%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM782^1 : 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 : n027.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 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 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 : 3 ( 3 usr; 3 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(func_def_3,type,
z0: rat ).
tff(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
tff(f10,plain,
z0 != z0,
inference(definition_unfolding,[status(thm)],[f6,f9]) ).
tff(f9,plain,
x0 = z0,
inference(definition_unfolding,[status(thm)],[f7,f8]) ).
tff(f8,plain,
y0 = z0,
inference(cnf_transformation,[status(thm)],[f2]) ).
tff(f2,axiom,
y0 = z0,
file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',j) ).
tff(f7,plain,
x0 = y0,
inference(cnf_transformation,[status(thm)],[f1]) ).
tff(f1,axiom,
x0 = y0,
file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',i) ).
tff(f6,plain,
x0 != z0,
inference(cnf_transformation,[status(thm)],[f5]) ).
tff(f5,plain,
x0 != z0,
inference(flattening,[status(thm)],[f4]) ).
tff(f4,negated_conjecture,
( ( ~ x0 ) = z0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f3,conjecture,
x0 = z0,
file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',satz80) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM782^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.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 11:14:22 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
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : NUM782^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Number Theory
% 0.19/0.45 % Problem : Landau theorem 80
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : x0 = z0
% 0.19/0.45
% 0.19/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : satz80 [Lan30]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % : Without extensionality : Theorem
% 0.19/0.45 % Rating : 0.00 v7.1.0, 0.12 v7.0.0, 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
% 0.19/0.45 % Syntax : Number of formulae : 7 ( 3 unt; 4 typ; 0 def)
% 0.19/0.45 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.45 % Number of connectives : 0 ( 0 ~; 0 |; 0 &; 0 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.19/0.45 % Number of types : 1 ( 1 usr)
% 0.19/0.45 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 4 ( 3 usr; 3 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments :
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(rat_type,type,
% 0.19/0.45 rat: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(x0,type,
% 0.19/0.45 x0: rat ).
% 0.19/0.45
% 0.19/0.45 thf(y0,type,
% 0.19/0.45 y0: rat ).
% 0.19/0.45
% 0.19/0.45 thf(z0,type,
% 0.19/0.45 z0: rat ).
% 0.19/0.45
% 0.19/0.45 thf(i,axiom,
% 0.19/0.45 x0 = y0 ).
% 0.19/0.45
% 0.19/0.45 thf(j,axiom,
% 0.19/0.45 y0 = z0 ).
% 0.19/0.45
% 0.19/0.45 thf(satz80,conjecture,
% 0.19/0.45 x0 = z0 ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 11:14:23 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2DTF30473.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(rat_type,type,
% 1.49/1.26 rat: $tType ).
% 1.49/1.26
% 1.49/1.26 thf(x0,type,
% 1.49/1.26 x0: rat ).
% 1.49/1.26
% 1.49/1.26 thf(y0,type,
% 1.49/1.26 y0: rat ).
% 1.49/1.26
% 1.49/1.26 thf(z0,type,
% 1.49/1.26 z0: rat ).
% 1.49/1.26
% 1.49/1.26 thf(i,axiom,
% 1.49/1.26 x0 = y0 ).
% 1.49/1.26
% 1.49/1.26 thf(j,axiom,
% 1.49/1.26 y0 = z0 ).
% 1.49/1.26
% 1.49/1.26 thf(satz80,conjecture,
% 1.49/1.26 x0 = z0 ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (30578)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_30473 for (2999ds/2Mi)
% 1.49/1.28 % (30578)First to succeed.
% 1.49/1.28 % (30578)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_30473
% 1.49/1.28 % SZS output start Proof for DTF2THF_30473
% 1.49/1.28 tff(type_def_5, type, rat: $tType).
% 1.49/1.28 tff(func_def_0, type, rat: $tType).
% 1.49/1.28 tff(func_def_1, type, x0: rat).
% 1.49/1.28 tff(func_def_2, type, y0: rat).
% 1.49/1.28 tff(func_def_3, type, z0: rat).
% 1.49/1.28 tff(f11,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.49/1.28 tff(f10,plain,(
% 1.49/1.28 z0 != z0),
% 1.49/1.28 inference(definition_unfolding,[status(thm)],[f6,f9])).
% 1.49/1.28 tff(f9,plain,(
% 1.49/1.28 x0 = z0),
% 1.49/1.28 inference(definition_unfolding,[status(thm)],[f7,f8])).
% 1.49/1.28 tff(f8,plain,(
% 1.49/1.28 y0 = z0),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f2])).
% 1.49/1.28 tff(f2,axiom,(
% 1.49/1.28 y0 = z0),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',j)).
% 1.49/1.28 tff(f7,plain,(
% 1.49/1.28 x0 = y0),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f1])).
% 1.49/1.28 tff(f1,axiom,(
% 1.49/1.28 x0 = y0),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',i)).
% 1.49/1.28 tff(f6,plain,(
% 1.49/1.28 x0 != z0),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f5])).
% 1.49/1.28 tff(f5,plain,(
% 1.49/1.28 x0 != z0),
% 1.49/1.28 inference(flattening,[status(thm)],[f4])).
% 1.49/1.28 tff(f4,negated_conjecture,(
% 1.49/1.28 ~x0 = z0),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f3])).
% 1.49/1.28 tff(f3,conjecture,(
% 1.49/1.28 x0 = z0),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.nb7XnNJfZA/DTF2THF_30473.p',satz80)).
% 1.49/1.28 % SZS output end Proof for DTF2THF_30473
% 1.49/1.28 % (30578)------------------------------
% 1.49/1.28 % (30578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (30578)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (30578)Memory used [KB]: 5373
% 1.49/1.28 % (30578)Time elapsed: 0.003 s
% 1.49/1.28 % (30578)Instructions burned: 1 (million)
% 1.49/1.28 % (30578)------------------------------
% 1.49/1.28 % (30578)------------------------------
% 1.49/1.28 % (30573)Success in time 0.005 s
%------------------------------------------------------------------------------