%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM647^1 : 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 : n008.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 09:24:04 AM UTC 2026
% Result : Theorem 1.66s 1.44s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 49 ( 11 ~; 4 |; 0 &; 32 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 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(f25,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f24,f16]) ).
thf(f16,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
y != z,
inference(flattening,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
y != z,
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
y = z,
file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',satz8a) ).
thf(f24,plain,
y = z,
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat] :
( ( ( pl @ x @ y )
!= ( pl @ x @ X0 ) )
| ( z = X0 ) ),
inference(superposition,[status(thm)],[f18,f17]) ).
thf(f17,plain,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',i) ).
thf(f18,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( pl @ X2 @ X0 )
!= ( pl @ X2 @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( pl @ X2 @ X0 )
!= ( pl @ X2 @ X1 ) )
| ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( pl @ X0 @ X1 )
!= ( pl @ X0 @ X2 ) )
| ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ( pl @ X0 @ X1 )
!= ( pl @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( X2 != X3 )
=> ( ( pl @ X1 @ X2 )
!= ( pl @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',satz8) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM647^1 : 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
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:09:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : NUM647^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.49 % Domain : Number Theory
% 0.27/0.49 % Problem : Landau theorem 8a
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : y = z
% 0.27/0.49
% 0.27/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.27/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.27/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : satz8a [Lan30]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % : Without extensionality : Theorem
% 0.27/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.27/0.49 % Syntax : Number of formulae : 9 ( 2 unt; 5 typ; 0 def)
% 0.27/0.49 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.27/0.49 % Number of connectives : 14 ( 4 ~; 0 |; 0 &; 8 @)
% 0.27/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 6 ( 3 avg)
% 0.27/0.49 % Number of types : 2 ( 1 usr)
% 0.27/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.27/0.49 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments :
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(nat_type,type,
% 0.27/0.49 nat: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(x,type,
% 0.27/0.49 x: nat ).
% 0.27/0.49
% 0.27/0.49 thf(y,type,
% 0.27/0.49 y: nat ).
% 0.27/0.49
% 0.27/0.49 thf(z,type,
% 0.27/0.49 z: nat ).
% 0.27/0.49
% 0.27/0.49 thf(pl,type,
% 0.27/0.49 pl: nat > nat > nat ).
% 0.27/0.49
% 0.27/0.49 thf(i,axiom,
% 0.27/0.49 ( ( pl @ x @ y )
% 0.27/0.49 = ( pl @ x @ z ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(et,axiom,
% 0.27/0.49 ! [Xa: $o] :
% 0.27/0.49 ( ~ ~ Xa
% 0.27/0.49 => Xa ) ).
% 0.27/0.49
% 0.27/0.49 thf(satz8,axiom,
% 0.27/0.49 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.27/0.49 ( ( Xy != Xz )
% 0.27/0.49 => ( ( pl @ Xx @ Xy )
% 0.27/0.49 != ( pl @ Xx @ Xz ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(satz8a,conjecture,
% 0.27/0.49 y = z ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.66/1.41 ---- Embedded in THF ---
% 1.66/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.41 %%% Generated on Tue Feb 24 11:09:10 EST 2026
% 1.66/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.41 %%% Logic specification used:
% 1.66/1.41 %%% thf(spec, logic, $$dhol).
% 1.66/1.41
% 1.66/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2DTF3725.p
% See solution above
% 1.66/1.41 ------------------------
% 1.66/1.42 ---- Cleaned THF ---
% 1.66/1.42 thf(nat_type,type,
% 1.66/1.42 nat: $tType ).
% 1.66/1.42
% 1.66/1.42 thf(x,type,
% 1.66/1.42 x: nat ).
% 1.66/1.42
% 1.66/1.42 thf(y,type,
% 1.66/1.42 y: nat ).
% 1.66/1.42
% 1.66/1.42 thf(z,type,
% 1.66/1.42 z: nat ).
% 1.66/1.42
% 1.66/1.42 thf(pl,type,
% 1.66/1.42 pl: nat > nat > nat ).
% 1.66/1.42
% 1.66/1.42 thf(i,axiom,
% 1.66/1.42 ( ( pl @ x @ y )
% 1.66/1.42 = ( pl @ x @ z ) ) ).
% 1.66/1.42
% 1.66/1.42 thf(et,axiom,
% 1.66/1.42 ! [Xa: $o] :
% 1.66/1.42 ( ~ ~ Xa
% 1.66/1.42 => Xa ) ).
% 1.66/1.42
% 1.66/1.42 thf(satz8,axiom,
% 1.66/1.42 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.66/1.42 ( ( Xy != Xz )
% 1.66/1.42 => ( ( pl @ Xx @ Xy )
% 1.66/1.42 != ( pl @ Xx @ Xz ) ) ) ).
% 1.66/1.42
% 1.66/1.42 thf(satz8a,conjecture,
% 1.66/1.42 y = z ).
% 1.66/1.42 ------------------------
% 1.66/1.44 % (3862)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3725 for (2999ds/18Mi)
% 1.66/1.44 % (3860)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_3725 for (2999ds/2Mi)
% 1.66/1.44 % (3856)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3725 for (2999ds/183Mi)
% 1.66/1.44 % (3858)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_3725 for (2999ds/27Mi)
% 1.66/1.44 % (3861)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_3725 for (2999ds/275Mi)
% 1.66/1.44 % (3859)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3725 for (2999ds/2Mi)
% 1.66/1.44 % (3857)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_3725 for (2999ds/4Mi)
% 1.66/1.44 % (3861)Refutation not found, incomplete strategy
% 1.66/1.44 % (3861)------------------------------
% 1.66/1.44 % (3861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (3861)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.44
% 1.66/1.44
% 1.66/1.44 % (3861)Memory used [KB]: 5373
% 1.66/1.44 % (3861)Time elapsed: 0.002 s
% 1.66/1.44 % (3861)Instructions burned: 1 (million)
% 1.66/1.44 % (3861)------------------------------
% 1.66/1.44 % (3861)------------------------------
% 1.66/1.44 % (3860)Instruction limit reached!
% 1.66/1.44 % (3860)------------------------------
% 1.66/1.44 % (3860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (3860)Termination reason: Unknown
% 1.66/1.44 % (3860)Termination phase: Saturation
% 1.66/1.44
% 1.66/1.44 % (3860)Memory used [KB]: 5500
% 1.66/1.44 % (3860)Time elapsed: 0.003 s
% 1.66/1.44 % (3860)Instructions burned: 2 (million)
% 1.66/1.44 % (3860)------------------------------
% 1.66/1.44 % (3860)------------------------------
% 1.66/1.44 % (3856)First to succeed.
% 1.66/1.44 % (3862)Also succeeded, but the first one will report.
% 1.66/1.44 % (3856)Refutation found. Thanks to Tanya!
% 1.66/1.44 % SZS status Theorem for DTF2THF_3725
% 1.66/1.44 % SZS output start Proof for DTF2THF_3725
% 1.66/1.44 thf(type_def_5, type, nat: $tType).
% 1.66/1.44 thf(func_def_0, type, nat: $tType).
% 1.66/1.44 thf(func_def_1, type, x: nat).
% 1.66/1.44 thf(func_def_2, type, y: nat).
% 1.66/1.44 thf(func_def_3, type, z: nat).
% 1.66/1.44 thf(func_def_4, type, pl: nat > nat > nat).
% 1.66/1.44 thf(f25,plain,(
% 1.66/1.44 $false),
% 1.66/1.44 inference(subsumption_resolution,[status(thm)],[f24,f16])).
% 1.66/1.44 thf(f16,plain,(
% 1.66/1.44 (y != z)),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.44 thf(f9,plain,(
% 1.66/1.44 (y != z)),
% 1.66/1.44 inference(flattening,[status(thm)],[f5])).
% 1.66/1.44 thf(f5,negated_conjecture,(
% 1.66/1.44 ~(y = z)),
% 1.66/1.44 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.44 thf(f4,conjecture,(
% 1.66/1.44 (y = z)),
% 1.66/1.44 file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',satz8a)).
% 1.66/1.44 thf(f24,plain,(
% 1.66/1.44 (y = z)),
% 1.66/1.44 inference(equality_resolution,[status(thm)],[f20])).
% 1.66/1.44 thf(f20,plain,(
% 1.66/1.44 ( ! [X0 : nat] : (((pl @ x @ y) != (pl @ x @ X0)) | (z = X0)) )),
% 1.66/1.44 inference(superposition,[status(thm)],[f18,f17])).
% 1.66/1.44 thf(f17,plain,(
% 1.66/1.44 ((pl @ x @ y) = (pl @ x @ z))),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f1])).
% 1.66/1.44 thf(f1,axiom,(
% 1.66/1.44 ((pl @ x @ y) = (pl @ x @ z))),
% 1.66/1.44 file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',i)).
% 1.66/1.44 thf(f18,plain,(
% 1.66/1.44 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ X2 @ X0) != (pl @ X2 @ X1)) | (X0 = X1)) )),
% 1.66/1.44 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.44 thf(f14,plain,(
% 1.66/1.44 ! [X0 : nat,X1 : nat,X2 : nat] : (((pl @ X2 @ X0) != (pl @ X2 @ X1)) | (X0 = X1))),
% 1.66/1.44 inference(rectify,[status(thm)],[f12])).
% 1.66/1.44 thf(f12,plain,(
% 1.66/1.44 ! [X1 : nat,X2 : nat,X0 : nat] : (((pl @ X0 @ X1) != (pl @ X0 @ X2)) | (X1 = X2))),
% 1.66/1.44 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.44 thf(f11,plain,(
% 1.66/1.44 ! [X0 : nat,X1 : nat,X2 : nat] : ((X1 != X2) => ((pl @ X0 @ X1) != (pl @ X0 @ X2)))),
% 1.66/1.44 inference(rectify,[status(thm)],[f3])).
% 1.66/1.44 thf(f3,axiom,(
% 1.66/1.44 ! [X1 : nat,X2 : nat,X3 : nat] : ((X2 != X3) => ((pl @ X1 @ X2) != (pl @ X1 @ X3)))),
% 1.66/1.44 file('/export/starexec/sandbox/tmp/tmp.kYvHu4lbE4/DTF2THF_3725.p',satz8)).
% 1.66/1.44 % SZS output end Proof for DTF2THF_3725
% 1.66/1.44 % (3856)------------------------------
% 1.66/1.44 % (3856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (3856)Termination reason: Refutation
% 1.66/1.44
% 1.66/1.44 % (3856)Memory used [KB]: 5500
% 1.66/1.44 % (3856)Time elapsed: 0.004 s
% 1.66/1.44 % (3856)Instructions burned: 1 (million)
% 1.66/1.44 % (3856)------------------------------
% 1.66/1.44 % (3856)------------------------------
% 1.66/1.44 % (3855)Success in time 0.019 s
%------------------------------------------------------------------------------