%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM635^1 : 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 : n006.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 09:24:00 AM UTC 2026
% Result : Theorem 1.63s 1.46s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 8 ~; 3 |; 0 &; 16 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 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,
suc: nat > nat ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f8]) ).
thf(f8,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
x != y,
file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',n) ).
thf(f14,plain,
x = y,
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat] :
( ( ( suc @ X0 )
!= ( suc @ x ) )
| ( y = X0 ) ),
inference(superposition,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( ( suc @ x )
= ( suc @ y ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( suc @ x )
= ( suc @ y ) ),
inference(flattening,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ( ( suc @ x )
!= ( suc @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ( suc @ x )
!= ( suc @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',satz1) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( ( suc @ X0 )
= ( suc @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',ax4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM635^1 : 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
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:08:30 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
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : NUM635^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.49 % Domain : Number Theory
% 0.28/0.49 % Problem : Landau theorem 1
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English : ~(suc x = suc y)
% 0.28/0.49
% 0.28/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.28/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.28/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.49 % Source : [Bro09]
% 0.28/0.49 % Names : satz1 [Lan30]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % : Without extensionality : Theorem
% 0.28/0.49 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 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
% 0.28/0.49 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 0 def)
% 0.28/0.49 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.28/0.49 % Number of connectives : 7 ( 2 ~; 0 |; 0 &; 4 @)
% 0.28/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 4 ( 3 avg)
% 0.28/0.49 % Number of types : 1 ( 1 usr)
% 0.28/0.49 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.28/0.49 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.28/0.49 % SPC : TH0_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments :
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(nat_type,type,
% 0.28/0.49 nat: $tType ).
% 0.28/0.49
% 0.28/0.49 thf(x,type,
% 0.28/0.49 x: nat ).
% 0.28/0.49
% 0.28/0.49 thf(y,type,
% 0.28/0.49 y: nat ).
% 0.28/0.49
% 0.28/0.49 thf(n,axiom,
% 0.28/0.49 x != y ).
% 0.28/0.49
% 0.28/0.49 thf(suc,type,
% 0.28/0.49 suc: nat > nat ).
% 0.28/0.49
% 0.28/0.49 thf(ax4,axiom,
% 0.28/0.49 ! [Xx: nat,Xy: nat] :
% 0.28/0.49 ( ( ( suc @ Xx )
% 0.28/0.49 = ( suc @ Xy ) )
% 0.28/0.49 => ( Xx = Xy ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(satz1,conjecture,
% 0.28/0.49 ( ( suc @ x )
% 0.28/0.49 != ( suc @ y ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.63/1.43 ---- Embedded in THF ---
% 1.63/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.43 %%% Generated on Tue Feb 24 11:08:31 EST 2026
% 1.63/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.43 %%% Logic specification used:
% 1.63/1.43 %%% thf(spec, logic, $$dhol).
% 1.63/1.43
% 1.63/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2DTF21489.p
% See solution above
% 1.63/1.43 ------------------------
% 1.63/1.44 ---- Cleaned THF ---
% 1.63/1.44 thf(nat_type,type,
% 1.63/1.44 nat: $tType ).
% 1.63/1.44
% 1.63/1.44 thf(x,type,
% 1.63/1.44 x: nat ).
% 1.63/1.44
% 1.63/1.44 thf(y,type,
% 1.63/1.44 y: nat ).
% 1.63/1.44
% 1.63/1.44 thf(n,axiom,
% 1.63/1.44 x != y ).
% 1.63/1.44
% 1.63/1.44 thf(suc,type,
% 1.63/1.44 suc: nat > nat ).
% 1.63/1.44
% 1.63/1.44 thf(ax4,axiom,
% 1.63/1.44 ! [Xx: nat,Xy: nat] :
% 1.63/1.44 ( ( ( suc @ Xx )
% 1.63/1.44 = ( suc @ Xy ) )
% 1.63/1.44 => ( Xx = Xy ) ) ).
% 1.63/1.44
% 1.63/1.44 thf(satz1,conjecture,
% 1.63/1.44 ( ( suc @ x )
% 1.63/1.44 != ( suc @ y ) ) ).
% 1.63/1.44 ------------------------
% 1.63/1.46 % (21595)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_21489 for (2999ds/27Mi)
% 1.63/1.46 % (21599)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21489 for (2999ds/18Mi)
% 1.63/1.46 % (21598)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_21489 for (2999ds/275Mi)
% 1.63/1.46 % (21594)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_21489 for (2999ds/4Mi)
% 1.63/1.46 % (21596)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21489 for (2999ds/2Mi)
% 1.63/1.46 % (21593)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21489 for (2999ds/183Mi)
% 1.63/1.46 % (21597)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_21489 for (2999ds/2Mi)
% 1.63/1.46 % (21597)Instruction limit reached!
% 1.63/1.46 % (21597)------------------------------
% 1.63/1.46 % (21597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.46 % (21597)Termination reason: Unknown
% 1.63/1.46 % (21597)Termination phase: Saturation
% 1.63/1.46
% 1.63/1.46 % (21597)Memory used [KB]: 5500
% 1.63/1.46 % (21597)Time elapsed: 0.003 s
% 1.63/1.46 % (21597)Instructions burned: 2 (million)
% 1.63/1.46 % (21597)------------------------------
% 1.63/1.46 % (21597)------------------------------
% 1.63/1.46 % (21598)First to succeed.
% 1.63/1.46 % (21599)Also succeeded, but the first one will report.
% 1.63/1.46 % (21593)Also succeeded, but the first one will report.
% 1.63/1.46 % (21598)Refutation found. Thanks to Tanya!
% 1.63/1.46 % SZS status Theorem for DTF2THF_21489
% 1.63/1.46 % SZS output start Proof for DTF2THF_21489
% 1.63/1.46 thf(type_def_5, type, nat: $tType).
% 1.63/1.46 thf(func_def_0, type, nat: $tType).
% 1.63/1.46 thf(func_def_1, type, x: nat).
% 1.63/1.46 thf(func_def_2, type, y: nat).
% 1.63/1.46 thf(func_def_3, type, suc: nat > nat).
% 1.63/1.46 thf(f15,plain,(
% 1.63/1.46 $false),
% 1.63/1.46 inference(subsumption_resolution,[status(thm)],[f14,f8])).
% 1.63/1.46 thf(f8,plain,(
% 1.63/1.46 (x != y)),
% 1.63/1.46 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.46 thf(f1,axiom,(
% 1.63/1.46 (x != y)),
% 1.63/1.46 file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',n)).
% 1.63/1.46 thf(f14,plain,(
% 1.63/1.46 (x = y)),
% 1.63/1.46 inference(equality_resolution,[status(thm)],[f11])).
% 1.63/1.46 thf(f11,plain,(
% 1.63/1.46 ( ! [X0 : nat] : (((suc @ X0) != (suc @ x)) | (y = X0)) )),
% 1.63/1.46 inference(superposition,[status(thm)],[f9,f10])).
% 1.63/1.46 thf(f10,plain,(
% 1.63/1.46 ((suc @ x) = (suc @ y))),
% 1.63/1.46 inference(cnf_transformation,[status(thm)],[f6])).
% 1.63/1.46 thf(f6,plain,(
% 1.63/1.46 ((suc @ x) = (suc @ y))),
% 1.63/1.46 inference(flattening,[status(thm)],[f4])).
% 1.63/1.46 thf(f4,negated_conjecture,(
% 1.63/1.46 ~((suc @ x) != (suc @ y))),
% 1.63/1.46 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.46 thf(f3,conjecture,(
% 1.63/1.46 ((suc @ x) != (suc @ y))),
% 1.63/1.46 file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',satz1)).
% 1.63/1.46 thf(f9,plain,(
% 1.63/1.46 ( ! [X0 : nat,X1 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1)) )),
% 1.63/1.46 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.46 thf(f7,plain,(
% 1.63/1.46 ! [X0 : nat,X1 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1))),
% 1.63/1.46 inference(ennf_transformation,[status(thm)],[f2])).
% 1.63/1.46 thf(f2,axiom,(
% 1.63/1.46 ! [X1 : nat,X0 : nat] : (((suc @ X0) = (suc @ X1)) => (X0 = X1))),
% 1.63/1.46 file('/export/starexec/sandbox/tmp/tmp.uTmcxHNKbZ/DTF2THF_21489.p',ax4)).
% 1.63/1.46 % SZS output end Proof for DTF2THF_21489
% 1.63/1.46 % (21598)------------------------------
% 1.63/1.46 % (21598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.46 % (21598)Termination reason: Refutation
% 1.63/1.46
% 1.63/1.46 % (21598)Memory used [KB]: 5500
% 1.63/1.46 % (21598)Time elapsed: 0.003 s
% 1.63/1.46 % (21598)Instructions burned: 1 (million)
% 1.63/1.46 % (21598)------------------------------
% 1.63/1.46 % (21598)------------------------------
% 1.63/1.46 % (21592)Success in time 0.019 s
%------------------------------------------------------------------------------