%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO131^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:53:27 AM UTC 2026
% Result : Theorem 1.18s 1.06s
% Output : Refutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 71 ( 6 ~; 0 |; 1 &; 60 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 2 !; 4 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(func_def_3,type,
g: $i > $i ).
thf(f10,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f9]) ).
thf(f9,plain,
$true != $true,
inference(superposition,[status(thm)],[f8,f7]) ).
thf(f7,plain,
( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
!= $true )
& ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true )
=> ? [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2iYVanZ9Tg/DTF2THF_1125.p',cEXAMPLE1) ).
thf(f8,plain,
! [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO131^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.28 % Computer : n016.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8042.1875MB
% 0.12/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Feb 24 14:25:36 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.39 ---- Original DTF file ---
% 0.15/0.39 thf(spec,logic,$$dhol).
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 % File : SYO131^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.39 % Domain : Syntactic
% 0.15/0.39 % Problem : TPS problem from BASIC-FO-THMS
% 0.15/0.39 % Version : Especial.
% 0.15/0.39 % English :
% 0.15/0.39
% 0.15/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.39 % Source : [Bro09]
% 0.15/0.39 % Names : tps_0709 [Bro09]
% 0.15/0.39
% 0.15/0.39 % Status : Theorem
% 0.15/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.15/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.15/0.39 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.15/0.39 % Maximal formula atoms : 2 ( 2 avg)
% 0.15/0.39 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 10 @)
% 0.15/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.39 % Maximal formula depth : 6 ( 6 avg)
% 0.15/0.39 % Number of types : 2 ( 0 usr)
% 0.15/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.39 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.15/0.39 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.15/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.39
% 0.15/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 thf(f,type,
% 0.15/0.39 f: $i > $i ).
% 0.15/0.39
% 0.15/0.39 thf(cR,type,
% 0.15/0.39 cR: $i > $i > $o ).
% 0.15/0.39
% 0.15/0.39 thf(a,type,
% 0.15/0.39 a: $i ).
% 0.15/0.39
% 0.15/0.39 thf(g,type,
% 0.15/0.39 g: $i > $i ).
% 0.15/0.39
% 0.15/0.39 thf(cEXAMPLE1,conjecture,
% 0.15/0.39 ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
% 0.15/0.39 => ? [Xx: $i] : ( cR @ Xx @ ( f @ Xx ) ) ) ).
% 0.15/0.39
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 ------------------------
% 1.18/1.03 ---- Embedded in THF ---
% 1.18/1.03 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.18/1.03 %%% Generated on Tue Feb 24 14:25:36 EST 2026
% 1.18/1.03 %%% using '$$dhol' embedding, version 1.3.0.
% 1.18/1.03 %%% Logic specification used:
% 1.18/1.03 %%% thf(spec, logic, $$dhol).
% 1.18/1.03
% 1.18/1.03 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2iYVanZ9Tg/DTF2DTF1125.p
% See solution above
% 1.18/1.03 ------------------------
% 1.18/1.04 ---- Cleaned THF ---
% 1.18/1.04 thf(f,type,
% 1.18/1.04 f: $i > $i ).
% 1.18/1.04
% 1.18/1.04 thf(cR,type,
% 1.18/1.04 cR: $i > $i > $o ).
% 1.18/1.04
% 1.18/1.04 thf(a,type,
% 1.18/1.04 a: $i ).
% 1.18/1.04
% 1.18/1.04 thf(g,type,
% 1.18/1.04 g: $i > $i ).
% 1.18/1.04
% 1.18/1.04 thf(cEXAMPLE1,conjecture,
% 1.18/1.04 ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
% 1.18/1.04 => ? [Xx: $i] : ( cR @ Xx @ ( f @ Xx ) ) ) ).
% 1.18/1.04 ------------------------
% 1.18/1.06 % (1253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1125 for (3000ds/183Mi)
% 1.18/1.06 % (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_1125 for (3000ds/4Mi)
% 1.18/1.06 % (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_1125 for (3000ds/2Mi)
% 1.18/1.06 % (1253)First to succeed.
% 1.18/1.06 % (1259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1125 for (3000ds/18Mi)
% 1.18/1.06 % (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_1125 for (3000ds/27Mi)
% 1.18/1.06 % (1256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1125 for (3000ds/2Mi)
% 1.18/1.06 % (1254)Also succeeded, but the first one will report.
% 1.18/1.06 % (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_1125 for (3000ds/275Mi)
% 1.18/1.06 % (1257)Instruction limit reached!
% 1.18/1.06 % (1257)------------------------------
% 1.18/1.06 % (1257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.18/1.06 % (1257)Termination reason: Unknown
% 1.18/1.06 % (1257)Termination phase: Saturation
% 1.18/1.06
% 1.18/1.06 % (1257)Memory used [KB]: 5500
% 1.18/1.06 % (1257)Time elapsed: 0.002 s
% 1.18/1.06 % (1257)Instructions burned: 2 (million)
% 1.18/1.06 % (1257)------------------------------
% 1.18/1.06 % (1257)------------------------------
% 1.18/1.06 % (1253)Refutation found. Thanks to Tanya!
% 1.18/1.06 % SZS status Theorem for DTF2THF_1125
% 1.18/1.06 % SZS output start Proof for DTF2THF_1125
% 1.18/1.06 thf(func_def_0, type, f: $i > $i).
% 1.18/1.06 thf(func_def_1, type, cR: $i > $i > $o).
% 1.18/1.06 thf(func_def_3, type, g: $i > $i).
% 1.18/1.06 thf(f10,plain,(
% 1.18/1.06 $false),
% 1.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 1.18/1.06 thf(f9,plain,(
% 1.18/1.06 ($true != $true)),
% 1.18/1.06 inference(superposition,[status(thm)],[f8,f7])).
% 1.18/1.06 thf(f7,plain,(
% 1.18/1.06 ((cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) = $true)),
% 1.18/1.06 inference(cnf_transformation,[status(thm)],[f6])).
% 1.18/1.06 thf(f6,plain,(
% 1.18/1.06 ! [X0 : $i] : ((cR @ X0 @ (f @ X0)) != $true) & ((cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) = $true)),
% 1.18/1.06 inference(ennf_transformation,[status(thm)],[f5])).
% 1.18/1.06 thf(f5,plain,(
% 1.18/1.06 ~(((cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) = $true) => ? [X0 : $i] : ((cR @ X0 @ (f @ X0)) = $true))),
% 1.18/1.06 inference(fool_elimination,[status(thm)],[f4])).
% 1.18/1.06 thf(f4,plain,(
% 1.18/1.06 ~((cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) => ? [X0 : $i] : (cR @ X0 @ (f @ X0)))),
% 1.18/1.06 inference(rectify,[status(thm)],[f2])).
% 1.18/1.06 thf(f2,negated_conjecture,(
% 1.18/1.06 ~((cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) => ? [X0 : $i] : (cR @ X0 @ (f @ X0)))),
% 1.18/1.06 inference(negated_conjecture,[status(cth)],[f1])).
% 1.18/1.06 thf(f1,conjecture,(
% 1.18/1.06 (cR @ (g @ (f @ a)) @ (f @ (g @ (f @ a)))) => ? [X0 : $i] : (cR @ X0 @ (f @ X0))),
% 1.18/1.06 file('/export/starexec/sandbox2/tmp/tmp.2iYVanZ9Tg/DTF2THF_1125.p',cEXAMPLE1)).
% 1.18/1.06 thf(f8,plain,(
% 1.18/1.06 ( ! [X0 : $i] : (((cR @ X0 @ (f @ X0)) != $true)) )),
% 1.18/1.06 inference(cnf_transformation,[status(thm)],[f6])).
% 1.18/1.06 % SZS output end Proof for DTF2THF_1125
% 1.18/1.06 % (1253)------------------------------
% 1.18/1.06 % (1253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.18/1.06 % (1253)Termination reason: Refutation
% 1.18/1.06
% 1.18/1.06 % (1253)Memory used [KB]: 5500
% 1.18/1.06 % (1253)Time elapsed: 0.002 s
% 1.18/1.06 % (1253)Instructions burned: 1 (million)
% 1.18/1.06 % (1253)------------------------------
% 1.18/1.06 % (1253)------------------------------
% 1.18/1.06 % (1252)Success in time 0.016 s
%------------------------------------------------------------------------------