%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO557^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:54:32 AM UTC 2026
% Result : Theorem 1.94s 1.65s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 105 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 120 ( 18 ~; 13 |; 0 &; 73 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 27 ( 14 ^; 10 !; 3 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_8,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK2: $i > $o ).
thf(f51,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f40,f48]) ).
thf(f48,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f20,f24]) ).
thf(f24,plain,
( ( $false
= ( sK2 @ ( eps @ sK2 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_1
<=> ( $false
= ( sK2 @ ( eps @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f20,plain,
( $true
= ( sK2 @ ( eps @ sK2 ) ) ),
inference(subsumption_resolution,[status(thm)],[f19,f12]) ).
thf(f12,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MhW7CWaQbn/DTF2THF_20060.p',choiceax) ).
thf(f19,plain,
( ( $true
= ( sK2 @ ( eps @ sK2 ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( ?? @ $i @ sK2 ) )
| ( $true
= ( sK2 @ ( eps @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK2 @ ( eps @ sK2 ) )
!= ( ?? @ $i @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK2 )
!= ( ?? @ $i @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
( ??
@ ( $i
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) )
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) )
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) )
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o] : ( ?? @ $i @ X0 ) )
!= ( ^ [X1: $i > $o] : ( X1 @ ( eps @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X0: $i > $o] : ( ?? @ $i @ X0 ) )
!= ( ^ [X0: $i > $o] : ( X0 @ ( eps @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X0: $i > $o] : ( ?? @ $i @ X0 ) )
= ( ^ [X0: $i > $o] : ( X0 @ ( eps @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MhW7CWaQbn/DTF2THF_20060.p',conj) ).
thf(f40,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f27,f20]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( sK2 @ X1 )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_2
<=> ! [X1: $i] :
( ( sK2 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f28,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f26,f22]) ).
thf(f18,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( $false
= ( sK2 @ ( eps @ sK2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK2 @ ( eps @ sK2 ) ) )
| ( $false
= ( ?? @ $i @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO557^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 14:33:33 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO557^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : Exists on $i can be expressed in terms of choice on $
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro11]
% 0.30/0.47 % Names : CHOICE29 [Bro11]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 0 def)
% 0.30/0.47 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.47 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 7 @)
% 0.30/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 5 ( 3 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.30/0.47 % ( 0 !!; 1 ??; 0 @@+; 0 @@-)
% 0.30/0.47 % Number of variables : 4 ( 2 ^; 1 !; 1 ?; 4 :)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : Since P (eps P) is equivalent to exists x . P x, (^P.P(eps P)) =
% 0.30/0.47 % (^P.?? P).
% 0.30/0.47 % : Note that this problem uses ?? for exists instead of the ?
% 0.30/0.47 % quantifier.
% 0.30/0.47 % Bugfixes : Added type argument to ??.
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(eps,type,
% 0.30/0.47 eps: ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(choiceax,axiom,
% 0.30/0.47 ! [P: $i > $o] :
% 0.30/0.47 ( ? [X: $i] : ( P @ X )
% 0.30/0.47 => ( P @ ( eps @ P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(conj,conjecture,
% 0.30/0.47 ( ( ^ [P: $i > $o] : ( P @ ( eps @ P ) ) )
% 0.30/0.47 = ( ^ [P: $i > $o] : ( ?? @ $i @ P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.94/1.61 ---- Embedded in THF ---
% 1.94/1.61 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.94/1.61 %%% Generated on Tue Feb 24 14:33:34 EST 2026
% 1.94/1.61 %%% using '$$dhol' embedding, version 1.3.0.
% 1.94/1.61 %%% Logic specification used:
% 1.94/1.61 %%% thf(spec, logic, $$dhol).
% 1.94/1.61
% 1.94/1.61 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MhW7CWaQbn/DTF2DTF20060.p
% See solution above
% 1.94/1.61 ------------------------
% 1.94/1.62 ---- Cleaned THF ---
% 1.94/1.62 thf(eps,type,
% 1.94/1.62 eps: ( $i > $o ) > $i ).
% 1.94/1.62
% 1.94/1.62 thf(choiceax,axiom,
% 1.94/1.62 ! [P: $i > $o] :
% 1.94/1.62 ( ? [X: $i] : ( P @ X )
% 1.94/1.62 => ( P @ ( eps @ P ) ) ) ).
% 1.94/1.62
% 1.94/1.62 thf(conj,conjecture,
% 1.94/1.62 ( ( ^ [P: $i > $o] : ( P @ ( eps @ P ) ) )
% 1.94/1.62 = ( ^ [P: $i > $o] : ( ?? @ $i @ P ) ) ) ).
% 1.94/1.62 ------------------------
% 1.94/1.64 % (20162)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_20060 for (3000ds/2Mi)
% 1.94/1.64 % (20158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20060 for (3000ds/183Mi)
% 1.94/1.64 % (20161)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20060 for (3000ds/2Mi)
% 1.94/1.64 % (20163)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_20060 for (3000ds/275Mi)
% 1.94/1.64 % (20159)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_20060 for (3000ds/4Mi)
% 1.94/1.64 % (20164)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20060 for (3000ds/18Mi)
% 1.94/1.64 % (20160)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_20060 for (3000ds/27Mi)
% 1.94/1.64 % (20162)Refutation not found, incomplete strategy
% 1.94/1.64 % (20162)------------------------------
% 1.94/1.64 % (20162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.64 % (20162)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.64
% 1.94/1.64
% 1.94/1.64 % (20162)Memory used [KB]: 5500
% 1.94/1.64 % (20162)Time elapsed: 0.003 s
% 1.94/1.64 % (20162)Instructions burned: 1 (million)
% 1.94/1.64 % (20162)------------------------------
% 1.94/1.64 % (20162)------------------------------
% 1.94/1.64 % (20161)Instruction limit reached!
% 1.94/1.64 % (20161)------------------------------
% 1.94/1.64 % (20161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.64 % (20161)Termination reason: Unknown
% 1.94/1.64 % (20161)Termination phase: Saturation
% 1.94/1.64
% 1.94/1.64 % (20161)Memory used [KB]: 5500
% 1.94/1.64 % (20161)Time elapsed: 0.004 s
% 1.94/1.64 % (20161)Instructions burned: 2 (million)
% 1.94/1.64 % (20161)------------------------------
% 1.94/1.64 % (20161)------------------------------
% 1.94/1.64 % (20163)First to succeed.
% 1.94/1.65 % (20160)Also succeeded, but the first one will report.
% 1.94/1.65 % (20159)Instruction limit reached!
% 1.94/1.65 % (20159)------------------------------
% 1.94/1.65 % (20159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.65 % (20159)Termination reason: Unknown
% 1.94/1.65 % (20159)Termination phase: Saturation
% 1.94/1.65
% 1.94/1.65 % (20159)Memory used [KB]: 5500
% 1.94/1.65 % (20159)Time elapsed: 0.005 s
% 1.94/1.65 % (20159)Instructions burned: 5 (million)
% 1.94/1.65 % (20159)------------------------------
% 1.94/1.65 % (20159)------------------------------
% 1.94/1.65 % (20163)Refutation found. Thanks to Tanya!
% 1.94/1.65 % SZS status Theorem for DTF2THF_20060
% 1.94/1.65 % SZS output start Proof for DTF2THF_20060
% 1.94/1.65 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.94/1.65 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 1.94/1.65 thf(func_def_10, type, sK2: $i > $o).
% 1.94/1.65 thf(f51,plain,(
% 1.94/1.65 $false),
% 1.94/1.65 inference(avatar_sat_refutation,[status(thm)],[f28,f40,f48])).
% 1.94/1.65 thf(f48,plain,(
% 1.94/1.65 ~spl0_1),
% 1.94/1.65 inference(avatar_contradiction_clause,[status(thm)],[f47])).
% 1.94/1.65 thf(f47,plain,(
% 1.94/1.65 $false | ~spl0_1),
% 1.94/1.65 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.94/1.65 thf(f43,plain,(
% 1.94/1.65 ($true = $false) | ~spl0_1),
% 1.94/1.65 inference(superposition,[status(thm)],[f20,f24])).
% 1.94/1.65 thf(f24,plain,(
% 1.94/1.65 ($false = (sK2 @ (eps @ sK2))) | ~spl0_1),
% 1.94/1.65 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.94/1.65 thf(f22,definition,(
% 1.94/1.65 spl0_1 <=> ($false = (sK2 @ (eps @ sK2)))),
% 1.94/1.65 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.94/1.65 thf(f20,plain,(
% 1.94/1.65 ($true = (sK2 @ (eps @ sK2)))),
% 1.94/1.65 inference(subsumption_resolution,[status(thm)],[f19,f12])).
% 1.94/1.65 thf(f12,plain,(
% 1.94/1.65 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (eps @ X0)) = $true) | ((X0 @ X1) != $true)) )),
% 1.94/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.94/1.65 thf(f10,plain,(
% 1.94/1.65 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true))),
% 1.94/1.65 inference(ennf_transformation,[status(thm)],[f6])).
% 1.94/1.65 thf(f6,plain,(
% 1.94/1.65 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps @ X0)) = $true))),
% 1.94/1.65 inference(fool_elimination,[status(thm)],[f5])).
% 1.94/1.65 thf(f5,plain,(
% 1.94/1.65 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.94/1.65 inference(rectify,[status(thm)],[f1])).
% 1.94/1.65 thf(f1,axiom,(
% 1.94/1.65 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.94/1.65 file('/export/starexec/sandbox/tmp/tmp.MhW7CWaQbn/DTF2THF_20060.p',choiceax)).
% 1.94/1.65 thf(f19,plain,(
% 1.94/1.65 ($true = (sK2 @ (eps @ sK2))) | ($true = (sK2 @ sK3))),
% 1.94/1.65 inference(sigma_clausification,[status(thm)],[f16])).
% 1.94/1.65 thf(f16,plain,(
% 1.94/1.65 ($true = (?? @ $i @ sK2)) | ($true = (sK2 @ (eps @ sK2)))),
% 1.94/1.65 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.94/1.65 thf(f15,plain,(
% 1.94/1.65 ((sK2 @ (eps @ sK2)) != (?? @ $i @ sK2))),
% 1.94/1.65 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.94/1.65 thf(f14,plain,(
% 1.94/1.65 (((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK2) != (?? @ $i @ sK2))),
% 1.94/1.65 inference(negative_extensionality,[status(thm)],[f13])).
% 1.94/1.65 thf(f13,plain,(
% 1.94/1.65 (?? @ $i != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 1.94/1.65 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.94/1.65 thf(f11,plain,(
% 1.94/1.65 ((^[Y0 : $i > $o]: (?? @ $i @ Y0)) != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 1.94/1.65 inference(cnf_transformation,[status(thm)],[f9])).
% 1.94/1.65 thf(f9,plain,(
% 1.94/1.65 ((^[Y0 : $i > $o]: (?? @ $i @ Y0)) != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 1.94/1.65 inference(flattening,[status(thm)],[f8])).
% 1.94/1.65 thf(f8,plain,(
% 1.94/1.65 ~((^[Y0 : $i > $o]: (?? @ $i @ Y0)) = (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 1.94/1.65 inference(fool_elimination,[status(thm)],[f7])).
% 1.94/1.65 thf(f7,plain,(
% 1.94/1.65 ~((^[X0 : $i > $o] : (?? @ $i @ X0)) = (^[X1 : $i > $o] : (X1 @ (eps @ X1))))),
% 1.94/1.65 inference(rectify,[status(thm)],[f3])).
% 1.94/1.65 thf(f3,negated_conjecture,(
% 1.94/1.65 ~((^[X0 : $i > $o] : (?? @ $i @ X0)) = (^[X0 : $i > $o] : (X0 @ (eps @ X0))))),
% 1.94/1.65 inference(negated_conjecture,[status(cth)],[f2])).
% 1.94/1.65 thf(f2,conjecture,(
% 1.94/1.65 ((^[X0 : $i > $o] : (?? @ $i @ X0)) = (^[X0 : $i > $o] : (X0 @ (eps @ X0))))),
% 1.94/1.65 file('/export/starexec/sandbox/tmp/tmp.MhW7CWaQbn/DTF2THF_20060.p',conj)).
% 1.94/1.65 thf(f40,plain,(
% 1.94/1.65 ~spl0_2),
% 1.94/1.65 inference(avatar_contradiction_clause,[status(thm)],[f39])).
% 1.94/1.65 thf(f39,plain,(
% 1.94/1.65 $false | ~spl0_2),
% 1.94/1.65 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.94/1.65 thf(f36,plain,(
% 1.94/1.65 ($true = $false) | ~spl0_2),
% 1.94/1.65 inference(superposition,[status(thm)],[f27,f20])).
% 1.94/1.65 thf(f27,plain,(
% 1.94/1.65 ( ! [X1 : $i] : (((sK2 @ X1) = $false)) ) | ~spl0_2),
% 1.94/1.65 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.94/1.65 thf(f26,definition,(
% 1.94/1.65 spl0_2 <=> ! [X1 : $i] : ((sK2 @ X1) = $false)),
% 1.94/1.65 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.94/1.65 thf(f28,plain,(
% 1.94/1.65 spl0_1 | spl0_2),
% 1.94/1.65 inference(avatar_split_clause,[status(thm)],[f18,f26,f22])).
% 1.94/1.65 thf(f18,plain,(
% 1.94/1.65 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | ($false = (sK2 @ (eps @ sK2)))) )),
% 1.94/1.65 inference(pi_clausification,[status(thm)],[f17])).
% 1.94/1.65 thf(f17,plain,(
% 1.94/1.65 ($false = (sK2 @ (eps @ sK2))) | ($false = (?? @ $i @ sK2))),
% 1.94/1.65 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.94/1.65 % SZS output end Proof for DTF2THF_20060
% 1.94/1.65 % (20163)------------------------------
% 1.94/1.65 % (20163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.65 % (20163)Termination reason: Refutation
% 1.94/1.65
% 1.94/1.65 % (20163)Memory used [KB]: 5500
% 1.94/1.65 % (20163)Time elapsed: 0.004 s
% 1.94/1.65 % (20163)Instructions burned: 2 (million)
% 1.94/1.65 % (20163)------------------------------
% 1.94/1.65 % (20163)------------------------------
% 1.94/1.65 % (20157)Success in time 0.007 s
%------------------------------------------------------------------------------