%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO039^2 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 09:53:13 AM UTC 2026
% Result : Theorem 1.43s 1.29s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 52 ( 15 ~; 1 |; 0 &; 36 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f9]) ).
thf(f9,plain,
( ( h @ $true )
= ( h @ $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( h @ $true )
= ( h @ $false ) )
!= $false ),
inference(equality_resolution,[status(thm)],[f7]) ).
thf(f7,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ $true )
= ( h @ $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(flattening,[status(thm)],[f4]) ).
thf(f4,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
= ( h @ $false ) ),
file('/export/starexec/sandbox/tmp/tmp.1MSkrjjfWO/DTF2THF_3255.p',1) ).
thf(f14,plain,
( ( h @ $true )
!= ( h @ $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
!= ( ( h @ $true )
= ( h @ $false ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
!= ( ( h @ $true )
= ( h @ $false ) ) )
| ( ( h @ $false )
!= ( h @ $false ) ) ),
inference(constrained_superposition,[status(thm)],[f7,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO039^2 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:23:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.48 ---- Original DTF file ---
% 0.30/0.48 thf(spec,logic,$$dhol).
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 % File : SYO039^2 : TPTP v9.2.1. Released v4.1.0.
% 0.30/0.48 % Domain : Syntactic
% 0.30/0.48 % Problem : Unsatisfiable basic formula 1
% 0.30/0.48 % Version : Especial.
% 0.30/0.48 % Theorem formulation : As a conjecture rather than UNS set.
% 0.30/0.48 % English :
% 0.30/0.48
% 0.30/0.48 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.30/0.48 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.30/0.48 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.30/0.48 % Source : [BS09a]
% 0.30/0.48 % Names : basic1 [Bro09]
% 0.30/0.48
% 0.30/0.48 % Status : Theorem
% 0.30/0.48 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 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, 0.20 v5.3.0, 0.40 v5.0.0, 0.60 v4.1.0
% 0.30/0.48 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.48 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.30/0.48 % Maximal formula atoms : 1 ( 5 avg)
% 0.30/0.48 % Number of connectives : 5 ( 1 ~; 0 |; 0 &; 4 @)
% 0.30/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.48 % Maximal formula depth : 1 ( 1 avg)
% 0.30/0.48 % Number of types : 2 ( 0 usr)
% 0.30/0.48 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.30/0.48 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.30/0.48 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.30/0.48 % SPC : TH0_THM_EQU_NAR
% 0.30/0.48
% 0.30/0.48 % Comments : The fragment of simple type theory that restricts equations to
% 0.30/0.48 % base types and disallows lambda abstraction and quantification is
% 0.30/0.48 % decidable. This is an example.
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 thf(h,type,
% 0.30/0.48 h: $o > $i ).
% 0.30/0.48
% 0.30/0.48 thf(1,conjecture,
% 0.30/0.48 ( ( h
% 0.30/0.48 @ ( ( h @ $false )
% 0.30/0.48 = ( h @ ~ $false ) ) )
% 0.30/0.48 = ( h @ $false ) ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 1.43/1.26 ---- Embedded in THF ---
% 1.43/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.26 %%% Generated on Tue Feb 24 14:23:19 EST 2026
% 1.43/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.26 %%% Logic specification used:
% 1.43/1.26 %%% thf(spec, logic, $$dhol).
% 1.43/1.26
% 1.43/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1MSkrjjfWO/DTF2DTF3255.p
% See solution above
% 1.43/1.26 ------------------------
% 1.43/1.27 ---- Cleaned THF ---
% 1.43/1.27 thf(h,type,
% 1.43/1.27 h: $o > $i ).
% 1.43/1.27
% 1.43/1.27 thf(1,conjecture,
% 1.43/1.27 ( ( h
% 1.43/1.27 @ ( ( h @ $false )
% 1.43/1.27 = ( h @ ~ $false ) ) )
% 1.43/1.27 = ( h @ $false ) ) ).
% 1.43/1.27 ------------------------
% 1.43/1.28 % (3578)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_3255 for (2999ds/27Mi)
% 1.43/1.28 % (3576)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3255 for (2999ds/183Mi)
% 1.43/1.28 % (3578)Refutation not found, incomplete strategy
% 1.43/1.28 % (3578)------------------------------
% 1.43/1.28 % (3578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.28 % (3578)Termination reason: Refutation not found, incomplete strategy
% 1.43/1.28
% 1.43/1.28
% 1.43/1.28 % (3578)Memory used [KB]: 5373
% 1.43/1.28 % (3578)Time elapsed: 0.002 s
% 1.43/1.28 % (3578)Instructions burned: 1 (million)
% 1.43/1.28 % (3578)------------------------------
% 1.43/1.28 % (3578)------------------------------
% 1.43/1.29 % (3576)First to succeed.
% 1.43/1.29 % (3576)Refutation found. Thanks to Tanya!
% 1.43/1.29 % SZS status Theorem for DTF2THF_3255
% 1.43/1.29 % SZS output start Proof for DTF2THF_3255
% 1.43/1.29 thf(func_def_0, type, h: $o > $i).
% 1.43/1.29 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.43/1.29 thf(f15,plain,(
% 1.43/1.29 $false),
% 1.43/1.29 inference(subsumption_resolution,[status(thm)],[f14,f9])).
% 1.43/1.29 thf(f9,plain,(
% 1.43/1.29 ((h @ $true) = (h @ $false))),
% 1.43/1.29 inference(equality_proxy_clausification,[status(thm)],[f8])).
% 1.43/1.29 thf(f8,plain,(
% 1.43/1.29 (((h @ $true) = (h @ $false)) != $false)),
% 1.43/1.29 inference(equality_resolution,[status(thm)],[f7])).
% 1.43/1.29 thf(f7,plain,(
% 1.43/1.29 ((h @ $false) != (h @ ((h @ $true) = (h @ $false))))),
% 1.43/1.29 inference(boolean_simplification,[status(thm)],[f6])).
% 1.43/1.29 thf(f6,plain,(
% 1.43/1.29 ((h @ $false) != (h @ ((h @ (~ $false)) = (h @ $false))))),
% 1.43/1.29 inference(cnf_transformation,[status(thm)],[f5])).
% 1.43/1.29 thf(f5,plain,(
% 1.43/1.29 ((h @ $false) != (h @ ((h @ (~ $false)) = (h @ $false))))),
% 1.43/1.29 inference(flattening,[status(thm)],[f4])).
% 1.43/1.29 thf(f4,plain,(
% 1.43/1.29 ~((h @ $false) = (h @ ((h @ (~ $false)) = (h @ $false))))),
% 1.43/1.29 inference(fool_elimination,[status(thm)],[f2])).
% 1.43/1.29 thf(f2,negated_conjecture,(
% 1.43/1.29 ~((h @ ((h @ ~$false) = (h @ $false))) = (h @ $false))),
% 1.43/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.43/1.29 thf(f1,conjecture,(
% 1.43/1.29 ((h @ ((h @ ~$false) = (h @ $false))) = (h @ $false))),
% 1.43/1.29 file('/export/starexec/sandbox/tmp/tmp.1MSkrjjfWO/DTF2THF_3255.p',1)).
% 1.43/1.29 thf(f14,plain,(
% 1.43/1.29 ((h @ $true) != (h @ $false))),
% 1.43/1.29 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.43/1.29 thf(f13,plain,(
% 1.43/1.29 ($true != ((h @ $true) = (h @ $false)))),
% 1.43/1.29 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.43/1.29 thf(f10,plain,(
% 1.43/1.29 ($true != ((h @ $true) = (h @ $false))) | ((h @ $false) != (h @ $false))),
% 1.43/1.29 inference(constrained_superposition,[status(thm)],[f7,f9])).
% 1.43/1.29 % SZS output end Proof for DTF2THF_3255
% 1.43/1.29 % (3576)------------------------------
% 1.43/1.29 % (3576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (3576)Termination reason: Refutation
% 1.43/1.29
% 1.43/1.29 % (3576)Memory used [KB]: 5500
% 1.43/1.29 % (3576)Time elapsed: 0.002 s
% 1.43/1.29 % (3576)------------------------------
% 1.43/1.29 % (3576)------------------------------
% 1.43/1.29 % (3575)Success in time 0.011 s
%------------------------------------------------------------------------------