%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO212^5 : 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 : n029.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 09:53:41 AM UTC 2026
% Result : Theorem 1.52s 1.37s
% Output : Refutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO212^5 : 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
% 0.13/0.30 % Computer : n029.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 14:26:14 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SYO212^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.40 % Domain : Syntactic
% 0.18/0.40 % Problem : TPS problem from BASIC-HO-PROP-THMS
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Bro09]
% 0.18/0.40 % Names : tps_0668 [Bro09]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % 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 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.18/0.40 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.40 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.40 % Number of connectives : 6 ( 0 ~; 0 |; 2 &; 3 @)
% 0.18/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 5 ( 5 avg)
% 0.18/0.40 % Number of types : 1 ( 0 usr)
% 0.18/0.40 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.18/0.40 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.18/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf(b,type,
% 0.18/0.40 b: $o ).
% 0.18/0.40
% 0.18/0.40 thf(a,type,
% 0.18/0.40 a: $o ).
% 0.18/0.40
% 0.18/0.40 thf(cEMB2,conjecture,
% 0.18/0.40 ! [Xp: $o > $o] :
% 0.18/0.40 ( ( ( Xp @ a )
% 0.18/0.40 & ( Xp @ b ) )
% 0.18/0.40 => ( Xp
% 0.18/0.40 @ ( a
% 0.18/0.40 & b ) ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.52/1.34 ---- Embedded in THF ---
% 1.52/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.34 %%% Generated on Tue Feb 24 14:26:15 EST 2026
% 1.52/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.34 %%% Logic specification used:
% 1.52/1.34 %%% thf(spec, logic, $$dhol).
% 1.52/1.34
% 1.52/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6WJNR3fufM/DTF2DTF32397.p
% 1.52/1.34 thf(b, type, b: $o).
% 1.52/1.34 thf(a, type, a: $o).
% 1.52/1.34 thf(cEMB2, conjecture, (! [Xp:($o > $o)]: ((((Xp @ a) & (Xp @ b)) => (Xp @ (a & b)))))).
% 1.52/1.34 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.6WJNR3fufM/DTF2DTF32397.p
% 1.52/1.34 ------------------------
% 1.52/1.35 ---- Cleaned THF ---
% 1.52/1.35 thf(b,type,
% 1.52/1.35 b: $o ).
% 1.52/1.35
% 1.52/1.35 thf(a,type,
% 1.52/1.35 a: $o ).
% 1.52/1.35
% 1.52/1.35 thf(cEMB2,conjecture,
% 1.52/1.35 ! [Xp: $o > $o] :
% 1.52/1.35 ( ( ( Xp @ a )
% 1.52/1.35 & ( Xp @ b ) )
% 1.52/1.35 => ( Xp
% 1.52/1.35 @ ( a
% 1.52/1.35 & b ) ) ) ).
% 1.52/1.35 ------------------------
% 1.52/1.37 % (32500)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_32397 for (3000ds/275Mi)
% 1.52/1.37 % (32498)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32397 for (3000ds/2Mi)
% 1.52/1.37 % (32497)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_32397 for (3000ds/27Mi)
% 1.52/1.37 % (32495)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32397 for (3000ds/183Mi)
% 1.52/1.37 % (32501)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32397 for (3000ds/18Mi)
% 1.52/1.37 % (32499)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_32397 for (3000ds/2Mi)
% 1.52/1.37 % (32500)Refutation not found, incomplete strategy
% 1.52/1.37 % (32500)------------------------------
% 1.52/1.37 % (32500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.37 % (32500)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.37
% 1.52/1.37 % (32498)Refutation not found, incomplete strategy
% 1.52/1.37 % (32498)------------------------------
% 1.52/1.37 % (32498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.37 % (32498)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.37
% 1.52/1.37
% 1.52/1.37 % (32498)Memory used [KB]: 5500
% 1.52/1.37 % (32498)Time elapsed: 0.003 s
% 1.52/1.37 % (32498)Instructions burned: 1 (million)
% 1.52/1.37 % (32498)------------------------------
% 1.52/1.37 % (32498)------------------------------
% 1.52/1.37
% 1.52/1.37 % (32500)Memory used [KB]: 5500
% 1.52/1.37 % (32497)Refutation not found, incomplete strategy
% 1.52/1.37 % (32497)------------------------------
% 1.52/1.37 % (32497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.37 % (32497)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.37
% 1.52/1.37
% 1.52/1.37 % (32497)Memory used [KB]: 5500
% 1.52/1.37 % (32497)Time elapsed: 0.003 s
% 1.52/1.37 % (32497)Instructions burned: 1 (million)
% 1.52/1.37 % (32497)------------------------------
% 1.52/1.37 % (32497)------------------------------
% 1.52/1.37 % (32500)Time elapsed: 0.003 s
% 1.52/1.37 % (32500)Instructions burned: 2 (million)
% 1.52/1.37 % (32500)------------------------------
% 1.52/1.37 % (32500)------------------------------
% 1.52/1.37 % (32499)Refutation not found, incomplete strategy
% 1.52/1.37 % (32499)------------------------------
% 1.52/1.37 % (32499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.37 % (32499)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.37
% 1.52/1.37
% 1.52/1.37 % (32499)Memory used [KB]: 5500
% 1.52/1.37 % (32499)Time elapsed: 0.003 s
% 1.52/1.37 % (32499)Instructions burned: 1 (million)
% 1.52/1.37 % (32499)------------------------------
% 1.52/1.37 % (32499)------------------------------
% 1.52/1.37 % (32495)First to succeed.
% 1.52/1.37 % (32496)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_32397 for (3000ds/4Mi)
% 1.52/1.37 % (32501)Also succeeded, but the first one will report.
% 1.52/1.37 % (32495)Refutation found. Thanks to Tanya!
% 1.52/1.37 % SZS status Theorem for DTF2THF_32397
% 1.52/1.37 % SZS output start Proof for DTF2THF_32397
% 1.52/1.37 thf(func_def_6, type, sK0: $o > $o).
% 1.52/1.37 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 1.52/1.37 thf(f63,plain,(
% 1.52/1.37 $false),
% 1.52/1.37 inference(avatar_sat_refutation,[status(thm)],[f52,f57,f62])).
% 1.52/1.37 thf(f62,plain,(
% 1.52/1.37 ~spl1_3),
% 1.52/1.37 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.52/1.37 thf(f61,plain,(
% 1.52/1.37 $false | ~spl1_3),
% 1.52/1.37 inference(subsumption_resolution,[status(thm)],[f59,f60])).
% 1.52/1.37 thf(f60,plain,(
% 1.52/1.37 ((sK0 @ $false) != $true) | ~spl1_3),
% 1.52/1.37 inference(boolean_simplification,[status(thm)],[f58])).
% 1.52/1.37 thf(f58,plain,(
% 1.52/1.37 ($true != (sK0 @ ($false & a))) | ~spl1_3),
% 1.52/1.37 inference(superposition,[status(thm)],[f11,f44])).
% 1.52/1.37 thf(f44,plain,(
% 1.52/1.37 (b = $false) | ~spl1_3),
% 1.52/1.37 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.52/1.37 thf(f42,definition,(
% 1.52/1.37 spl1_3 <=> (b = $false)),
% 1.52/1.37 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.52/1.37 thf(f11,plain,(
% 1.52/1.37 ($true != (sK0 @ (b & a)))),
% 1.52/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.52/1.37 thf(f9,plain,(
% 1.52/1.37 ($true = (sK0 @ b)) & ($true != (sK0 @ (b & a))) & ((sK0 @ a) = $true)),
% 1.52/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.52/1.37 thf(f8,plain,(
% 1.52/1.37 ? [X0 : $o > $o] : (((X0 @ b) = $true) & ((X0 @ (b & a)) != $true) & ((X0 @ a) = $true)) => (($true = (sK0 @ b)) & ($true != (sK0 @ (b & a))) & ((sK0 @ a) = $true))),
% 1.52/1.37 introduced(definition,[],[choice_axiom])).
% 1.52/1.37 thf(f7,plain,(
% 1.52/1.37 ? [X0 : $o > $o] : (((X0 @ b) = $true) & ((X0 @ (b & a)) != $true) & ((X0 @ a) = $true))),
% 1.52/1.37 inference(flattening,[status(thm)],[f6])).
% 1.52/1.37 thf(f6,plain,(
% 1.52/1.37 ? [X0 : $o > $o] : (((X0 @ (b & a)) != $true) & (((X0 @ a) = $true) & ((X0 @ b) = $true)))),
% 1.52/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.37 thf(f5,plain,(
% 1.52/1.37 ~! [X0 : $o > $o] : ((((X0 @ a) = $true) & ((X0 @ b) = $true)) => ((X0 @ (b & a)) = $true))),
% 1.52/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.37 thf(f4,plain,(
% 1.52/1.37 ~! [X0 : $o > $o] : (((X0 @ a) & (X0 @ b)) => (X0 @ a & b))),
% 1.52/1.37 inference(rectify,[status(thm)],[f2])).
% 1.52/1.37 thf(f2,negated_conjecture,(
% 1.52/1.37 ~! [X0 : $o > $o] : (((X0 @ a) & (X0 @ b)) => (X0 @ a & b))),
% 1.52/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.37 thf(f1,conjecture,(
% 1.52/1.37 ! [X0 : $o > $o] : (((X0 @ a) & (X0 @ b)) => (X0 @ a & b))),
% 1.52/1.37 file('/export/starexec/sandbox/tmp/tmp.6WJNR3fufM/DTF2THF_32397.p',cEMB2)).
% 1.52/1.37 thf(f59,plain,(
% 1.52/1.37 ((sK0 @ $false) = $true) | ~spl1_3),
% 1.52/1.37 inference(superposition,[status(thm)],[f12,f44])).
% 1.52/1.37 thf(f12,plain,(
% 1.52/1.37 ($true = (sK0 @ b))),
% 1.52/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.52/1.37 thf(f57,plain,(
% 1.52/1.37 ~spl1_4),
% 1.52/1.37 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.52/1.37 thf(f56,plain,(
% 1.52/1.37 $false | ~spl1_4),
% 1.52/1.37 inference(subsumption_resolution,[status(thm)],[f55,f54])).
% 1.52/1.37 thf(f54,plain,(
% 1.52/1.37 ((sK0 @ $false) = $true) | ~spl1_4),
% 1.52/1.37 inference(superposition,[status(thm)],[f10,f48])).
% 1.52/1.37 thf(f48,plain,(
% 1.52/1.37 (a = $false) | ~spl1_4),
% 1.52/1.37 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.52/1.37 thf(f46,definition,(
% 1.52/1.37 spl1_4 <=> (a = $false)),
% 1.52/1.37 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.52/1.37 thf(f10,plain,(
% 1.52/1.37 ((sK0 @ a) = $true)),
% 1.52/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.52/1.37 thf(f55,plain,(
% 1.52/1.37 ((sK0 @ $false) != $true) | ~spl1_4),
% 1.52/1.37 inference(boolean_simplification,[status(thm)],[f53])).
% 1.52/1.37 thf(f53,plain,(
% 1.52/1.37 ((sK0 @ (b & $false)) != $true) | ~spl1_4),
% 1.52/1.37 inference(superposition,[status(thm)],[f11,f48])).
% 1.52/1.37 thf(f52,plain,(
% 1.52/1.37 spl1_4 | spl1_3),
% 1.52/1.37 inference(avatar_split_clause,[status(thm)],[f19,f42,f46])).
% 1.52/1.37 thf(f19,plain,(
% 1.52/1.37 (a = $false) | (b = $false)),
% 1.52/1.37 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.52/1.37 thf(f18,plain,(
% 1.52/1.37 (b = $false) | (a = $false) | (a = $false)),
% 1.52/1.37 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.37 thf(f17,plain,(
% 1.52/1.37 (a = $false) | ($false = (b & a))),
% 1.52/1.37 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.52/1.37 thf(f15,plain,(
% 1.52/1.37 (a != (b & a))),
% 1.52/1.37 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.52/1.37 thf(f14,plain,(
% 1.52/1.37 ($true != $true) | (a != (b & a))),
% 1.52/1.37 inference(constrained_superposition,[status(thm)],[f11,f10])).
% 1.52/1.37 % SZS output end Proof for DTF2THF_32397
% 1.52/1.37 % (32495)------------------------------
% 1.52/1.37 % (32495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.37 % (32495)Termination reason: Refutation
% 1.52/1.37
% 1.52/1.37 % (32495)Memory used [KB]: 5500
% 1.52/1.37 % (32495)Time elapsed: 0.004 s
% 1.52/1.37 % (32495)Instructions burned: 2 (million)
% 1.52/1.37 % (32495)------------------------------
% 1.52/1.37 % (32495)------------------------------
% 1.52/1.37 % (32494)Success in time 0.018 s
%------------------------------------------------------------------------------