%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO007^1 : 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 : n015.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 1.51s 1.21s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 77 ( 11 ~; 0 |; 4 &; 43 @)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 30 ( 16 ^; 10 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK3: $o > $o ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: $o > $o] : $true
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] : $true ) ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f12,f14,f13]) ).
thf(f13,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK1 = sK0 )
& ( $true
!= ( leibeq @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $o,X1: $o] :
( ( X0 = X1 )
& ( $true
!= ( leibeq @ X1 @ X0 ) ) )
=> ( ( sK1 = sK0 )
& ( $true
!= ( leibeq @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $o,X1: $o] :
( ( X0 = X1 )
& ( $true
!= ( leibeq @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $o,X1: $o] :
( ( X0 = X1 )
=> ( $true
= ( leibeq @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $o,X1: $o] :
( ( X0
<=> X1 )
=> ( leibeq @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X4: $o,X3: $o] :
( ( X4
<=> X3 )
=> ( leibeq @ X3 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X4: $o,X3: $o] :
( ( X4
<=> X3 )
=> ( leibeq @ X3 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.gsidic5pi5/DTF2THF_11838.p',conj) ).
thf(f14,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/sandbox2/tmp/tmp.gsidic5pi5/DTF2THF_11838.p',leibeq1) ).
thf(f12,plain,
( $true
!= ( leibeq @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO007^1 : 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
% 0.15/0.32 % Computer : n015.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 14:23:16 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SYO007^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.44 % Domain : Syntactic
% 0.17/0.44 % Problem : The non-trivial direction of Boolean extensionality
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.17/0.44 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Ben09]
% 0.17/0.44 % Names : Example 10 [BB05]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % : Without Boolean extensionality : CounterSatisfiable
% 0.17/0.44 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.00 v3.7.0
% 0.17/0.44 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.17/0.44 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.44 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.17/0.44 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 6 ( 4 avg)
% 0.17/0.44 % Number of types : 1 ( 0 usr)
% 0.17/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.17/0.44 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments :
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(leibeq1_type,type,
% 0.17/0.44 leibeq: $o > $o > $o ).
% 0.17/0.44
% 0.17/0.44 thf(leibeq1,definition,
% 0.17/0.44 ( leibeq
% 0.17/0.44 = ( ^ [U: $o,V: $o] :
% 0.17/0.44 ! [Q: $o > $o] :
% 0.17/0.44 ( ( Q @ U )
% 0.17/0.44 => ( Q @ V ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(conj,conjecture,
% 0.17/0.44 ! [A: $o,B: $o] :
% 0.17/0.44 ( ( A
% 0.17/0.44 <=> B )
% 0.17/0.44 => ( leibeq @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.39/1.18 ---- Embedded in THF ---
% 1.39/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.18 %%% Generated on Tue Feb 24 14:23:17 EST 2026
% 1.39/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.18 %%% Logic specification used:
% 1.39/1.18 %%% thf(spec, logic, $$dhol).
% 1.39/1.18
% 1.39/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gsidic5pi5/DTF2DTF11838.p
% See solution above
% 1.39/1.18 ------------------------
% 1.39/1.19 ---- Cleaned THF ---
% 1.39/1.19 thf(leibeq1_type,type,
% 1.39/1.19 leibeq: $o > $o > $o ).
% 1.39/1.19
% 1.39/1.19 thf(leibeq1,definition,
% 1.39/1.19 ( leibeq
% 1.39/1.19 = ( ^ [U: $o,V: $o] :
% 1.39/1.19 ! [Q: $o > $o] :
% 1.39/1.19 ( ( Q @ U )
% 1.39/1.19 => ( Q @ V ) ) ) ) ).
% 1.39/1.19
% 1.39/1.19 thf(conj,conjecture,
% 1.39/1.19 ! [A: $o,B: $o] :
% 1.39/1.19 ( ( A
% 1.39/1.19 <=> B )
% 1.39/1.19 => ( leibeq @ A @ B ) ) ).
% 1.39/1.19 ------------------------
% 1.51/1.20 % (12003)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_11838 for (2999ds/27Mi)
% 1.51/1.20 % (12003)First to succeed.
% 1.51/1.20 % (12004)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11838 for (2999ds/2Mi)
% 1.51/1.20 % (12004)Also succeeded, but the first one will report.
% 1.51/1.21 % (12003)Refutation found. Thanks to Tanya!
% 1.51/1.21 % SZS status Theorem for DTF2THF_11838
% 1.51/1.21 % SZS output start Proof for DTF2THF_11838
% 1.51/1.21 thf(func_def_0, type, leibeq: $o > $o > $o).
% 1.51/1.21 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.51/1.21 thf(func_def_14, type, sK3: $o > $o).
% 1.51/1.21 thf(f20,plain,(
% 1.51/1.21 $false),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.51/1.21 thf(f19,plain,(
% 1.51/1.21 ($false = $true)),
% 1.51/1.21 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.51/1.21 thf(f18,plain,(
% 1.51/1.21 ($false = ((^[Y0 : $o > $o]: ($true)) @ sK3))),
% 1.51/1.21 inference(sigma_clausification,[status(thm)],[f17])).
% 1.51/1.21 thf(f17,plain,(
% 1.51/1.21 ($true != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ($true))))),
% 1.51/1.21 inference(boolean_simplification,[status(thm)],[f16])).
% 1.51/1.21 thf(f16,plain,(
% 1.51/1.21 ($true != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ sK0) => (Y0 @ sK0)))))),
% 1.51/1.21 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.51/1.21 thf(f15,plain,(
% 1.51/1.21 ($true != ((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK0))),
% 1.51/1.21 inference(definition_unfolding,[status(thm)],[f12,f14,f13])).
% 1.51/1.21 thf(f13,plain,(
% 1.51/1.21 (sK1 = sK0)),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.21 thf(f11,plain,(
% 1.51/1.21 (sK1 = sK0) & ($true != (leibeq @ sK1 @ sK0))),
% 1.51/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.51/1.21 thf(f10,plain,(
% 1.51/1.21 ? [X0 : $o,X1 : $o] : ((X0 = X1) & ($true != (leibeq @ X1 @ X0))) => ((sK1 = sK0) & ($true != (leibeq @ sK1 @ sK0)))),
% 1.51/1.21 introduced(definition,[],[choice_axiom])).
% 1.51/1.21 thf(f9,plain,(
% 1.51/1.21 ? [X0 : $o,X1 : $o] : ((X0 = X1) & ($true != (leibeq @ X1 @ X0)))),
% 1.51/1.21 inference(ennf_transformation,[status(thm)],[f8])).
% 1.51/1.21 thf(f8,plain,(
% 1.51/1.21 ~! [X0 : $o,X1 : $o] : ((X0 = X1) => ($true = (leibeq @ X1 @ X0)))),
% 1.51/1.21 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.21 thf(f7,plain,(
% 1.51/1.21 ~! [X0 : $o,X1 : $o] : ((X0 <=> X1) => (leibeq @ X1 @ X0))),
% 1.51/1.21 inference(rectify,[status(thm)],[f3])).
% 1.51/1.21 thf(f3,negated_conjecture,(
% 1.51/1.21 ~! [X4 : $o,X3 : $o] : ((X4 <=> X3) => (leibeq @ X3 @ X4))),
% 1.51/1.21 inference(negated_conjecture,[status(cth)],[f2])).
% 1.51/1.21 thf(f2,conjecture,(
% 1.51/1.21 ! [X4 : $o,X3 : $o] : ((X4 <=> X3) => (leibeq @ X3 @ X4))),
% 1.51/1.21 file('/export/starexec/sandbox2/tmp/tmp.gsidic5pi5/DTF2THF_11838.p',conj)).
% 1.51/1.21 thf(f14,plain,(
% 1.51/1.21 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f6])).
% 1.51/1.21 thf(f6,plain,(
% 1.51/1.21 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.51/1.21 inference(fool_elimination,[status(thm)],[f5])).
% 1.51/1.21 thf(f5,plain,(
% 1.51/1.21 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.51/1.21 inference(rectify,[status(thm)],[f1])).
% 1.51/1.21 thf(f1,axiom,(
% 1.51/1.21 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.51/1.21 file('/export/starexec/sandbox2/tmp/tmp.gsidic5pi5/DTF2THF_11838.p',leibeq1)).
% 1.51/1.21 thf(f12,plain,(
% 1.51/1.21 ($true != (leibeq @ sK1 @ sK0))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.21 % SZS output end Proof for DTF2THF_11838
% 1.51/1.21 % (12003)------------------------------
% 1.51/1.21 % (12003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (12003)Termination reason: Refutation
% 1.51/1.21
% 1.51/1.21 % (12003)Memory used [KB]: 5500
% 1.51/1.21 % (12003)Time elapsed: 0.002 s
% 1.51/1.21 % (12003)------------------------------
% 1.51/1.21 % (12003)------------------------------
% 1.51/1.21 % (12000)Success in time 0.012 s
%------------------------------------------------------------------------------