%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO030^1 : 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 : n023.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 09:53:10 AM UTC 2026
% Result : Theorem 1.63s 1.45s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 34 equ; 1 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 121 ( 7 ~; 7 |; 0 &; 94 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 3 usr; 4 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 44 ( 15 ^; 23 !; 6 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_10,type,
sK0: ( $o > $o ) > $o ).
thf(func_def_13,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f119,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $false )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true = $false )
| ( ( $false = $false )
= $false ) ),
inference(superposition,[status(thm)],[f37,f69]) ).
thf(f69,plain,
( ( sK0 @ ( (=) @ $false ) )
= $false ),
inference(leibniz_equality_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $o > $o] :
( ( $false
= ( X0 @ $false ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $o > $o] :
( ( $true = $false )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $false
= ( X0 @ $false ) ) ),
inference(superposition,[status(thm)],[f37,f38]) ).
thf(f38,plain,
! [X0: $o > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $o > $o] :
( ( sK0 @ X0 )
= ( X0 @ ( sK0 @ X0 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $o > $o,X1: $o > $o] :
( ( $true
= ( X1 @ ( sK0 @ X0 ) ) )
| ( ( X1 @ ( X0 @ ( sK0 @ X0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $o > $o,X1: $o > $o] :
( ( ( X1 @ ( X0 @ ( sK0 @ X0 ) ) )
=> ( X1 @ ( sK0 @ X0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $o > $o,X1: $o > $o] :
( ( ^ [Y0: $o > $o] :
( ( Y0 @ ( X0 @ ( sK0 @ X0 ) ) )
=> ( Y0 @ ( sK0 @ X0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $o > $o] :
( $true
= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( X0 @ ( sK0 @ X0 ) ) )
=> ( Y0 @ ( sK0 @ X0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $o > $o] :
( $true
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( X0 @ ( sK0 @ X0 ) )
@ ( sK0 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,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.Dk1HrBO9K8/DTF2THF_20377.p',leibeq) ).
thf(f13,plain,
! [X0: $o > $o] :
( ( leibeq @ ( X0 @ ( sK0 @ X0 ) ) @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $o > $o] :
( ( leibeq @ ( X0 @ ( sK0 @ X0 ) ) @ ( sK0 @ X0 ) )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
! [X0: $o > $o] :
( ? [X1: $o] :
( ( leibeq @ ( X0 @ X1 ) @ X1 )
= $true )
=> ( ( leibeq @ ( X0 @ ( sK0 @ X0 ) ) @ ( sK0 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X0: $o > $o] :
? [X1: $o] :
( ( leibeq @ ( X0 @ X1 ) @ X1 )
= $true ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ~ ! [X0: $o > $o] :
? [X1: $o] :
( ( leibeq @ ( X0 @ X1 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ! [X0: $o > $o] :
? [X1: $o] : ( leibeq @ ( X0 @ X1 ) @ X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ~ ! [X3: $o > $o] :
? [X0: $o] : ( leibeq @ ( X3 @ X0 ) @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
~ ! [X3: $o > $o] :
? [X0: $o] : ( leibeq @ ( X3 @ X0 ) @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.Dk1HrBO9K8/DTF2THF_20377.p',conj) ).
thf(f37,plain,
! [X0: $o > $o] :
( ( ( sK0 @ X0 )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO030^1 : 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 : n023.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 14:22:19 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
% 0.28/0.50 ---- Original DTF file ---
% 0.28/0.50 thf(spec,logic,$$dhol).
% 0.28/0.50 %------------------------------------------------------------------------------
% 0.28/0.50 % File : SYO030^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.50 % Domain : Syntactic
% 0.28/0.50 % Problem : Not every unary connective is the identity
% 0.28/0.50 % Version : Especial.
% 0.28/0.50 % English :
% 0.28/0.50
% 0.28/0.50 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.28/0.50 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.28/0.50 % Source : [Ben09]
% 0.28/0.50 % Names : Example 26a [BB05]
% 0.28/0.50
% 0.28/0.50 % Status : Theorem
% 0.28/0.50 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.28/0.50 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.28/0.50 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.28/0.50 % Maximal formula atoms : 1 ( 1 avg)
% 0.28/0.50 % Number of connectives : 7 ( 1 ~; 0 |; 0 &; 5 @)
% 0.28/0.50 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.50 % Maximal formula depth : 7 ( 4 avg)
% 0.28/0.50 % Number of types : 1 ( 0 usr)
% 0.28/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.50 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.28/0.50 % Number of variables : 5 ( 2 ^; 2 !; 1 ?; 5 :)
% 0.28/0.50 % SPC : TH0_THM_EQU_NAR
% 0.28/0.50
% 0.28/0.50 % Comments : Requires set comprehension
% 0.28/0.50 %------------------------------------------------------------------------------
% 0.28/0.50 thf(leibeq_decl,type,
% 0.28/0.50 leibeq: $o > $o > $o ).
% 0.28/0.50
% 0.28/0.50 thf(leibeq,definition,
% 0.28/0.50 ( leibeq
% 0.28/0.50 = ( ^ [X: $o,Y: $o] :
% 0.28/0.50 ! [P: $o > $o] :
% 0.28/0.50 ( ( P @ X )
% 0.28/0.50 => ( P @ Y ) ) ) ) ).
% 0.28/0.50
% 0.28/0.50 thf(conj,conjecture,
% 0.28/0.50 ~ ! [F: $o > $o] :
% 0.28/0.50 ? [X: $o] : ( leibeq @ ( F @ X ) @ X ) ).
% 0.28/0.50
% 0.28/0.50 %------------------------------------------------------------------------------
% 0.28/0.50 ------------------------
% 1.63/1.41 ---- Embedded in THF ---
% 1.63/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.41 %%% Generated on Tue Feb 24 14:22:20 EST 2026
% 1.63/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.41 %%% Logic specification used:
% 1.63/1.41 %%% thf(spec, logic, $$dhol).
% 1.63/1.41
% 1.63/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Dk1HrBO9K8/DTF2DTF20377.p
% See solution above
% 1.63/1.41 ------------------------
% 1.63/1.42 ---- Cleaned THF ---
% 1.63/1.42 thf(leibeq_decl,type,
% 1.63/1.42 leibeq: $o > $o > $o ).
% 1.63/1.42
% 1.63/1.42 thf(leibeq,definition,
% 1.63/1.42 ( leibeq
% 1.63/1.42 = ( ^ [X: $o,Y: $o] :
% 1.63/1.42 ! [P: $o > $o] :
% 1.63/1.42 ( ( P @ X )
% 1.63/1.42 => ( P @ Y ) ) ) ) ).
% 1.63/1.42
% 1.63/1.42 thf(conj,conjecture,
% 1.63/1.42 ~ ! [F: $o > $o] :
% 1.63/1.42 ? [X: $o] : ( leibeq @ ( F @ X ) @ X ) ).
% 1.63/1.42 ------------------------
% 1.63/1.44 % (20483)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_20377 for (3000ds/27Mi)
% 1.63/1.44 % (20484)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20377 for (3000ds/2Mi)
% 1.63/1.44 % (20482)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_20377 for (3000ds/4Mi)
% 1.63/1.44 % (20481)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20377 for (3000ds/183Mi)
% 1.63/1.44 % (20485)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_20377 for (3000ds/2Mi)
% 1.63/1.44 % (20487)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20377 for (3000ds/18Mi)
% 1.63/1.44 % (20486)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_20377 for (3000ds/275Mi)
% 1.63/1.44 % (20486)Refutation not found, incomplete strategy
% 1.63/1.44 % (20486)------------------------------
% 1.63/1.44 % (20486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (20486)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.44
% 1.63/1.44
% 1.63/1.44 % (20486)Memory used [KB]: 5500
% 1.63/1.44 % (20486)Time elapsed: 0.002 s
% 1.63/1.44 % (20486)Instructions burned: 1 (million)
% 1.63/1.44 % (20486)------------------------------
% 1.63/1.44 % (20486)------------------------------
% 1.63/1.44 % (20483)Refutation not found, incomplete strategy
% 1.63/1.44 % (20483)------------------------------
% 1.63/1.44 % (20483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (20484)Instruction limit reached!
% 1.63/1.44 % (20484)------------------------------
% 1.63/1.44 % (20484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (20483)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.44
% 1.63/1.44
% 1.63/1.44 % (20484)Termination reason: Unknown
% 1.63/1.44 % (20483)Memory used [KB]: 5500
% 1.63/1.44 % (20484)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (20483)Time elapsed: 0.003 s
% 1.63/1.44 % (20483)Instructions burned: 2 (million)
% 1.63/1.44 % (20484)Memory used [KB]: 5500
% 1.63/1.44 % (20483)------------------------------
% 1.63/1.44 % (20483)------------------------------
% 1.63/1.44 % (20484)Time elapsed: 0.003 s
% 1.63/1.44 % (20484)Instructions burned: 2 (million)
% 1.63/1.44 % (20484)------------------------------
% 1.63/1.44 % (20484)------------------------------
% 1.63/1.44 % (20485)Instruction limit reached!
% 1.63/1.44 % (20485)------------------------------
% 1.63/1.44 % (20485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (20485)Termination reason: Unknown
% 1.63/1.44 % (20485)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (20485)Memory used [KB]: 5500
% 1.63/1.44 % (20485)Time elapsed: 0.003 s
% 1.63/1.44 % (20485)Instructions burned: 2 (million)
% 1.63/1.44 % (20485)------------------------------
% 1.63/1.44 % (20485)------------------------------
% 1.63/1.44 % (20482)Instruction limit reached!
% 1.63/1.44 % (20482)------------------------------
% 1.63/1.44 % (20482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (20482)Termination reason: Unknown
% 1.63/1.44 % (20482)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (20482)Memory used [KB]: 5500
% 1.63/1.44 % (20482)Time elapsed: 0.006 s
% 1.63/1.44 % (20482)Instructions burned: 5 (million)
% 1.63/1.44 % (20482)------------------------------
% 1.63/1.44 % (20482)------------------------------
% 1.63/1.45 % (20487)First to succeed.
% 1.63/1.45 % (20487)Refutation found. Thanks to Tanya!
% 1.63/1.45 % SZS status Theorem for DTF2THF_20377
% 1.63/1.45 % SZS output start Proof for DTF2THF_20377
% 1.63/1.45 thf(func_def_0, type, leibeq: $o > $o > $o).
% 1.63/1.45 thf(func_def_10, type, sK0: ($o > $o) > $o).
% 1.63/1.45 thf(func_def_13, type, ph2: !>[X0: $tType]:(X0)).
% 1.63/1.45 thf(f119,plain,(
% 1.63/1.45 $false),
% 1.63/1.45 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.63/1.45 thf(f118,plain,(
% 1.63/1.45 ($true = $false)),
% 1.63/1.45 inference(boolean_simplification,[status(thm)],[f117])).
% 1.63/1.45 thf(f117,plain,(
% 1.63/1.45 (($false = $false) = $false)),
% 1.63/1.45 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.63/1.45 thf(f106,plain,(
% 1.63/1.45 ($true = $false) | (($false = $false) = $false)),
% 1.63/1.45 inference(superposition,[status(thm)],[f37,f69])).
% 1.63/1.45 thf(f69,plain,(
% 1.63/1.45 ((sK0 @ (= @ $false)) = $false)),
% 1.63/1.45 inference(leibniz_equality_elimination,[status(thm)],[f57])).
% 1.63/1.45 thf(f57,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (($false = (X0 @ $false)) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.63/1.45 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.63/1.45 thf(f51,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (($true = $false) | ((X0 @ (sK0 @ X0)) = $true) | ($false = (X0 @ $false))) )),
% 1.63/1.45 inference(superposition,[status(thm)],[f37,f38])).
% 1.63/1.45 thf(f38,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (((sK0 @ X0) = $false) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.63/1.45 thf(f20,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (((sK0 @ X0) = (X0 @ (sK0 @ X0)))) )),
% 1.63/1.45 inference(leibniz_equality_elimination,[status(thm)],[f18])).
% 1.63/1.45 thf(f18,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o,X1 : $o > $o] : (($true = (X1 @ (sK0 @ X0))) | ((X1 @ (X0 @ (sK0 @ X0))) = $false)) )),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.63/1.45 thf(f17,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o,X1 : $o > $o] : ((((X1 @ (X0 @ (sK0 @ X0))) => (X1 @ (sK0 @ X0))) = $true)) )),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.63/1.45 thf(f16,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o,X1 : $o > $o] : ((((^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0)))) @ X1) = $true)) )),
% 1.63/1.45 inference(pi_clausification,[status(thm)],[f15])).
% 1.63/1.45 thf(f15,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (($true = (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0))))))) )),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.63/1.45 thf(f14,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (($true = ((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0)))) )),
% 1.63/1.45 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.63/1.45 thf(f12,plain,(
% 1.63/1.45 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.45 thf(f8,plain,(
% 1.63/1.45 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(fool_elimination,[status(thm)],[f7])).
% 1.63/1.45 thf(f7,plain,(
% 1.63/1.45 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.63/1.45 inference(rectify,[status(thm)],[f1])).
% 1.63/1.45 thf(f1,axiom,(
% 1.63/1.45 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.63/1.45 file('/export/starexec/sandbox/tmp/tmp.Dk1HrBO9K8/DTF2THF_20377.p',leibeq)).
% 1.63/1.45 thf(f13,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0)) = $true)) )),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.45 thf(f11,plain,(
% 1.63/1.45 ! [X0 : $o > $o] : ((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0)) = $true)),
% 1.63/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.63/1.45 thf(f10,plain,(
% 1.63/1.45 ! [X0 : $o > $o] : (? [X1 : $o] : ((leibeq @ (X0 @ X1) @ X1) = $true) => ((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0)) = $true))),
% 1.63/1.45 introduced(definition,[],[choice_axiom])).
% 1.63/1.45 thf(f9,plain,(
% 1.63/1.45 ! [X0 : $o > $o] : ? [X1 : $o] : ((leibeq @ (X0 @ X1) @ X1) = $true)),
% 1.63/1.45 inference(flattening,[status(thm)],[f6])).
% 1.63/1.45 thf(f6,plain,(
% 1.63/1.45 ~~! [X0 : $o > $o] : ? [X1 : $o] : ((leibeq @ (X0 @ X1) @ X1) = $true)),
% 1.63/1.45 inference(fool_elimination,[status(thm)],[f5])).
% 1.63/1.45 thf(f5,plain,(
% 1.63/1.45 ~~! [X0 : $o > $o] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 1.63/1.45 inference(rectify,[status(thm)],[f3])).
% 1.63/1.45 thf(f3,negated_conjecture,(
% 1.63/1.45 ~~! [X3 : $o > $o] : ? [X0 : $o] : (leibeq @ (X3 @ X0) @ X0)),
% 1.63/1.45 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.45 thf(f2,conjecture,(
% 1.63/1.45 ~! [X3 : $o > $o] : ? [X0 : $o] : (leibeq @ (X3 @ X0) @ X0)),
% 1.63/1.45 file('/export/starexec/sandbox/tmp/tmp.Dk1HrBO9K8/DTF2THF_20377.p',conj)).
% 1.63/1.45 thf(f37,plain,(
% 1.63/1.45 ( ! [X0 : $o > $o] : (((sK0 @ X0) = $true) | ((X0 @ (sK0 @ X0)) = $false)) )),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.63/1.45 % SZS output end Proof for DTF2THF_20377
% 1.63/1.45 % (20487)------------------------------
% 1.63/1.45 % (20487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (20487)Termination reason: Refutation
% 1.63/1.45
% 1.63/1.45 % (20487)Memory used [KB]: 5500
% 1.63/1.45 % (20487)Time elapsed: 0.009 s
% 1.63/1.45 % (20487)Instructions burned: 12 (million)
% 1.63/1.45 % (20487)------------------------------
% 1.63/1.45 % (20487)------------------------------
% 1.63/1.45 % (20480)Success in time 0.021 s
%------------------------------------------------------------------------------