%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM781^3 : TPTP v9.2.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:24:41 AM UTC 2026
% Result : Theorem 0.32s 1.33s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
vEPSILON:
!>[X0: $tType] : sTfun(sTfun(X0,$o),X0) ).
fof(f7,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f6]) ).
fof(f6,plain,
cX != cX,
inference(definition_unfolding,[status(thm)],[f5,f4]) ).
fof(f4,plain,
cY = cX,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f3,plain,
( cY != cX
& cY = cX ),
inference(ennf_transformation,[status(thm)],[f2]) ).
fof(f2,negated_conjecture,
~ ( cY = cX
=> cY = cX ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1,conjecture,
( cY = cX
=> cY = cX ),
file('/export/starexec/sandbox2/tmp/tmp.mbcZAzFr5W/DTF2THF_17665.p',cTHM76) ).
fof(f5,plain,
cY != cX,
inference(cnf_transformation,[status(thm)],[f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM781^3 : TPTP v9.2.1. Released v5.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.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 11:13:54 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : NUM781^3 : TPTP v9.2.1. Released v5.1.0.
% 0.26/0.47 % Domain : Number Theory
% 0.26/0.47 % Problem : Landau theorem 79
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English : Symmetry of equality.
% 0.26/0.47
% 0.26/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.26/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Bro09]
% 0.26/0.47 % Names : tps_0019 [Bro09]
% 0.26/0.47 % : THM76 [TPS]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0
% 0.26/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.26/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.26/0.47 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 0 @)
% 0.26/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 2 ( 2 avg)
% 0.26/0.47 % Number of types : 1 ( 0 usr)
% 0.26/0.47 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.47 % :
% 0.26/0.47 % : Renamed from SYO343^5
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(cY,type,
% 0.26/0.47 cY: $i ).
% 0.26/0.47
% 0.26/0.47 thf(cX,type,
% 0.26/0.47 cX: $i ).
% 0.26/0.47
% 0.26/0.47 thf(cTHM76,conjecture,
% 0.26/0.47 ( ( cY = cX )
% 0.26/0.47 => ( cX = cY ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 11:13:55 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mbcZAzFr5W/DTF2DTF17665.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.31 thf(cY,type,
% 0.32/1.31 cY: $i ).
% 0.32/1.31
% 0.32/1.31 thf(cX,type,
% 0.32/1.31 cX: $i ).
% 0.32/1.31
% 0.32/1.31 thf(cTHM76,conjecture,
% 0.32/1.31 ( ( cY = cX )
% 0.32/1.31 => ( cX = cY ) ) ).
% 0.32/1.31 ------------------------
% 0.32/1.33 % (17881)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_17665 for (2999ds/27Mi)
% 0.32/1.33 % (17881)First to succeed.
% 0.32/1.33 % (17881)Refutation found. Thanks to Tanya!
% 0.32/1.33 % SZS status Theorem for DTF2THF_17665
% 0.32/1.33 % SZS output start Proof for DTF2THF_17665
% 0.32/1.33 tff(func_def_2, type, vEPSILON: !>[X0: $tType]:(sTfun(sTfun(X0,$o),X0))).
% 0.32/1.33 fof(f7,plain,(
% 0.32/1.33 $false),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f6])).
% 0.32/1.33 fof(f6,plain,(
% 0.32/1.33 cX != cX),
% 0.32/1.33 inference(definition_unfolding,[status(thm)],[f5,f4])).
% 0.32/1.33 fof(f4,plain,(
% 0.32/1.33 cY = cX),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f3])).
% 0.32/1.33 fof(f3,plain,(
% 0.32/1.33 cY != cX & cY = cX),
% 0.32/1.33 inference(ennf_transformation,[status(thm)],[f2])).
% 0.32/1.33 fof(f2,negated_conjecture,(
% 0.32/1.33 ~(cY = cX => cY = cX)),
% 0.32/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.33 fof(f1,conjecture,(
% 0.32/1.33 cY = cX => cY = cX),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.mbcZAzFr5W/DTF2THF_17665.p',cTHM76)).
% 0.32/1.33 fof(f5,plain,(
% 0.32/1.33 cY != cX),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f3])).
% 0.32/1.33 % SZS output end Proof for DTF2THF_17665
% 0.32/1.33 % (17881)------------------------------
% 0.32/1.33 % (17881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (17881)Termination reason: Refutation
% 0.32/1.33
% 0.32/1.33 % (17881)Memory used [KB]: 5373
% 0.32/1.33 % (17881)Time elapsed: 0.001 s
% 0.32/1.33 % (17881)------------------------------
% 0.32/1.33 % (17881)------------------------------
% 0.32/1.33 % (17878)Success in time 0.013 s
%------------------------------------------------------------------------------