%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM635^2 : 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 : n023.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 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 18 ~; 4 |; 5 &; 28 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 15 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
succ: $i > $i ).
thf(func_def_5,type,
sK0: ( $i > $o ) > $i ).
thf(f33,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f32,f23]) ).
thf(f23,plain,
sK1 != sK2,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( succ @ sK2 )
= ( succ @ sK1 ) )
& ( sK1 != sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
& ( X0 != X1 ) )
=> ( ( ( succ @ sK2 )
= ( succ @ sK1 ) )
& ( sK1 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: $i,X1: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
& ( X0 != X1 ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
? [X1: $i,X0: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d3A1ln8vne/DTF2THF_21468.p',satz1) ).
thf(f32,plain,
sK1 = sK2,
inference(equality_resolution,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( ( succ @ X0 )
!= ( succ @ sK1 ) )
| ( sK2 = X0 ) ),
inference(superposition,[status(thm)],[f25,f24]) ).
thf(f24,plain,
( ( succ @ sK2 )
= ( succ @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
!= ( succ @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
!= ( succ @ X1 ) )
| ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i,X0: $i] :
( ( ( succ @ X0 )
!= ( succ @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.d3A1ln8vne/DTF2THF_21468.p',succ_injective) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM635^2 : 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 : n023.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 11:09:34 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM635^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [TPTP]
% 0.29/0.46 % Names : satz1 [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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 v4.0.0, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 6 ( 1 unt; 2 typ; 0 def)
% 0.29/0.46 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.29/0.46 % Number of connectives : 18 ( 3 ~; 0 |; 1 &; 10 @)
% 0.29/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(one_type,type,
% 0.29/0.46 one: $i ).
% 0.29/0.46
% 0.29/0.46 thf(succ_type,type,
% 0.29/0.46 succ: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(one_is_first,axiom,
% 0.29/0.46 ! [X: $i] :
% 0.29/0.46 ( ( succ @ X )
% 0.29/0.46 != one ) ).
% 0.29/0.46
% 0.29/0.46 thf(succ_injective,axiom,
% 0.29/0.46 ! [X: $i,Y: $i] :
% 0.29/0.46 ( ( ( succ @ X )
% 0.29/0.46 = ( succ @ Y ) )
% 0.29/0.46 => ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(induction,axiom,
% 0.29/0.46 ! [M: $i > $o] :
% 0.29/0.46 ( ( ( M @ one )
% 0.29/0.46 & ! [X: $i] :
% 0.29/0.46 ( ( M @ X )
% 0.29/0.46 => ( M @ ( succ @ X ) ) ) )
% 0.29/0.46 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz1,conjecture,
% 0.29/0.46 ! [X: $i,Y: $i] :
% 0.29/0.46 ( ( X != Y )
% 0.29/0.46 => ( ( succ @ X )
% 0.29/0.46 != ( succ @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 11:09:35 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.d3A1ln8vne/DTF2DTF21468.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(one_type,type,
% 1.50/1.26 one: $i ).
% 1.50/1.26
% 1.50/1.26 thf(succ_type,type,
% 1.50/1.26 succ: $i > $i ).
% 1.50/1.26
% 1.50/1.26 thf(one_is_first,axiom,
% 1.50/1.26 ! [X: $i] :
% 1.50/1.26 ( ( succ @ X )
% 1.50/1.26 != one ) ).
% 1.50/1.26
% 1.50/1.26 thf(succ_injective,axiom,
% 1.50/1.26 ! [X: $i,Y: $i] :
% 1.50/1.26 ( ( ( succ @ X )
% 1.50/1.26 = ( succ @ Y ) )
% 1.50/1.26 => ( X = Y ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(induction,axiom,
% 1.50/1.26 ! [M: $i > $o] :
% 1.50/1.26 ( ( ( M @ one )
% 1.50/1.26 & ! [X: $i] :
% 1.50/1.26 ( ( M @ X )
% 1.50/1.26 => ( M @ ( succ @ X ) ) ) )
% 1.50/1.26 => ! [Y: $i] : ( M @ Y ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(satz1,conjecture,
% 1.50/1.26 ! [X: $i,Y: $i] :
% 1.50/1.26 ( ( X != Y )
% 1.50/1.26 => ( ( succ @ X )
% 1.50/1.26 != ( succ @ Y ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (21751)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21468 for (3000ds/18Mi)
% 1.50/1.27 % (21751)First to succeed.
% 1.50/1.27 % (21751)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_21468
% 1.50/1.27 % SZS output start Proof for DTF2THF_21468
% 1.50/1.27 thf(func_def_1, type, succ: $i > $i).
% 1.50/1.27 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.50/1.27 thf(f33,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f32,f23])).
% 1.50/1.27 thf(f23,plain,(
% 1.50/1.27 (sK1 != sK2)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f18,plain,(
% 1.50/1.27 ((succ @ sK2) = (succ @ sK1)) & (sK1 != sK2)),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f17])).
% 1.50/1.27 thf(f17,plain,(
% 1.50/1.27 ? [X0 : $i,X1 : $i] : (((succ @ X0) = (succ @ X1)) & (X0 != X1)) => (((succ @ sK2) = (succ @ sK1)) & (sK1 != sK2))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f16,plain,(
% 1.50/1.27 ? [X0 : $i,X1 : $i] : (((succ @ X0) = (succ @ X1)) & (X0 != X1))),
% 1.50/1.27 inference(rectify,[status(thm)],[f13])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 ? [X1 : $i,X0 : $i] : (((succ @ X0) = (succ @ X1)) & (X0 != X1))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ~! [X1 : $i,X0 : $i] : ((X0 != X1) => ((succ @ X0) != (succ @ X1)))),
% 1.50/1.27 inference(rectify,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,negated_conjecture,(
% 1.50/1.27 ~! [X1 : $i,X0 : $i] : ((X0 != X1) => ((succ @ X0) != (succ @ X1)))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.50/1.27 thf(f4,conjecture,(
% 1.50/1.27 ! [X1 : $i,X0 : $i] : ((X0 != X1) => ((succ @ X0) != (succ @ X1)))),
% 1.50/1.27 file('/export/starexec/sandbox/tmp/tmp.d3A1ln8vne/DTF2THF_21468.p',satz1)).
% 1.50/1.27 thf(f32,plain,(
% 1.50/1.27 (sK1 = sK2)),
% 1.50/1.27 inference(equality_resolution,[status(thm)],[f28])).
% 1.50/1.27 thf(f28,plain,(
% 1.50/1.27 ( ! [X0 : $i] : (((succ @ X0) != (succ @ sK1)) | (sK2 = X0)) )),
% 1.50/1.27 inference(superposition,[status(thm)],[f25,f24])).
% 1.50/1.27 thf(f24,plain,(
% 1.50/1.27 ((succ @ sK2) = (succ @ sK1))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f25,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (((succ @ X0) != (succ @ X1)) | (X0 = X1)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f19])).
% 1.50/1.27 thf(f19,plain,(
% 1.50/1.27 ! [X0 : $i,X1 : $i] : (((succ @ X0) != (succ @ X1)) | (X0 = X1))),
% 1.50/1.27 inference(rectify,[status(thm)],[f10])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 ! [X1 : $i,X0 : $i] : (((succ @ X0) != (succ @ X1)) | (X0 = X1))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,axiom,(
% 1.50/1.27 ! [X0 : $i,X1 : $i] : (((succ @ X0) = (succ @ X1)) => (X0 = X1))),
% 1.50/1.27 file('/export/starexec/sandbox/tmp/tmp.d3A1ln8vne/DTF2THF_21468.p',succ_injective)).
% 1.50/1.27 % SZS output end Proof for DTF2THF_21468
% 1.50/1.27 % (21751)------------------------------
% 1.50/1.27 % (21751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (21751)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (21751)Memory used [KB]: 5500
% 1.50/1.27 % (21751)Time elapsed: 0.003 s
% 1.50/1.27 % (21751)Instructions burned: 2 (million)
% 1.50/1.27 % (21751)------------------------------
% 1.50/1.27 % (21751)------------------------------
% 1.50/1.27 % (21744)Success in time 0.011 s
%------------------------------------------------------------------------------