ( ^ [Xphi: $i > $o] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(exuE1,conjecture,
% 0.31/0.46 ! [Xphi: $i > $o] :
% 0.31/0.46 ( ( exu
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.46 => ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.45/1.25 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 12:24:28 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8XwMtOHCY0/DTF2DTF29278.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(exu_type,type,
% 1.45/1.27 exu: ( $i > $o ) > $o ).
% 1.45/1.27
% 1.45/1.27 thf(exu,definition,
% 1.45/1.27 ( exu
% 1.45/1.27 = ( ^ [Xphi: $i > $o] :
% 1.45/1.27 ? [Xx: $i] :
% 1.45/1.27 ( ( Xphi @ Xx )
% 1.45/1.27 & ! [Xy: $i] :
% 1.45/1.27 ( ( Xphi @ Xy )
% 1.45/1.27 => ( Xx = Xy ) ) ) ) ) ).
% 1.45/1.27
% 1.45/1.27 thf(exuE1,conjecture,
% 1.45/1.27 ! [Xphi: $i > $o] :
% 1.45/1.27 ( ( exu
% 1.45/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.45/1.27 => ? [Xx: $i] :
% 1.45/1.27 ( ( Xphi @ Xx )
% 1.45/1.27 & ! [Xy: $i] :
% 1.45/1.27 ( ( Xphi @ Xy )
% 1.45/1.27 => ( Xx = Xy ) ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.28 % (29434)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29278 for (3000ds/183Mi)
% 1.45/1.28 % (29440)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29278 for (3000ds/18Mi)
% 1.45/1.28 % (29434)First to succeed.
% 1.45/1.28 % (29440)Also succeeded, but the first one will report.
% 1.45/1.28 % (29435)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29278 for (3000ds/4Mi)
% 1.45/1.28 % (29434)Refutation found. Thanks to Tanya!
% 1.45/1.28 % SZS status Theorem for DTF2THF_29278
% 1.45/1.28 % SZS output start Proof for DTF2THF_29278
% 1.45/1.28 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.45/1.28 thf(func_def_13, type, sK0: $i > $o).
% 1.45/1.28 thf(func_def_14, type, sK1: $i > $i).
% 1.45/1.28 thf(f43,plain,(
% 1.45/1.28 $false),
% 1.45/1.28 inference(subsumption_resolution,[status(thm)],[f41,f22])).
% 1.45/1.28 thf(f22,plain,(
% 1.45/1.28 ((sK0 @ sK3) = $true)),
% 1.45/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.45/1.28 thf(f21,plain,(
% 1.45/1.28 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0)))) & (sK0 @ sK3)))),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.45/1.28 thf(f20,plain,(
% 1.45/1.28 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK3))),
% 1.45/1.28 inference(sigma_clausification,[status(thm)],[f19])).
% 1.45/1.28 thf(f19,plain,(
% 1.45/1.28 ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))))),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.45/1.28 thf(f18,plain,(
% 1.45/1.28 ($true = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.45/1.28 inference(definition_unfolding,[status(thm)],[f16,f17])).
% 1.45/1.28 thf(f17,plain,(
% 1.45/1.28 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.28 thf(f6,plain,(
% 1.45/1.28 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.45/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.45/1.28 thf(f5,plain,(
% 1.45/1.28 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.45/1.28 inference(rectify,[status(thm)],[f1])).
% 1.45/1.28 thf(f1,axiom,(
% 1.45/1.28 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.45/1.28 file('/export/starexec/sandbox2/tmp/tmp.8XwMtOHCY0/DTF2THF_29278.p',exu)).
% 1.45/1.28 thf(f16,plain,(
% 1.45/1.28 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.28 thf(f13,plain,(
% 1.45/1.28 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X1 : $i] : ((((sK1 @ X1) != X1) & ((sK0 @ (sK1 @ X1)) = $true)) | ($true != (sK0 @ X1)))),
% 1.45/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12,f11])).
% 1.45/1.28 thf(f11,plain,(
% 1.45/1.28 ? [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ((X0 @ X2) = $true)) | ((X0 @ X1) != $true))) => (($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ($true = (sK0 @ X2))) | ($true != (sK0 @ X1))))),
% 1.45/1.28 introduced(definition,[],[choice_axiom])).
% 1.45/1.28 thf(f12,plain,(
% 1.45/1.28 ! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ($true = (sK0 @ X2))) => (((sK1 @ X1) != X1) & ((sK0 @ (sK1 @ X1)) = $true)))),
% 1.45/1.28 introduced(definition,[],[choice_axiom])).
% 1.45/1.28 thf(f10,plain,(
% 1.45/1.28 ? [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ((X0 @ X2) = $true)) | ((X0 @ X1) != $true)))),
% 1.45/1.28 inference(ennf_transformation,[status(thm)],[f9])).
% 1.45/1.28 thf(f9,plain,(
% 1.45/1.28 ~! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) => ? [X1 : $i] : (((X0 @ X1) = $true) & ! [X2 : $i] : (((X0 @ X2) = $true) => (X1 = X2))))),
% 1.45/1.28 inference(rectify,[status(thm)],[f8])).
% 1.45/1.28 thf(f8,plain,(
% 1.45/1.28 ~! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) => ? [X2 : $i] : (! [X3 : $i] : (((X0 @ X3) = $true) => (X2 = X3)) & ((X0 @ X2) = $true)))),
% 1.45/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.45/1.28 thf(f7,plain,(
% 1.45/1.28 ~! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : (! [X3 : $i] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2)))),
% 1.45/1.28 inference(rectify,[status(thm)],[f3])).
% 1.45/1.28 thf(f3,negated_conjecture,(
% 1.45/1.28 ~! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))),
% 1.45/1.28 inference(negated_conjecture,[status(cth)],[f2])).
% 1.45/1.28 thf(f2,conjecture,(
% 1.45/1.28 ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))),
% 1.45/1.28 file('/export/starexec/sandbox2/tmp/tmp.8XwMtOHCY0/DTF2THF_29278.p',exuE1)).
% 1.45/1.28 thf(f41,plain,(
% 1.45/1.28 ((sK0 @ sK3) != $true)),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.45/1.28 thf(f39,plain,(
% 1.45/1.28 (sK3 != sK3) | ((sK0 @ sK3) != $true)),
% 1.45/1.28 inference(superposition,[status(thm)],[f29,f38])).
% 1.45/1.28 thf(f38,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (((sK1 @ X0) = sK3) | ((sK0 @ X0) != $true)) )),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.45/1.28 thf(f33,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (((sK1 @ X0) = sK3) | ($false = $true) | ((sK0 @ X0) != $true)) )),
% 1.45/1.28 inference(superposition,[status(thm)],[f14,f27])).
% 1.45/1.28 thf(f27,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | (sK3 = X1)) )),
% 1.45/1.28 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.45/1.28 thf(f26,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((sK3 = X1) = $true)) )),
% 1.45/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.45/1.28 thf(f25,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (($true = ((sK0 @ X1) => (sK3 = X1)))) )),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.45/1.28 thf(f24,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0))) @ X1))) )),
% 1.45/1.28 inference(pi_clausification,[status(thm)],[f23])).
% 1.45/1.28 thf(f23,plain,(
% 1.45/1.28 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK3 = Y0)))) = $true)),
% 1.45/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.45/1.28 thf(f14,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (((sK0 @ (sK1 @ X1)) = $true) | ($true != (sK0 @ X1))) )),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.28 thf(f29,plain,(
% 1.45/1.28 ((sK1 @ sK3) != sK3)),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.45/1.28 thf(f28,plain,(
% 1.45/1.28 ((sK1 @ sK3) != sK3) | ($true != $true)),
% 1.45/1.28 inference(superposition,[status(thm)],[f15,f22])).
% 1.45/1.28 thf(f15,plain,(
% 1.45/1.28 ( ! [X1 : $i] : (($true != (sK0 @ X1)) | ((sK1 @ X1) != X1)) )),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.28 % SZS output end Proof for DTF2THF_29278
% 1.45/1.28 % (29434)------------------------------
% 1.45/1.28 % (29434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (29434)Termination reason: Refutation
% 1.45/1.28
% 1.45/1.28 % (29434)Memory used [KB]: 5500
% 1.45/1.28 % (29434)Time elapsed: 0.003 s
% 1.45/1.28 % (29434)Instructions burned: 2 (million)
% 1.45/1.28 % (29434)------------------------------
% 1.45/1.28 % (29434)------------------------------
% 1.45/1.28 % (29433)Success in time 0.013 s
%------------------------------------------------------------------------------