%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO039^1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 09:53:12 AM UTC 2026
% Result : Unsatisfiable 1.66s 1.41s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 36 ( 10 ~; 0 |; 0 &; 26 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
h: $o > $i ).
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f10,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9,f7]) ).
thf(f7,plain,
( ( h @ $false )
= ( h @ $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $false
!= ( ( h @ $true )
= ( h @ $false ) ) ),
inference(equality_resolution,[status(thm)],[f5]) ).
thf(f5,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ $true )
= ( h @ $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f4]) ).
thf(f4,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
file('/export/starexec/sandbox/tmp/tmp.g3JvkDcKRP/DTF2THF_1154.p',1) ).
thf(f9,plain,
( ( h @ $false )
!= ( h @ $true ) ),
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( h
@ ( ( h @ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
inference(backward_demodulation,[status(thm)],[f5,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO039^1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n007.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 14:21:38 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO039^1 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : Unsatisfiable basic formula 1
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.19/0.47 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.19/0.47 % Source : [BS09a]
% 0.19/0.47 % Names :
% 0.19/0.47
% 0.19/0.47 % Status : Unsatisfiable
% 0.19/0.47 % Rating : 0.00 v5.3.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.47 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 5 avg)
% 0.19/0.47 % Number of connectives : 6 ( 2 ~; 0 |; 0 &; 4 @)
% 0.19/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 2 ( 2 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.47 % SPC : TH0_UNS_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : The fragment of simple type theory that restricts equations to
% 0.19/0.47 % base types and disallows lambda abstraction and quantification is
% 0.19/0.47 % decidable. This is an example.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(h,type,
% 0.19/0.47 h: $o > $i ).
% 0.19/0.47
% 0.19/0.47 thf(1,axiom,
% 0.19/0.47 ( ( h
% 0.19/0.47 @ ( ( h @ $false )
% 0.19/0.47 = ( h @ ~ $false ) ) )
% 0.19/0.47 != ( h @ $false ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.49/1.38 ---- Embedded in THF ---
% 1.49/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.38 %%% Generated on Tue Feb 24 14:21:39 EST 2026
% 1.49/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.38 %%% Logic specification used:
% 1.49/1.38 %%% thf(spec, logic, $$dhol).
% 1.49/1.38
% 1.49/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g3JvkDcKRP/DTF2DTF1154.p
% See solution above
% 1.49/1.38 ------------------------
% 1.49/1.39 ---- Cleaned THF ---
% 1.49/1.39 thf(h,type,
% 1.49/1.39 h: $o > $i ).
% 1.49/1.39
% 1.49/1.39 thf(1,axiom,
% 1.49/1.39 ( ( h
% 1.49/1.39 @ ( ( h @ $false )
% 1.49/1.39 = ( h @ ~ $false ) ) )
% 1.49/1.39 != ( h @ $false ) ) ).
% 1.49/1.39 ------------------------
% 1.66/1.41 % (1258)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_1154 for (3000ds/275Mi)
% 1.66/1.41 % (1253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1154 for (3000ds/183Mi)
% 1.66/1.41 % (1259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1154 for (3000ds/18Mi)
% 1.66/1.41 % (1254)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_1154 for (3000ds/4Mi)
% 1.66/1.41 % (1255)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_1154 for (3000ds/27Mi)
% 1.66/1.41 % (1256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1154 for (3000ds/2Mi)
% 1.66/1.41 % (1257)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_1154 for (3000ds/2Mi)
% 1.66/1.41 % (1258)Refutation not found, incomplete strategy
% 1.66/1.41 % (1258)------------------------------
% 1.66/1.41 % (1258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1258)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (1258)Memory used [KB]: 5373
% 1.66/1.41 % (1258)Time elapsed: 0.002 s
% 1.66/1.41 % (1258)Instructions burned: 1 (million)
% 1.66/1.41 % (1258)------------------------------
% 1.66/1.41 % (1258)------------------------------
% 1.66/1.41 % (1257)Refutation not found, incomplete strategy
% 1.66/1.41 % (1257)------------------------------
% 1.66/1.41 % (1257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1257)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (1257)Memory used [KB]: 5373
% 1.66/1.41 % (1257)Time elapsed: 0.002 s
% 1.66/1.41 % (1257)------------------------------
% 1.66/1.41 % (1257)------------------------------
% 1.66/1.41 % (1256)Refutation not found, incomplete strategy
% 1.66/1.41 % (1256)------------------------------
% 1.66/1.41 % (1256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1256)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (1256)Memory used [KB]: 5373
% 1.66/1.41 % (1256)Time elapsed: 0.003 s
% 1.66/1.41 % (1256)Instructions burned: 1 (million)
% 1.66/1.41 % (1256)------------------------------
% 1.66/1.41 % (1256)------------------------------
% 1.66/1.41 % (1255)Refutation not found, incomplete strategy
% 1.66/1.41 % (1255)------------------------------
% 1.66/1.41 % (1255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1255)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (1255)Memory used [KB]: 5373
% 1.66/1.41 % (1255)Time elapsed: 0.003 s
% 1.66/1.41 % (1255)Instructions burned: 1 (million)
% 1.66/1.41 % (1255)------------------------------
% 1.66/1.41 % (1255)------------------------------
% 1.66/1.41 % (1254)Refutation not found, incomplete strategy
% 1.66/1.41 % (1254)------------------------------
% 1.66/1.41 % (1254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1254)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (1254)Memory used [KB]: 5373
% 1.66/1.41 % (1254)Time elapsed: 0.003 s
% 1.66/1.41 % (1254)Instructions burned: 1 (million)
% 1.66/1.41 % (1259)First to succeed.
% 1.66/1.41 % (1254)------------------------------
% 1.66/1.41 % (1254)------------------------------
% 1.66/1.41 % (1253)Also succeeded, but the first one will report.
% 1.66/1.41 % (1259)Refutation found. Thanks to Tanya!
% 1.66/1.41 % SZS status Unsatisfiable for DTF2THF_1154
% 1.66/1.41 % SZS output start Proof for DTF2THF_1154
% 1.66/1.41 thf(func_def_0, type, h: $o > $i).
% 1.66/1.41 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.41 thf(f10,plain,(
% 1.66/1.41 $false),
% 1.66/1.41 inference(subsumption_resolution,[status(thm)],[f9,f7])).
% 1.66/1.41 thf(f7,plain,(
% 1.66/1.41 ((h @ $false) = (h @ $true))),
% 1.66/1.41 inference(equality_proxy_clausification,[status(thm)],[f6])).
% 1.66/1.41 thf(f6,plain,(
% 1.66/1.41 ($false != ((h @ $true) = (h @ $false)))),
% 1.66/1.41 inference(equality_resolution,[status(thm)],[f5])).
% 1.66/1.41 thf(f5,plain,(
% 1.66/1.41 ((h @ $false) != (h @ ((h @ $true) = (h @ $false))))),
% 1.66/1.41 inference(boolean_simplification,[status(thm)],[f4])).
% 1.66/1.41 thf(f4,plain,(
% 1.66/1.41 ((h @ $false) != (h @ ((h @ (~ $false)) = (h @ $false))))),
% 1.66/1.41 inference(cnf_transformation,[status(thm)],[f3])).
% 1.66/1.41 thf(f3,plain,(
% 1.66/1.41 ((h @ $false) != (h @ ((h @ (~ $false)) = (h @ $false))))),
% 1.66/1.41 inference(fool_elimination,[status(thm)],[f1])).
% 1.66/1.41 thf(f1,axiom,(
% 1.66/1.41 ((h @ ((h @ ~$false) = (h @ $false))) != (h @ $false))),
% 1.66/1.41 file('/export/starexec/sandbox/tmp/tmp.g3JvkDcKRP/DTF2THF_1154.p',1)).
% 1.66/1.41 thf(f9,plain,(
% 1.66/1.41 ((h @ $false) != (h @ $true))),
% 1.66/1.41 inference(boolean_simplification,[status(thm)],[f8])).
% 1.66/1.41 thf(f8,plain,(
% 1.66/1.41 ((h @ ((h @ $false) = (h @ $false))) != (h @ $false))),
% 1.66/1.41 inference(backward_demodulation,[status(thm)],[f5,f7])).
% 1.66/1.41 % SZS output end Proof for DTF2THF_1154
% 1.66/1.41 % (1259)------------------------------
% 1.66/1.41 % (1259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (1259)Termination reason: Refutation
% 1.66/1.41
% 1.66/1.41 % (1259)Memory used [KB]: 5500
% 1.66/1.41 % (1259)Time elapsed: 0.003 s
% 1.66/1.41 % (1259)Instructions burned: 1 (million)
% 1.66/1.41 % (1259)------------------------------
% 1.66/1.41 % (1259)------------------------------
% 1.66/1.41 % (1252)Success in time 0.014 s
%------------------------------------------------------------------------------