%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO006^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 09:53:07 AM UTC 2026
% Result : Theorem 1.64s 1.40s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 185 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 139 ( 31 ~; 31 |; 4 &; 49 @)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 9 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 17 ^; 13 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f98,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f30,f39,f73,f76,f93,f97]) ).
thf(f97,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f87,f33]) ).
thf(f33,plain,
( ( sK1 != $false )
| spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_3
<=> ( sK1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f87,plain,
( ( sK1 = $false )
| ~ spl2_4 ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( ^ [Y0: $o] : Y0
@ sK1 )
= $false )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true = $false )
| ( ( ^ [Y0: $o] : Y0
@ sK1 )
= $false )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f19,f38]) ).
thf(f38,plain,
( ( sK0 = $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl2_4
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f19,plain,
! [X1: $o > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $o > $o] :
( $true
= ( ( X1 @ sK1 )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $o > $o] :
( ( ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f14,f12]) ).
thf(f12,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( leibeq
= ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vfZ6tm9Bjn/DTF2THF_7142.p',leibeq1) ).
thf(f14,plain,
( $true
= ( leibeq @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
= ( leibeq @ sK1 @ sK0 ) )
& ( sK1 != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $o,X1: $o] :
( ( $true
= ( leibeq @ X1 @ X0 ) )
& ( X0 != X1 ) )
=> ( ( $true
= ( leibeq @ sK1 @ sK0 ) )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $o,X1: $o] :
( ( $true
= ( leibeq @ X1 @ X0 ) )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $o,X1: $o] :
( ( $true
= ( leibeq @ X1 @ X0 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $o,X1: $o] :
( ( leibeq @ X1 @ X0 )
=> ( X0
<=> X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X4: $o,X3: $o] :
( ( leibeq @ X3 @ X4 )
=> ( X4
<=> X3 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X4: $o,X3: $o] :
( ( leibeq @ X3 @ X4 )
=> ( X4
<=> X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.vfZ6tm9Bjn/DTF2THF_7142.p',conj) ).
thf(f93,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f38,f25]) ).
thf(f25,plain,
( ( $true = sK0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl2_1
<=> ( $true = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f76,plain,
( spl2_4
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f75,f27,f36]) ).
thf(f27,definition,
( spl2_2
<=> ( $true = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f75,plain,
( ( sK0 = $false )
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f48,f28]) ).
thf(f28,plain,
( ( $true != sK1 )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f48,plain,
( ( $true = sK1 )
| ( sK0 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
sK1 = sK0,
inference(leibniz_equality_elimination,[status(thm)],[f19]) ).
thf(f73,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f29,f34]) ).
thf(f34,plain,
( ( sK1 = $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f29,plain,
( ( $true = sK1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f39,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f36,f32]) ).
thf(f21,plain,
( ( sK0 = $false )
| ( sK1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f30,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f27,f23]) ).
thf(f20,plain,
( ( $true = sK0 )
| ( $true = sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO006^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:20:41 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO006^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : The trivial direction of Boolean extensionality
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Ben09]
% 0.18/0.45 % Names : Example 9b [BB05]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.18/0.45 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 6 ( 4 avg)
% 0.18/0.45 % Number of types : 1 ( 0 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(leibeq1_type,type,
% 0.18/0.45 leibeq: $o > $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(leibeq1,definition,
% 0.18/0.45 ( leibeq
% 0.18/0.45 = ( ^ [U: $o,V: $o] :
% 0.18/0.45 ! [Q: $o > $o] :
% 0.18/0.45 ( ( Q @ U )
% 0.18/0.45 => ( Q @ V ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(conj,conjecture,
% 0.18/0.45 ! [A: $o,B: $o] :
% 0.18/0.45 ( ( leibeq @ A @ B )
% 0.18/0.45 => ( A
% 0.18/0.45 <=> B ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 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 14:20:42 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.vfZ6tm9Bjn/DTF2DTF7142.p
% See solution above
% 1.47/1.37 ------------------------
% 1.47/1.38 ---- Cleaned THF ---
% 1.47/1.38 thf(leibeq1_type,type,
% 1.47/1.38 leibeq: $o > $o > $o ).
% 1.47/1.38
% 1.47/1.38 thf(leibeq1,definition,
% 1.47/1.38 ( leibeq
% 1.47/1.38 = ( ^ [U: $o,V: $o] :
% 1.47/1.38 ! [Q: $o > $o] :
% 1.47/1.38 ( ( Q @ U )
% 1.47/1.38 => ( Q @ V ) ) ) ) ).
% 1.47/1.38
% 1.47/1.38 thf(conj,conjecture,
% 1.47/1.38 ! [A: $o,B: $o] :
% 1.47/1.38 ( ( leibeq @ A @ B )
% 1.47/1.38 => ( A
% 1.47/1.38 <=> B ) ) ).
% 1.47/1.38 ------------------------
% 1.64/1.40 % (7241)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_7142 for (3000ds/27Mi)
% 1.64/1.40 % (7240)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_7142 for (3000ds/4Mi)
% 1.64/1.40 % (7243)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_7142 for (3000ds/2Mi)
% 1.64/1.40 % (7239)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7142 for (3000ds/183Mi)
% 1.64/1.40 % (7245)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7142 for (3000ds/18Mi)
% 1.64/1.40 % (7244)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_7142 for (3000ds/275Mi)
% 1.64/1.40 % (7242)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7142 for (3000ds/2Mi)
% 1.64/1.40 % (7242)Instruction limit reached!
% 1.64/1.40 % (7242)------------------------------
% 1.64/1.40 % (7242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7242)Termination reason: Unknown
% 1.64/1.40 % (7242)Termination phase: Saturation
% 1.64/1.40
% 1.64/1.40 % (7242)Memory used [KB]: 5373
% 1.64/1.40 % (7242)Time elapsed: 0.003 s
% 1.64/1.40 % (7242)Instructions burned: 2 (million)
% 1.64/1.40 % (7242)------------------------------
% 1.64/1.40 % (7242)------------------------------
% 1.64/1.40 % (7243)Instruction limit reached!
% 1.64/1.40 % (7243)------------------------------
% 1.64/1.40 % (7243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7243)Termination reason: Unknown
% 1.64/1.40 % (7243)Termination phase: Saturation
% 1.64/1.40
% 1.64/1.40 % (7243)Memory used [KB]: 5373
% 1.64/1.40 % (7243)Time elapsed: 0.003 s
% 1.64/1.40 % (7243)Instructions burned: 2 (million)
% 1.64/1.40 % (7243)------------------------------
% 1.64/1.40 % (7243)------------------------------
% 1.64/1.40 % (7241)Refutation not found, incomplete strategy
% 1.64/1.40 % (7241)------------------------------
% 1.64/1.40 % (7241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7241)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.40
% 1.64/1.40
% 1.64/1.40 % (7241)Memory used [KB]: 5500
% 1.64/1.40 % (7241)Time elapsed: 0.003 s
% 1.64/1.40 % (7241)Instructions burned: 1 (million)
% 1.64/1.40 % (7241)------------------------------
% 1.64/1.40 % (7241)------------------------------
% 1.64/1.40 % (7244)Refutation not found, incomplete strategy
% 1.64/1.40 % (7244)------------------------------
% 1.64/1.40 % (7244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7244)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.40
% 1.64/1.40
% 1.64/1.40 % (7244)Memory used [KB]: 5500
% 1.64/1.40 % (7244)Time elapsed: 0.004 s
% 1.64/1.40 % (7244)Instructions burned: 2 (million)
% 1.64/1.40 % (7244)------------------------------
% 1.64/1.40 % (7244)------------------------------
% 1.64/1.40 % (7240)Instruction limit reached!
% 1.64/1.40 % (7240)------------------------------
% 1.64/1.40 % (7240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7240)Termination reason: Unknown
% 1.64/1.40 % (7240)Termination phase: Saturation
% 1.64/1.40
% 1.64/1.40 % (7240)Memory used [KB]: 5500
% 1.64/1.40 % (7240)Time elapsed: 0.005 s
% 1.64/1.40 % (7240)Instructions burned: 4 (million)
% 1.64/1.40 % (7240)------------------------------
% 1.64/1.40 % (7240)------------------------------
% 1.64/1.40 % (7239)First to succeed.
% 1.64/1.40 % (7245)Also succeeded, but the first one will report.
% 1.64/1.40 % (7239)Refutation found. Thanks to Tanya!
% 1.64/1.40 % SZS status Theorem for DTF2THF_7142
% 1.64/1.40 % SZS output start Proof for DTF2THF_7142
% 1.64/1.40 thf(func_def_0, type, leibeq: $o > $o > $o).
% 1.64/1.40 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 1.64/1.40 thf(f98,plain,(
% 1.64/1.40 $false),
% 1.64/1.40 inference(avatar_sat_refutation,[status(thm)],[f30,f39,f73,f76,f93,f97])).
% 1.64/1.40 thf(f97,plain,(
% 1.64/1.40 spl2_3 | ~spl2_4),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.64/1.40 thf(f96,plain,(
% 1.64/1.40 $false | (spl2_3 | ~spl2_4)),
% 1.64/1.40 inference(subsumption_resolution,[status(thm)],[f87,f33])).
% 1.64/1.40 thf(f33,plain,(
% 1.64/1.40 (sK1 != $false) | spl2_3),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.40 thf(f32,definition,(
% 1.64/1.40 spl2_3 <=> (sK1 = $false)),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.64/1.40 thf(f87,plain,(
% 1.64/1.40 (sK1 = $false) | ~spl2_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.64/1.40 thf(f86,plain,(
% 1.64/1.40 (((^[Y0 : $o]: (Y0)) @ sK1) = $false) | ~spl2_4),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.64/1.40 thf(f85,plain,(
% 1.64/1.40 ($true = $false) | (((^[Y0 : $o]: (Y0)) @ sK1) = $false) | ~spl2_4),
% 1.64/1.40 inference(superposition,[status(thm)],[f19,f38])).
% 1.64/1.40 thf(f38,plain,(
% 1.64/1.40 (sK0 = $false) | ~spl2_4),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.64/1.40 thf(f36,definition,(
% 1.64/1.40 spl2_4 <=> (sK0 = $false)),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.64/1.40 thf(f19,plain,(
% 1.64/1.40 ( ! [X1 : $o > $o] : (($true = (X1 @ sK0)) | ((X1 @ sK1) = $false)) )),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.64/1.40 thf(f18,plain,(
% 1.64/1.40 ( ! [X1 : $o > $o] : (($true = ((X1 @ sK1) => (X1 @ sK0)))) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.64/1.40 thf(f17,plain,(
% 1.64/1.40 ( ! [X1 : $o > $o] : ((((^[Y0 : $o > $o]: ((Y0 @ sK1) => (Y0 @ sK0))) @ X1) = $true)) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f16])).
% 1.64/1.40 thf(f16,plain,(
% 1.64/1.40 ((!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ sK1) => (Y0 @ sK0)))) = $true)),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.64/1.40 thf(f15,plain,(
% 1.64/1.40 (((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK1 @ sK0) = $true)),
% 1.64/1.40 inference(definition_unfolding,[status(thm)],[f14,f12])).
% 1.64/1.40 thf(f12,plain,(
% 1.64/1.40 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f6])).
% 1.64/1.40 thf(f6,plain,(
% 1.64/1.40 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.40 thf(f5,plain,(
% 1.64/1.40 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.64/1.40 inference(rectify,[status(thm)],[f1])).
% 1.64/1.40 thf(f1,axiom,(
% 1.64/1.40 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.64/1.40 file('/export/starexec/sandbox/tmp/tmp.vfZ6tm9Bjn/DTF2THF_7142.p',leibeq1)).
% 1.64/1.40 thf(f14,plain,(
% 1.64/1.40 ($true = (leibeq @ sK1 @ sK0))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.40 thf(f11,plain,(
% 1.64/1.40 ($true = (leibeq @ sK1 @ sK0)) & (sK1 != sK0)),
% 1.64/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.64/1.40 thf(f10,plain,(
% 1.64/1.40 ? [X0 : $o,X1 : $o] : (($true = (leibeq @ X1 @ X0)) & (X0 != X1)) => (($true = (leibeq @ sK1 @ sK0)) & (sK1 != sK0))),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 thf(f9,plain,(
% 1.64/1.40 ? [X0 : $o,X1 : $o] : (($true = (leibeq @ X1 @ X0)) & (X0 != X1))),
% 1.64/1.40 inference(ennf_transformation,[status(thm)],[f8])).
% 1.64/1.40 thf(f8,plain,(
% 1.64/1.40 ~! [X0 : $o,X1 : $o] : (($true = (leibeq @ X1 @ X0)) => (X0 = X1))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.40 thf(f7,plain,(
% 1.64/1.40 ~! [X0 : $o,X1 : $o] : ((leibeq @ X1 @ X0) => (X0 <=> X1))),
% 1.64/1.40 inference(rectify,[status(thm)],[f3])).
% 1.64/1.40 thf(f3,negated_conjecture,(
% 1.64/1.40 ~! [X4 : $o,X3 : $o] : ((leibeq @ X3 @ X4) => (X4 <=> X3))),
% 1.64/1.40 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.40 thf(f2,conjecture,(
% 1.64/1.40 ! [X4 : $o,X3 : $o] : ((leibeq @ X3 @ X4) => (X4 <=> X3))),
% 1.64/1.40 file('/export/starexec/sandbox/tmp/tmp.vfZ6tm9Bjn/DTF2THF_7142.p',conj)).
% 1.64/1.40 thf(f93,plain,(
% 1.64/1.40 ~spl2_1 | ~spl2_4),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f92])).
% 1.64/1.40 thf(f92,plain,(
% 1.64/1.40 $false | (~spl2_1 | ~spl2_4)),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.64/1.40 thf(f81,plain,(
% 1.64/1.40 ($true = $false) | (~spl2_1 | ~spl2_4)),
% 1.64/1.40 inference(superposition,[status(thm)],[f38,f25])).
% 1.64/1.40 thf(f25,plain,(
% 1.64/1.40 ($true = sK0) | ~spl2_1),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.64/1.40 thf(f23,definition,(
% 1.64/1.40 spl2_1 <=> ($true = sK0)),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.64/1.40 thf(f76,plain,(
% 1.64/1.40 spl2_4 | spl2_2),
% 1.64/1.40 inference(avatar_split_clause,[status(thm)],[f75,f27,f36])).
% 1.64/1.40 thf(f27,definition,(
% 1.64/1.40 spl2_2 <=> ($true = sK1)),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.64/1.40 thf(f75,plain,(
% 1.64/1.40 (sK0 = $false) | spl2_2),
% 1.64/1.40 inference(subsumption_resolution,[status(thm)],[f48,f28])).
% 1.64/1.40 thf(f28,plain,(
% 1.64/1.40 ($true != sK1) | spl2_2),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.64/1.40 thf(f48,plain,(
% 1.64/1.40 ($true = sK1) | (sK0 = $false)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.64/1.40 thf(f40,plain,(
% 1.64/1.40 (sK1 = sK0)),
% 1.64/1.40 inference(leibniz_equality_elimination,[status(thm)],[f19])).
% 1.64/1.40 thf(f73,plain,(
% 1.64/1.40 ~spl2_2 | ~spl2_3),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.64/1.40 thf(f72,plain,(
% 1.64/1.40 $false | (~spl2_2 | ~spl2_3)),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.64/1.40 thf(f64,plain,(
% 1.64/1.40 ($true = $false) | (~spl2_2 | ~spl2_3)),
% 1.64/1.40 inference(superposition,[status(thm)],[f29,f34])).
% 1.64/1.40 thf(f34,plain,(
% 1.64/1.40 (sK1 = $false) | ~spl2_3),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.40 thf(f29,plain,(
% 1.64/1.40 ($true = sK1) | ~spl2_2),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.64/1.40 thf(f39,plain,(
% 1.64/1.40 spl2_3 | spl2_4),
% 1.64/1.40 inference(avatar_split_clause,[status(thm)],[f21,f36,f32])).
% 1.64/1.40 thf(f21,plain,(
% 1.64/1.40 (sK0 = $false) | (sK1 = $false)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.64/1.40 thf(f13,plain,(
% 1.64/1.40 (sK1 != sK0)),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.40 thf(f30,plain,(
% 1.64/1.40 spl2_1 | spl2_2),
% 1.64/1.40 inference(avatar_split_clause,[status(thm)],[f20,f27,f23])).
% 1.64/1.40 thf(f20,plain,(
% 1.64/1.40 ($true = sK0) | ($true = sK1)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.64/1.40 % SZS output end Proof for DTF2THF_7142
% 1.64/1.40 % (7239)------------------------------
% 1.64/1.40 % (7239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (7239)Termination reason: Refutation
% 1.64/1.40
% 1.64/1.40 % (7239)Memory used [KB]: 5500
% 1.64/1.40 % (7239)Time elapsed: 0.006 s
% 1.64/1.40 % (7239)Instructions burned: 4 (million)
% 1.64/1.40 % (7239)------------------------------
% 1.64/1.40 % (7239)------------------------------
% 1.64/1.40 % (7238)Success in time 0.011 s
%------------------------------------------------------------------------------