%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM674^1 : TPTP v9.2.1. Released v3.7.0.
% 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 09:24:13 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% 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; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 24 ( 4 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(f9,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f8]) ).
thf(f8,plain,
( ( pl @ z @ y )
!= ( pl @ z @ y ) ),
inference(definition_unfolding,[status(thm)],[f6,f7]) ).
thf(f7,plain,
x = y,
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
x = y,
file('/export/starexec/sandbox/tmp/tmp.gXdwAelaYt/DTF2THF_32703.p',i) ).
thf(f6,plain,
( ( pl @ z @ x )
!= ( pl @ z @ y ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( pl @ z @ x )
!= ( pl @ z @ y ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( pl @ z @ x )
!= ( pl @ z @ y ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( pl @ z @ x )
= ( pl @ z @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.gXdwAelaYt/DTF2THF_32703.p',satz19e) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM674^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.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 11:11:31 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : NUM674^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Number Theory
% 0.19/0.46 % Problem : Landau theorem 19e
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : pl z x = pl z y
% 0.19/0.46
% 0.19/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : satz19e [Lan30]
% 0.19/0.46 % : satz32e [Lan30]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % : Without extensionality : Theorem
% 0.19/0.46 % 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
% 0.19/0.46 % Syntax : Number of formulae : 7 ( 2 unt; 5 typ; 0 def)
% 0.19/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.19/0.46 % Number of types : 1 ( 1 usr)
% 0.19/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(nat_type,type,
% 0.19/0.46 nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(x,type,
% 0.19/0.46 x: nat ).
% 0.19/0.46
% 0.19/0.46 thf(y,type,
% 0.19/0.46 y: nat ).
% 0.19/0.46
% 0.19/0.46 thf(z,type,
% 0.19/0.46 z: nat ).
% 0.19/0.46
% 0.19/0.46 thf(i,axiom,
% 0.19/0.46 x = y ).
% 0.19/0.46
% 0.19/0.46 thf(pl,type,
% 0.19/0.46 pl: nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(satz19e,conjecture,
% 0.19/0.46 ( ( pl @ z @ x )
% 0.19/0.46 = ( pl @ z @ y ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 11:11:32 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gXdwAelaYt/DTF2DTF32703.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(nat_type,type,
% 1.49/1.25 nat: $tType ).
% 1.49/1.25
% 1.49/1.25 thf(x,type,
% 1.49/1.25 x: nat ).
% 1.49/1.25
% 1.49/1.25 thf(y,type,
% 1.49/1.25 y: nat ).
% 1.49/1.25
% 1.49/1.25 thf(z,type,
% 1.49/1.25 z: nat ).
% 1.49/1.25
% 1.49/1.25 thf(i,axiom,
% 1.49/1.25 x = y ).
% 1.49/1.25
% 1.49/1.25 thf(pl,type,
% 1.49/1.25 pl: nat > nat > nat ).
% 1.49/1.25
% 1.49/1.25 thf(satz19e,conjecture,
% 1.49/1.25 ( ( pl @ z @ x )
% 1.49/1.25 = ( pl @ z @ y ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.27 % (342)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32703 for (3000ds/183Mi)
% 1.49/1.27 % (342)First to succeed.
% 1.49/1.27 % (348)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32703 for (3000ds/18Mi)
% 1.49/1.27 % (348)Also succeeded, but the first one will report.
% 1.49/1.27 % (342)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_32703
% 1.49/1.27 % SZS output start Proof for DTF2THF_32703
% 1.49/1.27 thf(type_def_5, type, nat: $tType).
% 1.49/1.27 thf(func_def_0, type, nat: $tType).
% 1.49/1.27 thf(func_def_1, type, x: nat).
% 1.49/1.27 thf(func_def_2, type, y: nat).
% 1.49/1.27 thf(func_def_3, type, z: nat).
% 1.49/1.27 thf(func_def_4, type, pl: nat > nat > nat).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 ((pl @ z @ y) != (pl @ z @ y))),
% 1.49/1.27 inference(definition_unfolding,[status(thm)],[f6,f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 (x = y)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f1])).
% 1.49/1.27 thf(f1,axiom,(
% 1.49/1.27 (x = y)),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.gXdwAelaYt/DTF2THF_32703.p',i)).
% 1.49/1.27 thf(f6,plain,(
% 1.49/1.27 ((pl @ z @ x) != (pl @ z @ y))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,plain,(
% 1.49/1.27 ((pl @ z @ x) != (pl @ z @ y))),
% 1.49/1.27 inference(flattening,[status(thm)],[f3])).
% 1.49/1.27 thf(f3,negated_conjecture,(
% 1.49/1.27 ~((pl @ z @ x) = (pl @ z @ y))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.49/1.27 thf(f2,conjecture,(
% 1.49/1.27 ((pl @ z @ x) = (pl @ z @ y))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.gXdwAelaYt/DTF2THF_32703.p',satz19e)).
% 1.49/1.27 % SZS output end Proof for DTF2THF_32703
% 1.49/1.27 % (342)------------------------------
% 1.49/1.27 % (342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (342)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (342)Memory used [KB]: 5373
% 1.49/1.27 % (342)Time elapsed: 0.002 s
% 1.49/1.27 % (342)------------------------------
% 1.49/1.27 % (342)------------------------------
% 1.49/1.27 % (341)Success in time 0.002 s
%------------------------------------------------------------------------------