%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO087^5 : 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 : 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 09:53:21 AM UTC 2026
% Result : Theorem 1.65s 1.46s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 184 ( 49 equ)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 114 ( 46 ~; 17 |; 39 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of FOOLs : 98 ( 98 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 7 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 2 ( 0 !; 2 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
tff(f33,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f30,f32]) ).
tff(f32,plain,
spl0_2,
inference(avatar_split_clause,[status(thm)],[f31,f25]) ).
tff(f25,definition,
( spl0_2
<=> ( cQ = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
tff(f31,plain,
cQ = $true,
inference(subsumption_resolution,[status(thm)],[f12,f10]) ).
tff(f10,plain,
cR != $true,
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f9,plain,
( ( ( ( cQ != $true )
& ( cP != $true ) )
| ( ( cQ = $true )
& ( cP = $true ) ) )
& ( ( ( cQ != $true )
& ( cR = $true ) )
| ( ( cR != $true )
& ( cQ = $true ) ) )
& ( cP != $true )
& ( cR != $true ) ),
inference(flattening,[status(thm)],[f8]) ).
tff(f8,plain,
( ( cR != $true )
& ( ( ( cQ != $true )
& ( cP != $true ) )
| ( ( cQ = $true )
& ( cP = $true ) ) )
& ( ( ( cQ != $true )
& ( cR = $true ) )
| ( ( cR != $true )
& ( cQ = $true ) ) )
& ( cP != $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
tff(f7,plain,
~ ( ( ( ( ( cQ != $true )
& ( cR = $true ) )
| ( ( cR != $true )
& ( cQ = $true ) ) )
& ( cP != $true ) )
=> ( ( ( ( cQ != $true )
& ( cP != $true ) )
| ( ( cQ = $true )
& ( cP = $true ) ) )
=> ( cR = $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
tff(f6,plain,
~ ( ( ( cP != $true )
& ( ( ( cR = $true )
& ( cQ != $true ) )
| ( ( cQ = $true )
& ( cR != $true ) ) ) )
=> ( ( ( ( cP != $true )
& ( cQ != $true ) )
| ( ( cQ = $true )
& ( cP = $true ) ) )
=> ( cR = $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
tff(f5,plain,
~ ( ( ~ cP
& ( ( cR
& ~ cQ )
| ( cQ
& ~ cR ) ) )
=> ( ( ( ~ cP
& ~ cQ )
| ( cP
& cQ ) )
=> cR ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ? [X0: $i] :
( ( ~ cP
& ( ( cR
& ~ cQ )
| ( cQ
& ~ cR ) ) )
=> ( ( ( ~ cP
& ~ cQ )
| ( cP
& cQ ) )
=> cR ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
? [X0: $i] :
( ( ~ cP
& ( ( cR
& ~ cQ )
| ( cQ
& ~ cR ) ) )
=> ( ( ( ~ cP
& ~ cQ )
| ( cP
& cQ ) )
=> cR ) ),
file('/export/starexec/sandbox/tmp/tmp.TeD0zv1lvD/DTF2THF_15787.p',cTHM50_13) ).
tff(f12,plain,
( ( cQ = $true )
| ( cR = $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f30,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f18,f21,f25]) ).
tff(f21,definition,
( spl0_1
<=> ( cP = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
tff(f18,plain,
( ( cQ != $true )
| ( cP = $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f29,plain,
~ spl0_1,
inference(avatar_split_clause,[status(thm)],[f11,f21]) ).
tff(f11,plain,
cP != $true,
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO087^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.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 14:24:16 EST 2026
% 0.21/0.35 % CPUTime :
% 0.21/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SYO087^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.49 % Domain : Syntactic
% 0.29/0.49 % Problem : TPS problem THM50-13
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English : Simple formula for debugging.
% 0.29/0.49
% 0.29/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Bro09]
% 0.29/0.49 % Names : tps_0131 [Bro09]
% 0.29/0.49 % : THM50-13 [TPS]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.29/0.49 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.49 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 10 ( 10 avg)
% 0.29/0.49 % Number of connectives : 14 ( 5 ~; 2 |; 5 &; 0 @)
% 0.29/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.49 % Number of types : 2 ( 0 usr)
% 0.29/0.49 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.29/0.49 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.29/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(cR,type,
% 0.29/0.49 cR: $o ).
% 0.29/0.49
% 0.29/0.49 thf(cQ,type,
% 0.29/0.49 cQ: $o ).
% 0.29/0.49
% 0.29/0.49 thf(cP,type,
% 0.29/0.49 cP: $o ).
% 0.29/0.49
% 0.29/0.49 thf(cTHM50_13,conjecture,
% 0.29/0.49 ? [Xx: $i] :
% 0.29/0.49 ( ( ~ cP
% 0.29/0.49 & ( ( cQ
% 0.29/0.49 & ~ cR )
% 0.29/0.49 | ( ~ cQ
% 0.29/0.49 & cR ) ) )
% 0.29/0.49 => ( ( ( cP
% 0.29/0.49 & cQ )
% 0.29/0.49 | ( ~ cP
% 0.29/0.49 & ~ cQ ) )
% 0.29/0.49 => cR ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.65/1.43 ---- Embedded in THF ---
% 1.65/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.43 %%% Generated on Tue Feb 24 14:24:17 EST 2026
% 1.65/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.43 %%% Logic specification used:
% 1.65/1.43 %%% thf(spec, logic, $$dhol).
% 1.65/1.43
% 1.65/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TeD0zv1lvD/DTF2DTF15787.p
% See solution above
% 1.65/1.43 ------------------------
% 1.65/1.44 ---- Cleaned THF ---
% 1.65/1.44 thf(cR,type,
% 1.65/1.44 cR: $o ).
% 1.65/1.44
% 1.65/1.44 thf(cQ,type,
% 1.65/1.44 cQ: $o ).
% 1.65/1.44
% 1.65/1.44 thf(cP,type,
% 1.65/1.44 cP: $o ).
% 1.65/1.44
% 1.65/1.44 thf(cTHM50_13,conjecture,
% 1.65/1.44 ? [Xx: $i] :
% 1.65/1.44 ( ( ~ cP
% 1.65/1.44 & ( ( cQ
% 1.65/1.44 & ~ cR )
% 1.65/1.44 | ( ~ cQ
% 1.65/1.44 & cR ) ) )
% 1.65/1.44 => ( ( ( cP
% 1.65/1.44 & cQ )
% 1.65/1.44 | ( ~ cP
% 1.65/1.44 & ~ cQ ) )
% 1.65/1.44 => cR ) ) ).
% 1.65/1.44 ------------------------
% 1.65/1.46 % (15888)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_15787 for (3000ds/2Mi)
% 1.65/1.46 % (15887)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15787 for (3000ds/2Mi)
% 1.65/1.46 % (15884)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15787 for (3000ds/183Mi)
% 1.65/1.46 % (15885)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_15787 for (3000ds/4Mi)
% 1.65/1.46 % (15889)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_15787 for (3000ds/275Mi)
% 1.65/1.46 % (15886)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_15787 for (3000ds/27Mi)
% 1.65/1.46 % (15890)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15787 for (3000ds/18Mi)
% 1.65/1.46 % (15889)First to succeed.
% 1.65/1.46 % (15885)Also succeeded, but the first one will report.
% 1.65/1.46 % (15884)Also succeeded, but the first one will report.
% 1.65/1.46 % (15889)Refutation found. Thanks to Tanya!
% 1.65/1.46 % SZS status Theorem for DTF2THF_15787
% 1.65/1.46 % SZS output start Proof for DTF2THF_15787
% 1.65/1.46 tff(f33,plain,(
% 1.65/1.46 $false),
% 1.65/1.46 inference(avatar_sat_refutation,[status(thm)],[f29,f30,f32])).
% 1.65/1.46 tff(f32,plain,(
% 1.65/1.46 spl0_2),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f31,f25])).
% 1.65/1.46 tff(f25,definition,(
% 1.65/1.46 spl0_2 <=> (cQ = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.46 tff(f31,plain,(
% 1.65/1.46 (cQ = $true)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f12,f10])).
% 1.65/1.46 tff(f10,plain,(
% 1.65/1.46 (cR != $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.46 tff(f9,plain,(
% 1.65/1.46 (((cQ != $true) & (cP != $true)) | ((cQ = $true) & (cP = $true))) & (((cQ != $true) & (cR = $true)) | ((cR != $true) & (cQ = $true))) & (cP != $true) & (cR != $true)),
% 1.65/1.46 inference(flattening,[status(thm)],[f8])).
% 1.65/1.46 tff(f8,plain,(
% 1.65/1.46 ((cR != $true) & (((cQ != $true) & (cP != $true)) | ((cQ = $true) & (cP = $true)))) & ((((cQ != $true) & (cR = $true)) | ((cR != $true) & (cQ = $true))) & (cP != $true))),
% 1.65/1.46 inference(ennf_transformation,[status(thm)],[f7])).
% 1.65/1.46 tff(f7,plain,(
% 1.65/1.46 ~(((((cQ != $true) & (cR = $true)) | ((cR != $true) & (cQ = $true))) & (cP != $true)) => ((((cQ != $true) & (cP != $true)) | ((cQ = $true) & (cP = $true))) => (cR = $true)))),
% 1.65/1.46 inference(flattening,[status(thm)],[f6])).
% 1.65/1.46 tff(f6,plain,(
% 1.65/1.46 ~((~(cP = $true) & (((cR = $true) & ~(cQ = $true)) | ((cQ = $true) & ~(cR = $true)))) => (((~(cP = $true) & ~(cQ = $true)) | ((cQ = $true) & (cP = $true))) => (cR = $true)))),
% 1.65/1.46 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.46 tff(f5,plain,(
% 1.65/1.46 ~((~cP & ((cR & ~cQ) | (cQ & ~cR))) => (((~cP & ~cQ) | (cP & cQ)) => cR))),
% 1.65/1.46 inference(rectify,[status(thm)],[f2])).
% 1.65/1.46 tff(f2,negated_conjecture,(
% 1.65/1.46 ~? [X0 : $i] : ((~cP & ((cR & ~cQ) | (cQ & ~cR))) => (((~cP & ~cQ) | (cP & cQ)) => cR))),
% 1.65/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.46 tff(f1,conjecture,(
% 1.65/1.46 ? [X0 : $i] : ((~cP & ((cR & ~cQ) | (cQ & ~cR))) => (((~cP & ~cQ) | (cP & cQ)) => cR))),
% 1.65/1.46 file('/export/starexec/sandbox/tmp/tmp.TeD0zv1lvD/DTF2THF_15787.p',cTHM50_13)).
% 1.65/1.46 tff(f12,plain,(
% 1.65/1.46 (cQ = $true) | (cR = $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.46 tff(f30,plain,(
% 1.65/1.46 ~spl0_2 | spl0_1),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f18,f21,f25])).
% 1.65/1.46 tff(f21,definition,(
% 1.65/1.46 spl0_1 <=> (cP = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.46 tff(f18,plain,(
% 1.65/1.46 (cQ != $true) | (cP = $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.46 tff(f29,plain,(
% 1.65/1.46 ~spl0_1),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f11,f21])).
% 1.65/1.46 tff(f11,plain,(
% 1.65/1.46 (cP != $true)),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.46 % SZS output end Proof for DTF2THF_15787
% 1.65/1.46 % (15889)------------------------------
% 1.65/1.46 % (15889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15889)Termination reason: Refutation
% 1.65/1.46
% 1.65/1.46 % (15889)Memory used [KB]: 5373
% 1.65/1.46 % (15889)Time elapsed: 0.003 s
% 1.65/1.46 % (15889)Instructions burned: 1 (million)
% 1.65/1.46 % (15889)------------------------------
% 1.65/1.46 % (15889)------------------------------
% 1.65/1.46 % (15883)Success in time 0.018 s
%------------------------------------------------------------------------------