%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU504^2 : 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 : n004.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 09:34:58 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 123 ( 10 ~; 0 |; 14 &; 70 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 6 con; 0-2 aty)
% ( 6 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 48 ( 27 ^; 12 !; 9 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK0: $i > $o ).
thf(func_def_18,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK3: ( $i > $o ) > $i > $i ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
$true != $true,
inference(superposition,[status(thm)],[f19,f49]) ).
thf(f49,plain,
( ( sK0 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) )
& ( sK0 @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f18,f16]) ).
thf(f16,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
file('/export/starexec/sandbox2/tmp/tmp.sjXWhu7XOp/DTF2THF_21383.p',exu) ).
thf(f18,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i] :
( $true
!= ( sK0 @ X1 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( exuE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
=> ( ! [X1: $i] :
( $true
!= ( sK0 @ X1 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $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] :
( ( X0 @ X1 )
= $true ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( exuE1 = $true )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] : ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sjXWhu7XOp/DTF2THF_21383.p',exuE3e) ).
thf(f19,plain,
! [X1: $i] :
( $true
!= ( sK0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU504^2 : 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
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:24:41 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU504^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.28/0.46 % Version : Especial > Reduced > Especial.
% 0.28/0.46 % English : (! phi:i>o.exu (^ x:i.phi x) -> (? x:i.phi x))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC006l [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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 v4.1.0, 0.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.28/0.46 % Number of atoms : 9 ( 4 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.28/0.46 % Number of connectives : 16 ( 0 ~; 0 |; 2 &; 9 @)
% 0.28/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 7 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 10 ( 3 ^; 4 !; 3 ?; 10 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=406
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e,conjecture,
% 0.28/0.46 ( exuE1
% 0.28/0.46 => ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 12:24:42 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sjXWhu7XOp/DTF2DTF21383.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(exu_type,type,
% 1.48/1.28 exu: ( $i > $o ) > $o ).
% 1.48/1.28
% 1.48/1.28 thf(exu,definition,
% 1.48/1.28 ( exu
% 1.48/1.28 = ( ^ [Xphi: $i > $o] :
% 1.48/1.28 ? [Xx: $i] :
% 1.48/1.28 ( ( Xphi @ Xx )
% 1.48/1.28 & ! [Xy: $i] :
% 1.48/1.28 ( ( Xphi @ Xy )
% 1.48/1.28 => ( Xx = Xy ) ) ) ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(exuE1_type,type,
% 1.48/1.28 exuE1: $o ).
% 1.48/1.28
% 1.48/1.28 thf(exuE1,definition,
% 1.48/1.28 ( exuE1
% 1.48/1.28 = ( ! [Xphi: $i > $o] :
% 1.48/1.28 ( ( exu
% 1.48/1.28 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.28 => ? [Xx: $i] :
% 1.48/1.28 ( ( Xphi @ Xx )
% 1.48/1.28 & ! [Xy: $i] :
% 1.48/1.28 ( ( Xphi @ Xy )
% 1.48/1.28 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(exuE3e,conjecture,
% 1.48/1.28 ( exuE1
% 1.48/1.28 => ! [Xphi: $i > $o] :
% 1.48/1.28 ( ( exu
% 1.48/1.28 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.28 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ).
% 1.48/1.28 ------------------------
% 1.64/1.30 % (21655)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21383 for (2999ds/27Mi)
% 1.64/1.30 % (21657)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21383 for (2999ds/2Mi)
% 1.64/1.30 % (21657)Instruction limit reached!
% 1.64/1.30 % (21657)------------------------------
% 1.64/1.30 % (21657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (21657)Termination reason: Unknown
% 1.64/1.30 % (21657)Termination phase: Property scanning
% 1.64/1.30
% 1.64/1.30 % (21657)Memory used [KB]: 895
% 1.64/1.30 % (21657)Time elapsed: 0.003 s
% 1.64/1.30 % (21657)Instructions burned: 2 (million)
% 1.64/1.30 % (21657)------------------------------
% 1.64/1.30 % (21657)------------------------------
% 1.64/1.30 % (21655)First to succeed.
% 1.64/1.31 % (21653)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21383 for (2999ds/183Mi)
% 1.64/1.31 % (21654)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21383 for (2999ds/4Mi)
% 1.64/1.31 % (21655)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_21383
% 1.64/1.31 % SZS output start Proof for DTF2THF_21383
% 1.64/1.31 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.64/1.31 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.31 thf(func_def_15, type, sK0: $i > $o).
% 1.64/1.31 thf(func_def_18, type, sK2: ($i > $o) > $i).
% 1.64/1.31 thf(func_def_19, type, sK3: ($i > $o) > $i > $i).
% 1.64/1.31 thf(f56,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.64/1.31 thf(f55,plain,(
% 1.64/1.31 ($true != $true)),
% 1.64/1.31 inference(superposition,[status(thm)],[f19,f49])).
% 1.64/1.31 thf(f49,plain,(
% 1.64/1.31 ((sK0 @ sK4) = $true)),
% 1.64/1.31 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.64/1.31 thf(f48,plain,(
% 1.64/1.31 (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK4 = Y0)))) & (sK0 @ sK4)) = $true)),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.64/1.31 thf(f47,plain,(
% 1.64/1.31 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK4))),
% 1.64/1.31 inference(sigma_clausification,[status(thm)],[f46])).
% 1.64/1.31 thf(f46,plain,(
% 1.64/1.31 ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))))),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.31 thf(f21,plain,(
% 1.64/1.31 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f18,f16])).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.sjXWhu7XOp/DTF2THF_21383.p',exu)).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 (! [X1 : $i] : ($true != (sK0 @ X1)) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & (exuE1 = $true)),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) => (! [X1 : $i] : ($true != (sK0 @ X1)) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 ? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) & (exuE1 = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 ~((exuE1 = $true) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X1 : $i] : ((X0 @ X1) = $true)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f11])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 ~((exuE1 = $true) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : ((X0 @ X2) = $true)))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 ~(exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : (X0 @ X2)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f4])).
% 1.64/1.31 thf(f4,negated_conjecture,(
% 1.64/1.31 ~(exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (X0 @ X1)))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.31 thf(f3,conjecture,(
% 1.64/1.31 exuE1 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (X0 @ X1))),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.sjXWhu7XOp/DTF2THF_21383.p',exuE3e)).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 ( ! [X1 : $i] : (($true != (sK0 @ X1))) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_21383
% 1.64/1.31 % (21655)------------------------------
% 1.64/1.31 % (21655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (21655)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (21655)Memory used [KB]: 5500
% 1.64/1.31 % (21655)Time elapsed: 0.005 s
% 1.64/1.31 % (21655)Instructions burned: 3 (million)
% 1.64/1.31 % (21655)------------------------------
% 1.64/1.31 % (21655)------------------------------
% 1.64/1.31 % (21652)Success in time 0.018 s
%------------------------------------------------------------------------------