%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO547^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:54:31 AM UTC 2026
% Result : Theorem 1.64s 1.40s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 121 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 144 ( 47 ~; 11 |; 4 &; 73 @)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 19 ^; 11 !; 11 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epscomp: ( $i > $o ) > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f38,f45]) ).
thf(f45,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(backward_demodulation,[status(thm)],[f23,f31]) ).
thf(f31,plain,
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl2_1
<=> ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f23,plain,
( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( sK0
@ ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f21]) ).
thf(f21,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) )
= epscomp ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) )
= epscomp ),
file('/export/starexec/sandbox/tmp/tmp.ESy8oXXhHN/DTF2THF_17247.p',epscompd) ).
thf(f20,plain,
( ( sK0 @ ( epscomp @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK0 @ ( epscomp @ sK0 ) )
= $true )
& ( $true
!= ( sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i > $o] :
( ( ( X0 @ ( epscomp @ X0 ) )
= $true )
& ? [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
=> ( ( ( sK0 @ ( epscomp @ sK0 ) )
= $true )
& ? [X1: $i] :
( $true
!= ( sK0 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X1: $i] :
( $true
!= ( sK0 @ X1 ) )
=> ( $true
!= ( sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
? [X0: $i > $o] :
( ( ( X0 @ ( epscomp @ X0 ) )
= $true )
& ? [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ESy8oXXhHN/DTF2THF_17247.p',choicecomp) ).
thf(f38,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f19,f34]) ).
thf(f34,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl2_2
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f19,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f35,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f33,f29]) ).
thf(f27,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ X1 ) )
= $false )
| ( $true
= ( ~ ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO547^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:33:39 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SYO547^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.45 % Domain : Syntactic
% 0.20/0.45 % Problem : Choice Complement
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : The choice operator applied to complements of predicates chooses
% 0.20/0.45 % an element not in the predicate, if there is one.
% 0.20/0.45
% 0.20/0.45 % Refs : [Bac10] Backes (2010), Tableaux for Higher-Order Logic with If
% 0.20/0.45 % : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro11]
% 0.20/0.45 % Names : CHOICE24 [Bro11]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.20/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 1 def)
% 0.20/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 1 ( 0 avg)
% 0.20/0.45 % Number of connectives : 13 ( 3 ~; 0 |; 0 &; 8 @)
% 0.20/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.45 % Number of variables : 6 ( 2 ^; 2 !; 2 ?; 6 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments :
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(eps,type,
% 0.20/0.45 eps: ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(choiceax,axiom,
% 0.20/0.45 ! [P: $i > $o] :
% 0.20/0.45 ( ? [X: $i] : ( P @ X )
% 0.20/0.45 => ( P @ ( eps @ P ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(epscomp,type,
% 0.20/0.45 epscomp: ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(epscompd,definition,
% 0.20/0.45 ( epscomp
% 0.20/0.45 = ( ^ [P: $i > $o] :
% 0.20/0.45 ( eps
% 0.20/0.45 @ ^ [X: $i] :
% 0.20/0.45 ~ ( P @ X ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(choicecomp,conjecture,
% 0.20/0.45 ! [P: $i > $o] :
% 0.20/0.45 ( ? [X: $i] :
% 0.20/0.45 ~ ( P @ X )
% 0.20/0.45 => ~ ( P @ ( epscomp @ P ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.47/1.37 ---- Embedded in THF ---
% 1.47/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.37 %%% Generated on Tue Feb 24 14:33:40 EST 2026
% 1.47/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.37 %%% Logic specification used:
% 1.47/1.37 %%% thf(spec, logic, $$dhol).
% 1.47/1.37
% 1.47/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ESy8oXXhHN/DTF2DTF17247.p
% See solution above
% 1.47/1.37 ------------------------
% 1.47/1.38 ---- Cleaned THF ---
% 1.47/1.38 thf(eps,type,
% 1.47/1.38 eps: ( $i > $o ) > $i ).
% 1.47/1.38
% 1.47/1.38 thf(choiceax,axiom,
% 1.47/1.38 ! [P: $i > $o] :
% 1.47/1.38 ( ? [X: $i] : ( P @ X )
% 1.47/1.38 => ( P @ ( eps @ P ) ) ) ).
% 1.47/1.38
% 1.47/1.38 thf(epscomp,type,
% 1.47/1.38 epscomp: ( $i > $o ) > $i ).
% 1.47/1.38
% 1.47/1.38 thf(epscompd,definition,
% 1.47/1.38 ( epscomp
% 1.47/1.38 = ( ^ [P: $i > $o] :
% 1.47/1.38 ( eps
% 1.47/1.38 @ ^ [X: $i] :
% 1.47/1.38 ~ ( P @ X ) ) ) ) ).
% 1.47/1.38
% 1.47/1.38 thf(choicecomp,conjecture,
% 1.47/1.38 ! [P: $i > $o] :
% 1.47/1.38 ( ? [X: $i] :
% 1.47/1.38 ~ ( P @ X )
% 1.47/1.38 => ~ ( P @ ( epscomp @ P ) ) ) ).
% 1.47/1.38 ------------------------
% 1.47/1.40 % (17345)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17247 for (3000ds/183Mi)
% 1.47/1.40 % (17348)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17247 for (3000ds/2Mi)
% 1.47/1.40 % (17347)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_17247 for (3000ds/27Mi)
% 1.47/1.40 % (17346)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_17247 for (3000ds/4Mi)
% 1.47/1.40 % (17349)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_17247 for (3000ds/2Mi)
% 1.47/1.40 % (17350)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_17247 for (3000ds/275Mi)
% 1.64/1.40 % (17351)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17247 for (3000ds/18Mi)
% 1.64/1.40 % (17350)Refutation not found, incomplete strategy
% 1.64/1.40 % (17350)------------------------------
% 1.64/1.40 % (17350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (17350)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.40
% 1.64/1.40
% 1.64/1.40 % (17350)Memory used [KB]: 5500
% 1.64/1.40 % (17350)Time elapsed: 0.002 s
% 1.64/1.40 % (17350)Instructions burned: 1 (million)
% 1.64/1.40 % (17350)------------------------------
% 1.64/1.40 % (17350)------------------------------
% 1.64/1.40 % (17348)Instruction limit reached!
% 1.64/1.40 % (17348)------------------------------
% 1.64/1.40 % (17348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (17348)Termination reason: Unknown
% 1.64/1.40 % (17348)Termination phase: Saturation
% 1.64/1.40 % (17349)Instruction limit reached!
% 1.64/1.40 % (17349)------------------------------
% 1.64/1.40 % (17349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40
% 1.64/1.40 % (17348)Memory used [KB]: 5500
% 1.64/1.40 % (17348)Time elapsed: 0.003 s
% 1.64/1.40 % (17348)Instructions burned: 2 (million)
% 1.64/1.40 % (17348)------------------------------
% 1.64/1.40 % (17348)------------------------------
% 1.64/1.40 % (17349)Termination reason: Unknown
% 1.64/1.40 % (17349)Termination phase: Saturation
% 1.64/1.40
% 1.64/1.40 % (17349)Memory used [KB]: 5500
% 1.64/1.40 % (17349)Time elapsed: 0.003 s
% 1.64/1.40 % (17349)Instructions burned: 2 (million)
% 1.64/1.40 % (17349)------------------------------
% 1.64/1.40 % (17349)------------------------------
% 1.64/1.40 % (17347)First to succeed.
% 1.64/1.40 % (17346)Instruction limit reached!
% 1.64/1.40 % (17346)------------------------------
% 1.64/1.40 % (17346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (17346)Termination reason: Unknown
% 1.64/1.40 % (17346)Termination phase: Saturation
% 1.64/1.40
% 1.64/1.40 % (17346)Memory used [KB]: 5500
% 1.64/1.40 % (17346)Time elapsed: 0.004 s
% 1.64/1.40 % (17346)Instructions burned: 4 (million)
% 1.64/1.40 % (17346)------------------------------
% 1.64/1.40 % (17346)------------------------------
% 1.64/1.40 % (17347)Refutation found. Thanks to Tanya!
% 1.64/1.40 % SZS status Theorem for DTF2THF_17247
% 1.64/1.40 % SZS output start Proof for DTF2THF_17247
% 1.64/1.40 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.64/1.40 thf(func_def_2, type, epscomp: ($i > $o) > $i).
% 1.64/1.40 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.40 thf(func_def_10, type, sK0: $i > $o).
% 1.64/1.40 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.64/1.40 thf(f46,plain,(
% 1.64/1.40 $false),
% 1.64/1.40 inference(avatar_sat_refutation,[status(thm)],[f35,f38,f45])).
% 1.64/1.40 thf(f45,plain,(
% 1.64/1.40 ~spl2_1),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.64/1.40 thf(f44,plain,(
% 1.64/1.40 $false | ~spl2_1),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.64/1.40 thf(f39,plain,(
% 1.64/1.40 ($true = $false) | ~spl2_1),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f23,f31])).
% 1.64/1.40 thf(f31,plain,(
% 1.64/1.40 ($false = (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0)))))) | ~spl2_1),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.64/1.40 thf(f29,definition,(
% 1.64/1.40 spl2_1 <=> ($false = (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0))))))),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.64/1.40 thf(f23,plain,(
% 1.64/1.40 ($true = (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0))))))),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.64/1.40 thf(f22,plain,(
% 1.64/1.40 ($true = (sK0 @ ((^[Y0 : $i > $o]: (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1))))) @ sK0)))),
% 1.64/1.40 inference(definition_unfolding,[status(thm)],[f20,f21])).
% 1.64/1.40 thf(f21,plain,(
% 1.64/1.40 (epscomp = (^[Y0 : $i > $o]: (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.40 thf(f11,plain,(
% 1.64/1.40 (epscomp = (^[Y0 : $i > $o]: (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.40 thf(f10,plain,(
% 1.64/1.40 ((^[X0 : $i > $o] : (eps @ (^[X1 : $i] : (~(X0 @ X1))))) = epscomp)),
% 1.64/1.40 inference(rectify,[status(thm)],[f2])).
% 1.64/1.40 thf(f2,axiom,(
% 1.64/1.40 ((^[X0 : $i > $o] : (eps @ (^[X1 : $i] : (~(X0 @ X1))))) = epscomp)),
% 1.64/1.40 file('/export/starexec/sandbox/tmp/tmp.ESy8oXXhHN/DTF2THF_17247.p',epscompd)).
% 1.64/1.40 thf(f20,plain,(
% 1.64/1.40 ((sK0 @ (epscomp @ sK0)) = $true)),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.64/1.40 thf(f17,plain,(
% 1.64/1.40 ((sK0 @ (epscomp @ sK0)) = $true) & ($true != (sK0 @ sK1))),
% 1.64/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f16,f15])).
% 1.64/1.40 thf(f15,plain,(
% 1.64/1.40 ? [X0 : $i > $o] : (((X0 @ (epscomp @ X0)) = $true) & ? [X1 : $i] : ((X0 @ X1) != $true)) => (((sK0 @ (epscomp @ sK0)) = $true) & ? [X1 : $i] : ($true != (sK0 @ X1)))),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 thf(f16,plain,(
% 1.64/1.40 ? [X1 : $i] : ($true != (sK0 @ X1)) => ($true != (sK0 @ sK1))),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 thf(f14,plain,(
% 1.64/1.40 ? [X0 : $i > $o] : (((X0 @ (epscomp @ X0)) = $true) & ? [X1 : $i] : ((X0 @ X1) != $true))),
% 1.64/1.40 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.40 thf(f12,plain,(
% 1.64/1.40 ~! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) != $true) => ((X0 @ (epscomp @ X0)) != $true))),
% 1.64/1.40 inference(flattening,[status(thm)],[f9])).
% 1.64/1.40 thf(f9,plain,(
% 1.64/1.40 ~! [X0 : $i > $o] : (? [X1 : $i] : ~((X0 @ X1) = $true) => ~((X0 @ (epscomp @ X0)) = $true))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.40 thf(f8,plain,(
% 1.64/1.40 ~! [X0 : $i > $o] : (? [X1 : $i] : ~(X0 @ X1) => ~(X0 @ (epscomp @ X0)))),
% 1.64/1.40 inference(rectify,[status(thm)],[f4])).
% 1.64/1.40 thf(f4,negated_conjecture,(
% 1.64/1.40 ~! [X0 : $i > $o] : (? [X1 : $i] : ~(X0 @ X1) => ~(X0 @ (epscomp @ X0)))),
% 1.64/1.40 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.40 thf(f3,conjecture,(
% 1.64/1.40 ! [X0 : $i > $o] : (? [X1 : $i] : ~(X0 @ X1) => ~(X0 @ (epscomp @ X0)))),
% 1.64/1.40 file('/export/starexec/sandbox/tmp/tmp.ESy8oXXhHN/DTF2THF_17247.p',choicecomp)).
% 1.64/1.40 thf(f38,plain,(
% 1.64/1.40 ~spl2_2),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 1.64/1.40 thf(f37,plain,(
% 1.64/1.40 $false | ~spl2_2),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.64/1.40 thf(f36,plain,(
% 1.64/1.40 ($true != $true) | ~spl2_2),
% 1.64/1.40 inference(superposition,[status(thm)],[f19,f34])).
% 1.64/1.40 thf(f34,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = (sK0 @ X1))) ) | ~spl2_2),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.64/1.40 thf(f33,definition,(
% 1.64/1.40 spl2_2 <=> ! [X1 : $i] : ($true = (sK0 @ X1))),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.64/1.40 thf(f19,plain,(
% 1.64/1.40 ($true != (sK0 @ sK1))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.64/1.40 thf(f35,plain,(
% 1.64/1.40 spl2_1 | spl2_2),
% 1.64/1.40 inference(avatar_split_clause,[status(thm)],[f27,f33,f29])).
% 1.64/1.40 thf(f27,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = (sK0 @ X1)) | ($false = (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0))))))) )),
% 1.64/1.40 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.64/1.40 thf(f26,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = (~ (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0))))))) | ($true = (sK0 @ X1))) )),
% 1.64/1.40 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.64/1.40 thf(f25,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((~ (sK0 @ X1)) = $false) | ($true = (~ (sK0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0)))))))) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.64/1.40 thf(f24,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (sK0 @ Y0))) @ (eps @ (^[Y0 : $i]: (~ (sK0 @ Y0)))))) | (((^[Y0 : $i]: (~ (sK0 @ Y0))) @ X1) = $false)) )),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 % SZS output end Proof for DTF2THF_17247
% 1.64/1.40 % (17347)------------------------------
% 1.64/1.40 % (17347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (17347)Termination reason: Refutation
% 1.64/1.40
% 1.64/1.40 % (17347)Memory used [KB]: 5500
% 1.64/1.40 % (17347)Time elapsed: 0.004 s
% 1.64/1.40 % (17347)Instructions burned: 2 (million)
% 1.64/1.40 % (17347)------------------------------
% 1.64/1.40 % (17347)------------------------------
% 1.64/1.40 % (17344)Success in time 0.018 s
%------------------------------------------------------------------------------