%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO348^5 : 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 : n024.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 09:54:00 AM UTC 2026
% Result : Theorem 1.55s 1.32s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 45 ( 8 ~; 0 |; 6 &; 19 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: $o > $o ).
thf(f13,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f12,f10]) ).
thf(f10,plain,
( $true
!= ( sK0 @ b ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( a = b )
& ( $true
!= ( sK0 @ b ) )
& ( ( sK0 @ a )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $o > $o] :
( ( ( X0 @ b )
!= $true )
& ( ( X0 @ a )
= $true ) )
=> ( ( $true
!= ( sK0 @ b ) )
& ( ( sK0 @ a )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ( a = b )
& ? [X0: $o > $o] :
( ( ( X0 @ b )
!= $true )
& ( ( X0 @ a )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( a = b )
=> ! [X0: $o > $o] :
( ( ( X0 @ a )
= $true )
=> ( ( X0 @ b )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( a
<=> b )
=> ! [X0: $o > $o] :
( ( X0 @ a )
=> ( X0 @ b ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( a
<=> b )
=> ! [X0: $o > $o] :
( ( X0 @ a )
=> ( X0 @ b ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( a
<=> b )
=> ! [X0: $o > $o] :
( ( X0 @ a )
=> ( X0 @ b ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ViZcYQlcEP/DTF2THF_11918.p',cE1EXT) ).
thf(f12,plain,
( $true
= ( sK0 @ b ) ),
inference(definition_unfolding,[status(thm)],[f9,f11]) ).
thf(f11,plain,
a = b,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f9,plain,
( ( sK0 @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO348^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n024.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Feb 24 09:28:10 EST 2026
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO348^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem E1EXT
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Example from [Ben99] p.115.
% 0.16/0.39
% 0.16/0.39 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0054 [Bro09]
% 0.16/0.39 % : E1EXT [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.39 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.16/0.39 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 2 @)
% 0.16/0.39 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 5 ( 5 avg)
% 0.16/0.39 % Number of types : 1 ( 0 usr)
% 0.16/0.39 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.16/0.39 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(b,type,
% 0.16/0.39 b: $o ).
% 0.16/0.39
% 0.16/0.39 thf(a,type,
% 0.16/0.39 a: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cE1EXT,conjecture,
% 0.16/0.39 ( ( a
% 0.16/0.39 <=> b )
% 0.16/0.39 => ! [P: $o > $o] :
% 0.16/0.39 ( ( P @ a )
% 0.16/0.39 => ( P @ b ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.36/1.28 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 09:28:11 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ViZcYQlcEP/DTF2DTF11918.p
% See solution above
% 1.36/1.29 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.30 thf(b,type,
% 1.36/1.30 b: $o ).
% 1.36/1.30
% 1.36/1.30 thf(a,type,
% 1.36/1.30 a: $o ).
% 1.36/1.30
% 1.36/1.30 thf(cE1EXT,conjecture,
% 1.36/1.30 ( ( a
% 1.36/1.30 <=> b )
% 1.36/1.30 => ! [P: $o > $o] :
% 1.36/1.30 ( ( P @ a )
% 1.36/1.30 => ( P @ b ) ) ) ).
% 1.36/1.30 ------------------------
% 1.55/1.31 % (12019)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_11918 for (3000ds/2Mi)
% 1.55/1.31 % (12015)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11918 for (3000ds/183Mi)
% 1.55/1.31 % (12016)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_11918 for (3000ds/4Mi)
% 1.55/1.31 % (12017)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_11918 for (3000ds/27Mi)
% 1.55/1.31 % (12018)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11918 for (3000ds/2Mi)
% 1.55/1.31 % (12020)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_11918 for (3000ds/275Mi)
% 1.55/1.31 % (12021)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11918 for (3000ds/18Mi)
% 1.55/1.32 % (12021)First to succeed.
% 1.55/1.32 % (12019)Instruction limit reached!
% 1.55/1.32 % (12019)------------------------------
% 1.55/1.32 % (12019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (12019)Termination reason: Unknown
% 1.55/1.32 % (12019)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (12019)Memory used [KB]: 5500
% 1.55/1.32 % (12019)Time elapsed: 0.003 s
% 1.55/1.32 % (12020)Also succeeded, but the first one will report.
% 1.55/1.32 % (12019)Instructions burned: 2 (million)
% 1.55/1.32 % (12019)------------------------------
% 1.55/1.32 % (12019)------------------------------
% 1.55/1.32 % (12015)Also succeeded, but the first one will report.
% 1.55/1.32 % (12021)Refutation found. Thanks to Tanya!
% 1.55/1.32 % SZS status Theorem for DTF2THF_11918
% 1.55/1.32 % SZS output start Proof for DTF2THF_11918
% 1.55/1.32 thf(func_def_5, type, sK0: $o > $o).
% 1.55/1.32 thf(f13,plain,(
% 1.55/1.32 $false),
% 1.55/1.32 inference(subsumption_resolution,[status(thm)],[f12,f10])).
% 1.55/1.32 thf(f10,plain,(
% 1.55/1.32 ($true != (sK0 @ b))),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.32 thf(f8,plain,(
% 1.55/1.32 (a = b) & (($true != (sK0 @ b)) & ((sK0 @ a) = $true))),
% 1.55/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.55/1.32 thf(f7,plain,(
% 1.55/1.32 ? [X0 : $o > $o] : (((X0 @ b) != $true) & ((X0 @ a) = $true)) => (($true != (sK0 @ b)) & ((sK0 @ a) = $true))),
% 1.55/1.32 introduced(definition,[],[choice_axiom])).
% 1.55/1.32 thf(f6,plain,(
% 1.55/1.32 (a = b) & ? [X0 : $o > $o] : (((X0 @ b) != $true) & ((X0 @ a) = $true))),
% 1.55/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.32 thf(f5,plain,(
% 1.55/1.32 ~((a = b) => ! [X0 : $o > $o] : (((X0 @ a) = $true) => ((X0 @ b) = $true)))),
% 1.55/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.32 thf(f4,plain,(
% 1.55/1.32 ~((a <=> b) => ! [X0 : $o > $o] : ((X0 @ a) => (X0 @ b)))),
% 1.55/1.32 inference(rectify,[status(thm)],[f2])).
% 1.55/1.32 thf(f2,negated_conjecture,(
% 1.55/1.32 ~((a <=> b) => ! [X0 : $o > $o] : ((X0 @ a) => (X0 @ b)))),
% 1.55/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.32 thf(f1,conjecture,(
% 1.55/1.32 (a <=> b) => ! [X0 : $o > $o] : ((X0 @ a) => (X0 @ b))),
% 1.55/1.32 file('/export/starexec/sandbox/tmp/tmp.ViZcYQlcEP/DTF2THF_11918.p',cE1EXT)).
% 1.55/1.32 thf(f12,plain,(
% 1.55/1.32 ($true = (sK0 @ b))),
% 1.55/1.32 inference(definition_unfolding,[status(thm)],[f9,f11])).
% 1.55/1.32 thf(f11,plain,(
% 1.55/1.32 (a = b)),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.32 thf(f9,plain,(
% 1.55/1.32 ((sK0 @ a) = $true)),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.32 % SZS output end Proof for DTF2THF_11918
% 1.55/1.32 % (12021)------------------------------
% 1.55/1.32 % (12021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (12021)Termination reason: Refutation
% 1.55/1.32
% 1.55/1.32 % (12021)Memory used [KB]: 5373
% 1.55/1.32 % (12021)Time elapsed: 0.002 s
% 1.55/1.32 % (12021)Instructions burned: 1 (million)
% 1.55/1.32 % (12021)------------------------------
% 1.55/1.32 % (12021)------------------------------
% 1.55/1.32 % (12014)Success in time 0.017 s
%------------------------------------------------------------------------------