%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM671^1 : 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 : n017.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 09:24:12 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% 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 @ y @ z )
!= ( pl @ y @ z ) ),
inference(definition_unfolding,[status(thm)],[f7,f6]) ).
thf(f6,plain,
x = y,
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
x = y,
file('/export/starexec/sandbox/tmp/tmp.uwx6b6FP7j/DTF2THF_3683.p',i) ).
thf(f7,plain,
( ( pl @ x @ z )
!= ( pl @ y @ z ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( pl @ x @ z )
!= ( pl @ y @ z ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( pl @ x @ z )
!= ( pl @ y @ z ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
file('/export/starexec/sandbox/tmp/tmp.uwx6b6FP7j/DTF2THF_3683.p',satz19b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM671^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.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 11:08:56 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
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : NUM671^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.49 % Domain : Number Theory
% 0.30/0.49 % Problem : Landau theorem 19b
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English : pl x z = pl y z
% 0.30/0.49
% 0.30/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.49 % Source : [Bro09]
% 0.30/0.49 % Names : satz19b [Lan30]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % : Without extensionality : Theorem
% 0.30/0.49 % 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
% 0.30/0.49 % Syntax : Number of formulae : 7 ( 2 unt; 5 typ; 0 def)
% 0.30/0.49 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.49 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.30/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 1 ( 1 avg)
% 0.30/0.49 % Number of types : 1 ( 1 usr)
% 0.30/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.30/0.49 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.30/0.49 % SPC : TH0_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments :
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(nat_type,type,
% 0.30/0.49 nat: $tType ).
% 0.30/0.49
% 0.30/0.49 thf(x,type,
% 0.30/0.49 x: nat ).
% 0.30/0.49
% 0.30/0.49 thf(y,type,
% 0.30/0.49 y: nat ).
% 0.30/0.49
% 0.30/0.49 thf(z,type,
% 0.30/0.49 z: nat ).
% 0.30/0.49
% 0.30/0.49 thf(i,axiom,
% 0.30/0.49 x = y ).
% 0.30/0.49
% 0.30/0.49 thf(pl,type,
% 0.30/0.49 pl: nat > nat > nat ).
% 0.30/0.49
% 0.30/0.49 thf(satz19b,conjecture,
% 0.30/0.49 ( ( pl @ x @ z )
% 0.30/0.49 = ( pl @ y @ z ) ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 11:08:57 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uwx6b6FP7j/DTF2DTF3683.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(nat_type,type,
% 1.66/1.43 nat: $tType ).
% 1.66/1.43
% 1.66/1.43 thf(x,type,
% 1.66/1.43 x: nat ).
% 1.66/1.43
% 1.66/1.43 thf(y,type,
% 1.66/1.43 y: nat ).
% 1.66/1.43
% 1.66/1.43 thf(z,type,
% 1.66/1.43 z: nat ).
% 1.66/1.43
% 1.66/1.43 thf(i,axiom,
% 1.66/1.43 x = y ).
% 1.66/1.43
% 1.66/1.43 thf(pl,type,
% 1.66/1.43 pl: nat > nat > nat ).
% 1.66/1.43
% 1.66/1.43 thf(satz19b,conjecture,
% 1.66/1.43 ( ( pl @ x @ z )
% 1.66/1.43 = ( pl @ y @ z ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (3790)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3683 for (3000ds/2Mi)
% 1.66/1.45 % (3788)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_3683 for (3000ds/4Mi)
% 1.66/1.45 % (3789)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_3683 for (3000ds/27Mi)
% 1.66/1.45 % (3787)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3683 for (3000ds/183Mi)
% 1.66/1.45 % (3791)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_3683 for (3000ds/2Mi)
% 1.66/1.45 % (3792)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_3683 for (3000ds/275Mi)
% 1.66/1.45 % (3793)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3683 for (3000ds/18Mi)
% 1.66/1.45 % (3787)First to succeed.
% 1.66/1.45 % (3792)Also succeeded, but the first one will report.
% 1.66/1.45 % (3788)Also succeeded, but the first one will report.
% 1.66/1.45 % (3787)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_3683
% 1.66/1.45 % SZS output start Proof for DTF2THF_3683
% 1.66/1.45 thf(type_def_5, type, nat: $tType).
% 1.66/1.45 thf(func_def_0, type, nat: $tType).
% 1.66/1.45 thf(func_def_1, type, x: nat).
% 1.66/1.45 thf(func_def_2, type, y: nat).
% 1.66/1.45 thf(func_def_3, type, z: nat).
% 1.66/1.45 thf(func_def_4, type, pl: nat > nat > nat).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f8])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 ((pl @ y @ z) != (pl @ y @ z))),
% 1.66/1.45 inference(definition_unfolding,[status(thm)],[f7,f6])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 (x = y)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f1])).
% 1.66/1.45 thf(f1,axiom,(
% 1.66/1.45 (x = y)),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.uwx6b6FP7j/DTF2THF_3683.p',i)).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 ((pl @ x @ z) != (pl @ y @ z))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.45 thf(f5,plain,(
% 1.66/1.45 ((pl @ x @ z) != (pl @ y @ z))),
% 1.66/1.45 inference(flattening,[status(thm)],[f3])).
% 1.66/1.45 thf(f3,negated_conjecture,(
% 1.66/1.45 ~((pl @ x @ z) = (pl @ y @ z))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f2])).
% 1.66/1.45 thf(f2,conjecture,(
% 1.66/1.45 ((pl @ x @ z) = (pl @ y @ z))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.uwx6b6FP7j/DTF2THF_3683.p',satz19b)).
% 1.66/1.45 % SZS output end Proof for DTF2THF_3683
% 1.66/1.45 % (3787)------------------------------
% 1.66/1.45 % (3787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (3787)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (3787)Memory used [KB]: 5373
% 1.66/1.45 % (3787)Time elapsed: 0.002 s
% 1.66/1.45 % (3787)Instructions burned: 1 (million)
% 1.66/1.45 % (3787)------------------------------
% 1.66/1.45 % (3787)------------------------------
% 1.66/1.45 % (3786)Success in time 0.017 s
%------------------------------------------------------------------------------