%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU549^2 : 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 : n011.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 09:35:13 AM UTC 2026
% Result : Theorem 1.55s 1.31s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 75 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 177 ( 12 ~; 4 |; 27 &; 95 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 7 con; 0-2 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 30 ^; 21 !; 15 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_13,type,
sK0: $i > $o ).
thf(f44,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f17]) ).
thf(f17,plain,
sK1 != sK2,
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( sK0 @ sK2 )
= $true )
& ( sK1 != sK2 )
& ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13,f12]) ).
thf(f12,plain,
( ? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X1 != X2 )
& ( ( X0 @ X1 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
=> ( ? [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( X1 != X2 )
& ( ( sK0 @ X1 )
= $true ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( X1 != X2 )
& ( ( sK0 @ X1 )
= $true ) )
=> ( ( ( sK0 @ sK2 )
= $true )
& ( sK1 != sK2 )
& ( $true
= ( sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X1 != X2 )
& ( ( X0 @ X1 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X1 )
= $true )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X2: $i,X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( X2 = X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X3: $i] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AwCbFAASV9/DTF2THF_1981.p',exuE3u) ).
thf(f41,plain,
sK1 = sK2,
inference(superposition,[status(thm)],[f39,f38]) ).
thf(f38,plain,
sK4 = sK2,
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( sK4 = sK2 )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f29,f18]) ).
thf(f18,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f29,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( sK4 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( $true
= ( sK4 = X1 ) )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
=> ( sK4 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) )
& ( sK0 @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,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)],[f15,f19]) ).
thf(f19,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,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.AwCbFAASV9/DTF2THF_1981.p',exu) ).
thf(f15,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f39,plain,
sK1 = sK4,
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( sK1 = sK4 )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f29,f16]) ).
thf(f16,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU549^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n011.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:26:17 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU549^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : Preliminary Notions - Equality Laws
% 0.17/0.38 % Version : Especial > Reduced > Especial.
% 0.17/0.38 % English : (! phi:i>o.exu (^ x:i.phi x) -> (! x:i.! y:i.phi x -> phi y ->
% 0.17/0.38 % x = y))
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC051l [Bro08]
% 0.17/0.38 % : ZFC058l [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % 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 v3.7.0
% 0.17/0.38 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.17/0.38 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 2 ( 2 avg)
% 0.17/0.38 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 6 @)
% 0.17/0.38 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 8 ( 5 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.17/0.38 % Number of variables : 7 ( 2 ^; 4 !; 1 ?; 7 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=407
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(exu_type,type,
% 0.17/0.38 exu: ( $i > $o ) > $o ).
% 0.17/0.38
% 0.17/0.38 thf(exu,definition,
% 0.17/0.38 ( exu
% 0.17/0.38 = ( ^ [Xphi: $i > $o] :
% 0.17/0.38 ? [Xx: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 & ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuE3u,conjecture,
% 0.17/0.38 ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 => ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.36/1.28 ---- Embedded in THF ---
% 1.36/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.28 %%% Generated on Tue Feb 24 12:26:18 EST 2026
% 1.36/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.28 %%% Logic specification used:
% 1.36/1.28 %%% thf(spec, logic, $$dhol).
% 1.36/1.28
% 1.36/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.AwCbFAASV9/DTF2DTF1981.p
% See solution above
% 1.36/1.28 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.29 thf(exu_type,type,
% 1.36/1.29 exu: ( $i > $o ) > $o ).
% 1.36/1.29
% 1.36/1.29 thf(exu,definition,
% 1.36/1.29 ( exu
% 1.36/1.29 = ( ^ [Xphi: $i > $o] :
% 1.36/1.29 ? [Xx: $i] :
% 1.36/1.29 ( ( Xphi @ Xx )
% 1.36/1.29 & ! [Xy: $i] :
% 1.36/1.29 ( ( Xphi @ Xy )
% 1.36/1.29 => ( Xx = Xy ) ) ) ) ) ).
% 1.36/1.29
% 1.36/1.29 thf(exuE3u,conjecture,
% 1.36/1.29 ! [Xphi: $i > $o] :
% 1.36/1.29 ( ( exu
% 1.36/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.36/1.29 => ! [Xx: $i,Xy: $i] :
% 1.36/1.29 ( ( Xphi @ Xx )
% 1.36/1.29 => ( ( Xphi @ Xy )
% 1.36/1.29 => ( Xx = Xy ) ) ) ) ).
% 1.36/1.29 ------------------------
% 1.55/1.31 % (2083)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_1981 for (2999ds/2Mi)
% 1.55/1.31 % (2080)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_1981 for (2999ds/4Mi)
% 1.55/1.31 % (2081)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_1981 for (2999ds/27Mi)
% 1.55/1.31 % (2079)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1981 for (2999ds/183Mi)
% 1.55/1.31 % (2084)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_1981 for (2999ds/275Mi)
% 1.55/1.31 % (2085)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1981 for (2999ds/18Mi)
% 1.55/1.31 % (2082)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1981 for (2999ds/2Mi)
% 1.55/1.31 % (2083)Instruction limit reached!
% 1.55/1.31 % (2083)------------------------------
% 1.55/1.31 % (2083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (2083)Termination reason: Unknown
% 1.55/1.31 % (2083)Termination phase: Property scanning
% 1.55/1.31
% 1.55/1.31 % (2083)Memory used [KB]: 895
% 1.55/1.31 % (2083)Time elapsed: 0.002 s
% 1.55/1.31 % (2083)Instructions burned: 2 (million)
% 1.55/1.31 % (2083)------------------------------
% 1.55/1.31 % (2083)------------------------------
% 1.55/1.31 % (2084)Refutation not found, incomplete strategy
% 1.55/1.31 % (2084)------------------------------
% 1.55/1.31 % (2084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (2084)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.31
% 1.55/1.31
% 1.55/1.31 % (2082)Instruction limit reached!
% 1.55/1.31 % (2082)------------------------------
% 1.55/1.31 % (2082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (2082)Termination reason: Unknown
% 1.55/1.31 % (2082)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (2082)Memory used [KB]: 5500
% 1.55/1.31 % (2082)Time elapsed: 0.003 s
% 1.55/1.31 % (2082)Instructions burned: 2 (million)
% 1.55/1.31 % (2082)------------------------------
% 1.55/1.31 % (2082)------------------------------
% 1.55/1.31 % (2084)Memory used [KB]: 5500
% 1.55/1.31 % (2084)Time elapsed: 0.002 s
% 1.55/1.31 % (2084)Instructions burned: 1 (million)
% 1.55/1.31 % (2084)------------------------------
% 1.55/1.31 % (2084)------------------------------
% 1.55/1.31 % (2079)First to succeed.
% 1.55/1.31 % (2080)Also succeeded, but the first one will report.
% 1.55/1.31 % (2081)Also succeeded, but the first one will report.
% 1.55/1.31 % (2079)Refutation found. Thanks to Tanya!
% 1.55/1.31 % SZS status Theorem for DTF2THF_1981
% 1.55/1.31 % SZS output start Proof for DTF2THF_1981
% 1.55/1.31 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.55/1.31 thf(func_def_13, type, sK0: $i > $o).
% 1.55/1.31 thf(f44,plain,(
% 1.55/1.31 $false),
% 1.55/1.31 inference(subsumption_resolution,[status(thm)],[f41,f17])).
% 1.55/1.31 thf(f17,plain,(
% 1.55/1.31 (sK1 != sK2)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.55/1.31 thf(f14,plain,(
% 1.55/1.31 (((sK0 @ sK2) = $true) & (sK1 != sK2) & ($true = (sK0 @ sK1))) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.55/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13,f12])).
% 1.55/1.31 thf(f12,plain,(
% 1.55/1.31 ? [X0 : $i > $o] : (? [X1 : $i,X2 : $i] : (((X0 @ X2) = $true) & (X1 != X2) & ((X0 @ X1) = $true)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) => (? [X2 : $i,X1 : $i] : (((sK0 @ X2) = $true) & (X1 != X2) & ((sK0 @ X1) = $true)) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 1.55/1.31 introduced(definition,[],[choice_axiom])).
% 1.55/1.31 thf(f13,plain,(
% 1.55/1.31 ? [X2 : $i,X1 : $i] : (((sK0 @ X2) = $true) & (X1 != X2) & ((sK0 @ X1) = $true)) => (((sK0 @ sK2) = $true) & (sK1 != sK2) & ($true = (sK0 @ sK1)))),
% 1.55/1.31 introduced(definition,[],[choice_axiom])).
% 1.55/1.31 thf(f11,plain,(
% 1.55/1.31 ? [X0 : $i > $o] : (? [X1 : $i,X2 : $i] : (((X0 @ X2) = $true) & (X1 != X2) & ((X0 @ X1) = $true)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true))),
% 1.55/1.31 inference(flattening,[status(thm)],[f10])).
% 1.55/1.31 thf(f10,plain,(
% 1.55/1.31 ? [X0 : $i > $o] : (? [X1 : $i,X2 : $i] : (((X1 != X2) & ((X0 @ X1) = $true)) & ((X0 @ X2) = $true)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true))),
% 1.55/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.55/1.31 thf(f9,plain,(
% 1.55/1.31 ~! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ! [X1 : $i,X2 : $i] : (((X0 @ X2) = $true) => (((X0 @ X1) = $true) => (X1 = X2))))),
% 1.55/1.31 inference(rectify,[status(thm)],[f6])).
% 1.55/1.31 thf(f6,plain,(
% 1.55/1.31 ~! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ! [X2 : $i,X3 : $i] : (((X0 @ X3) = $true) => (((X0 @ X2) = $true) => (X2 = X3))))),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.55/1.31 thf(f5,plain,(
% 1.55/1.31 ~! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))))),
% 1.55/1.31 inference(rectify,[status(thm)],[f3])).
% 1.55/1.31 thf(f3,negated_conjecture,(
% 1.55/1.31 ~! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))),
% 1.55/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.55/1.31 thf(f2,conjecture,(
% 1.55/1.31 ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))),
% 1.55/1.31 file('/export/starexec/sandbox2/tmp/tmp.AwCbFAASV9/DTF2THF_1981.p',exuE3u)).
% 1.55/1.31 thf(f41,plain,(
% 1.55/1.31 (sK1 = sK2)),
% 1.55/1.31 inference(superposition,[status(thm)],[f39,f38])).
% 1.55/1.31 thf(f38,plain,(
% 1.55/1.31 (sK4 = sK2)),
% 1.55/1.31 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.55/1.31 thf(f31,plain,(
% 1.55/1.31 (sK4 = sK2) | ($false = $true)),
% 1.55/1.31 inference(superposition,[status(thm)],[f29,f18])).
% 1.55/1.31 thf(f18,plain,(
% 1.55/1.31 ((sK0 @ sK2) = $true)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.55/1.31 thf(f29,plain,(
% 1.55/1.31 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (sK4 = X1)) )),
% 1.55/1.31 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.55/1.31 thf(f28,plain,(
% 1.55/1.31 ( ! [X1 : $i] : (($true = (sK4 = X1)) | ((sK0 @ X1) = $false)) )),
% 1.55/1.31 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.55/1.31 thf(f27,plain,(
% 1.55/1.31 ( ! [X1 : $i] : ((((sK0 @ X1) => (sK4 = X1)) = $true)) )),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.55/1.31 thf(f26,plain,(
% 1.55/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK4 = Y0))) @ X1))) )),
% 1.55/1.31 inference(pi_clausification,[status(thm)],[f25])).
% 1.55/1.31 thf(f25,plain,(
% 1.55/1.31 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK4 = Y0)))) = $true)),
% 1.55/1.31 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.55/1.31 thf(f23,plain,(
% 1.55/1.31 (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK4 = Y0)))) & (sK0 @ sK4)) = $true)),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.55/1.31 thf(f22,plain,(
% 1.55/1.31 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK4))),
% 1.55/1.31 inference(sigma_clausification,[status(thm)],[f21])).
% 1.55/1.31 thf(f21,plain,(
% 1.55/1.31 ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $true)),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.55/1.31 thf(f20,plain,(
% 1.55/1.31 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.55/1.31 inference(definition_unfolding,[status(thm)],[f15,f19])).
% 1.55/1.31 thf(f19,plain,(
% 1.55/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.31 thf(f8,plain,(
% 1.55/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.55/1.31 thf(f7,plain,(
% 1.55/1.31 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.55/1.31 inference(rectify,[status(thm)],[f1])).
% 1.55/1.31 thf(f1,axiom,(
% 1.55/1.31 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.55/1.31 file('/export/starexec/sandbox2/tmp/tmp.AwCbFAASV9/DTF2THF_1981.p',exu)).
% 1.55/1.31 thf(f15,plain,(
% 1.55/1.31 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.55/1.31 thf(f39,plain,(
% 1.55/1.31 (sK1 = sK4)),
% 1.55/1.31 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.55/1.31 thf(f30,plain,(
% 1.55/1.31 (sK1 = sK4) | ($false = $true)),
% 1.55/1.31 inference(superposition,[status(thm)],[f29,f16])).
% 1.55/1.31 thf(f16,plain,(
% 1.55/1.31 ($true = (sK0 @ sK1))),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.55/1.31 % SZS output end Proof for DTF2THF_1981
% 1.55/1.31 % (2079)------------------------------
% 1.55/1.31 % (2079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (2079)Termination reason: Refutation
% 1.55/1.31
% 1.55/1.31 % (2079)Memory used [KB]: 5500
% 1.55/1.31 % (2079)Time elapsed: 0.005 s
% 1.55/1.31 % (2079)Instructions burned: 2 (million)
% 1.55/1.31 % (2079)------------------------------
% 1.55/1.31 % (2079)------------------------------
% 1.55/1.31 % (2078)Success in time 0.018 s
%------------------------------------------------------------------------------