%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM781^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 09:24:41 AM UTC 2026
% Result : Theorem 0.81s 0.89s
% Output : Refutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
rat: $tType ).
tff(func_def_0,type,
rat: $tType ).
tff(func_def_1,type,
x0: rat ).
tff(func_def_2,type,
y0: rat ).
tff(f8,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f7]) ).
tff(f7,plain,
y0 != y0,
inference(definition_unfolding,[status(thm)],[f5,f6]) ).
tff(f6,plain,
x0 = y0,
inference(cnf_transformation,[status(thm)],[f1]) ).
tff(f1,axiom,
x0 = y0,
file('/export/starexec/sandbox2/tmp/tmp.b9s7c3Bawc/DTF2THF_27483.p',i) ).
tff(f5,plain,
x0 != y0,
inference(cnf_transformation,[status(thm)],[f4]) ).
tff(f4,plain,
x0 != y0,
inference(flattening,[status(thm)],[f3]) ).
tff(f3,negated_conjecture,
( ( ~ x0 ) = y0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f2,conjecture,
x0 = y0,
file('/export/starexec/sandbox2/tmp/tmp.b9s7c3Bawc/DTF2THF_27483.p',satz79) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM781^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 06:13:40 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : NUM781^1 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.31 % Domain : Number Theory
% 0.07/0.31 % Problem : Landau theorem 79
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English : y0 = x0
% 0.07/0.31
% 0.07/0.31 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.07/0.31 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.07/0.31 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : satz79 [Lan30]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % : Without extensionality : Theorem
% 0.07/0.31 % 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 v4.1.0, 0.00 v3.7.0
% 0.07/0.31 % Syntax : Number of formulae : 5 ( 2 unt; 3 typ; 0 def)
% 0.07/0.31 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.31 % Number of connectives : 0 ( 0 ~; 0 |; 0 &; 0 @)
% 0.07/0.31 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 1 ( 1 avg)
% 0.07/0.31 % Number of types : 1 ( 1 usr)
% 0.07/0.31 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.07/0.31 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments :
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(rat_type,type,
% 0.07/0.31 rat: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(x0,type,
% 0.07/0.31 x0: rat ).
% 0.07/0.31
% 0.07/0.31 thf(y0,type,
% 0.07/0.31 y0: rat ).
% 0.07/0.31
% 0.07/0.31 thf(i,axiom,
% 0.07/0.31 x0 = y0 ).
% 0.07/0.31
% 0.07/0.31 thf(satz79,conjecture,
% 0.07/0.31 y0 = x0 ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.81/0.87 ---- Embedded in THF ---
% 0.81/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.81/0.87 %%% Generated on Tue Feb 24 06:13:41 EST 2026
% 0.81/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.81/0.87 %%% Logic specification used:
% 0.81/0.87 %%% thf(spec, logic, $$dhol).
% 0.81/0.87
% 0.81/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.b9s7c3Bawc/DTF2DTF27483.p
% See solution above
% 0.81/0.87 ------------------------
% 0.81/0.88 ---- Cleaned THF ---
% 0.81/0.88 thf(rat_type,type,
% 0.81/0.88 rat: $tType ).
% 0.81/0.88
% 0.81/0.88 thf(x0,type,
% 0.81/0.88 x0: rat ).
% 0.81/0.88
% 0.81/0.88 thf(y0,type,
% 0.81/0.88 y0: rat ).
% 0.81/0.88
% 0.81/0.88 thf(i,axiom,
% 0.81/0.88 x0 = y0 ).
% 0.81/0.88
% 0.81/0.88 thf(satz79,conjecture,
% 0.81/0.88 y0 = x0 ).
% 0.81/0.88 ------------------------
% 0.81/0.89 % (27691)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_27483 for (3000ds/275Mi)
% 0.81/0.89 % (27687)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_27483 for (3000ds/4Mi)
% 0.81/0.89 % (27690)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_27483 for (3000ds/2Mi)
% 0.81/0.89 % (27688)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_27483 for (3000ds/27Mi)
% 0.81/0.89 % (27686)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27483 for (3000ds/183Mi)
% 0.81/0.89 % (27689)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27483 for (3000ds/2Mi)
% 0.81/0.89 % (27692)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27483 for (3000ds/18Mi)
% 0.81/0.89 % (27686)First to succeed.
% 0.81/0.89 % (27687)Also succeeded, but the first one will report.
% 0.81/0.89 % (27688)Also succeeded, but the first one will report.
% 0.81/0.89 % (27686)Refutation found. Thanks to Tanya!
% 0.81/0.89 % SZS status Theorem for DTF2THF_27483
% 0.81/0.89 % SZS output start Proof for DTF2THF_27483
% 0.81/0.89 tff(type_def_5, type, rat: $tType).
% 0.81/0.89 tff(func_def_0, type, rat: $tType).
% 0.81/0.89 tff(func_def_1, type, x0: rat).
% 0.81/0.89 tff(func_def_2, type, y0: rat).
% 0.81/0.89 tff(f8,plain,(
% 0.81/0.89 $false),
% 0.81/0.89 inference(trivial_inequality_removal,[status(thm)],[f7])).
% 0.81/0.89 tff(f7,plain,(
% 0.81/0.89 y0 != y0),
% 0.81/0.89 inference(definition_unfolding,[status(thm)],[f5,f6])).
% 0.81/0.89 tff(f6,plain,(
% 0.81/0.89 x0 = y0),
% 0.81/0.89 inference(cnf_transformation,[status(thm)],[f1])).
% 0.81/0.89 tff(f1,axiom,(
% 0.81/0.89 x0 = y0),
% 0.81/0.89 file('/export/starexec/sandbox2/tmp/tmp.b9s7c3Bawc/DTF2THF_27483.p',i)).
% 0.81/0.89 tff(f5,plain,(
% 0.81/0.89 x0 != y0),
% 0.81/0.89 inference(cnf_transformation,[status(thm)],[f4])).
% 0.81/0.89 tff(f4,plain,(
% 0.81/0.89 x0 != y0),
% 0.81/0.89 inference(flattening,[status(thm)],[f3])).
% 0.81/0.89 tff(f3,negated_conjecture,(
% 0.81/0.89 ~x0 = y0),
% 0.81/0.89 inference(negated_conjecture,[status(cth)],[f2])).
% 0.81/0.89 tff(f2,conjecture,(
% 0.81/0.89 x0 = y0),
% 0.81/0.89 file('/export/starexec/sandbox2/tmp/tmp.b9s7c3Bawc/DTF2THF_27483.p',satz79)).
% 0.81/0.89 % SZS output end Proof for DTF2THF_27483
% 0.81/0.89 % (27686)------------------------------
% 0.81/0.89 % (27686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (27686)Termination reason: Refutation
% 0.81/0.89
% 0.81/0.89 % (27686)Memory used [KB]: 5373
% 0.81/0.89 % (27686)Time elapsed: 0.002 s
% 0.81/0.89 % (27686)Instructions burned: 1 (million)
% 0.81/0.89 % (27686)------------------------------
% 0.81/0.89 % (27686)------------------------------
% 0.81/0.89 % (27685)Success in time 0.01 s
%------------------------------------------------------------------------------