%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM648^1 : 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 : n011.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 09:24:05 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 12 ~; 4 |; 10 &; 64 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 22 !; 6 ?; 28 :)
% 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,
pl: nat > nat > nat ).
thf(func_def_7,type,
sK0: nat ).
thf(func_def_8,type,
sK1: nat ).
thf(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f22,f14]) ).
thf(f14,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( x
= ( pl @ y @ sK0 ) )
& ( x
= ( pl @ y @ sK1 ) )
& ( sK1 != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11]) ).
thf(f11,plain,
( ? [X0: nat,X1: nat] :
( ( x
= ( pl @ y @ X0 ) )
& ( x
= ( pl @ y @ X1 ) )
& ( X0 != X1 ) )
=> ( ( x
= ( pl @ y @ sK0 ) )
& ( x
= ( pl @ y @ sK1 ) )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: nat,X1: nat] :
( ( x
= ( pl @ y @ X0 ) )
& ( x
= ( pl @ y @ X1 ) )
& ( X0 != X1 ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: nat,X1: nat] :
( ( X0 != X1 )
& ( x
= ( pl @ y @ X1 ) )
& ( x
= ( pl @ y @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: nat,X1: nat] :
( ( x
= ( pl @ y @ X0 ) )
=> ( ( x
= ( pl @ y @ X1 ) )
=> ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X3: nat,X4: nat] :
( ( x
= ( pl @ y @ X3 ) )
=> ( ( x
= ( pl @ y @ X4 ) )
=> ( X3 = X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X3: nat,X4: nat] :
( ( x
= ( pl @ y @ X3 ) )
=> ( ( x
= ( pl @ y @ X4 ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xQ32FlDi69/DTF2THF_30480.p',satz8b) ).
thf(f22,plain,
sK1 = sK0,
inference(equality_resolution,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat] :
( ( ( pl @ y @ sK0 )
!= ( pl @ y @ X0 ) )
| ( sK1 = X0 ) ),
inference(superposition,[status(thm)],[f13,f17]) ).
thf(f17,plain,
( ( pl @ y @ sK1 )
= ( pl @ y @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( x
= ( pl @ y @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f13,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( pl @ X1 @ X0 )
!= ( pl @ X1 @ X2 ) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( ( pl @ X1 @ X0 )
!= ( pl @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( X1 = X2 )
| ( ( pl @ X0 @ X1 )
!= ( pl @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( pl @ X0 @ X1 )
= ( pl @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: nat,X2: nat,X1: nat] :
( ( ( pl @ X0 @ X1 )
= ( pl @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.xQ32FlDi69/DTF2THF_30480.p',satz8a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM648^1 : 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
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 11:09:02 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NUM648^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Number Theory
% 0.29/0.45 % Problem : Landau theorem 8b
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : (forall x_0:nat.forall y_0:nat.x = pl y x_0 -> x = pl y y_0 ->
% 0.29/0.45 % x_0 = y_0)
% 0.29/0.45
% 0.29/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : satz8b [Lan30]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % : Without extensionality : Theorem
% 0.29/0.45 % 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 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 4 typ; 0 def)
% 0.29/0.45 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 3 ( 2 avg)
% 0.29/0.45 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 5 ( 5 avg)
% 0.29/0.45 % Number of types : 1 ( 1 usr)
% 0.29/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(nat_type,type,
% 0.29/0.45 nat: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(x,type,
% 0.29/0.45 x: nat ).
% 0.29/0.45
% 0.29/0.45 thf(y,type,
% 0.29/0.45 y: nat ).
% 0.29/0.45
% 0.29/0.45 thf(pl,type,
% 0.29/0.45 pl: nat > nat > nat ).
% 0.29/0.45
% 0.29/0.45 thf(satz8a,axiom,
% 0.29/0.45 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.29/0.45 ( ( ( pl @ Xx @ Xy )
% 0.29/0.45 = ( pl @ Xx @ Xz ) )
% 0.29/0.45 => ( Xy = Xz ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(satz8b,conjecture,
% 0.29/0.45 ! [Xx_0: nat,Xy_0: nat] :
% 0.29/0.45 ( ( x
% 0.29/0.45 = ( pl @ y @ Xx_0 ) )
% 0.29/0.45 => ( ( x
% 0.29/0.45 = ( pl @ y @ Xy_0 ) )
% 0.29/0.45 => ( Xx_0 = Xy_0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 11:09:03 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xQ32FlDi69/DTF2DTF30480.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(nat_type,type,
% 1.48/1.25 nat: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(x,type,
% 1.48/1.25 x: nat ).
% 1.48/1.25
% 1.48/1.25 thf(y,type,
% 1.48/1.25 y: nat ).
% 1.48/1.25
% 1.48/1.25 thf(pl,type,
% 1.48/1.25 pl: nat > nat > nat ).
% 1.48/1.25
% 1.48/1.25 thf(satz8a,axiom,
% 1.48/1.25 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.48/1.25 ( ( ( pl @ Xx @ Xy )
% 1.48/1.25 = ( pl @ Xx @ Xz ) )
% 1.48/1.25 => ( Xy = Xz ) ) ).
% 1.48/1.25
% 1.48/1.25 thf(satz8b,conjecture,
% 1.48/1.25 ! [Xx_0: nat,Xy_0: nat] :
% 1.48/1.25 ( ( x
% 1.48/1.25 = ( pl @ y @ Xx_0 ) )
% 1.48/1.25 => ( ( x
% 1.48/1.25 = ( pl @ y @ Xy_0 ) )
% 1.48/1.25 => ( Xx_0 = Xy_0 ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.26 % (30592)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30480 for (2999ds/18Mi)
% 1.48/1.26 % (30589)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30480 for (2999ds/2Mi)
% 1.48/1.26 % (30591)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_30480 for (2999ds/275Mi)
% 1.48/1.26 % (30592)First to succeed.
% 1.48/1.26 % (30589)Instruction limit reached!
% 1.48/1.26 % (30589)------------------------------
% 1.48/1.26 % (30589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (30589)Termination reason: Unknown
% 1.48/1.26 % (30589)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (30589)Memory used [KB]: 5500
% 1.48/1.26 % (30589)Time elapsed: 0.002 s
% 1.48/1.26 % (30589)Instructions burned: 2 (million)
% 1.48/1.26 % (30589)------------------------------
% 1.48/1.26 % (30589)------------------------------
% 1.48/1.26 % (30591)Also succeeded, but the first one will report.
% 1.48/1.27 % (30592)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_30480
% 1.48/1.27 % SZS output start Proof for DTF2THF_30480
% 1.48/1.27 thf(type_def_5, type, nat: $tType).
% 1.48/1.27 thf(func_def_0, type, nat: $tType).
% 1.48/1.27 thf(func_def_1, type, x: nat).
% 1.48/1.27 thf(func_def_2, type, y: nat).
% 1.48/1.27 thf(func_def_3, type, pl: nat > nat > nat).
% 1.48/1.27 thf(func_def_7, type, sK0: nat).
% 1.48/1.27 thf(func_def_8, type, sK1: nat).
% 1.48/1.27 thf(f23,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f22,f14])).
% 1.48/1.27 thf(f14,plain,(
% 1.48/1.27 (sK1 != sK0)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 thf(f12,plain,(
% 1.48/1.27 (x = (pl @ y @ sK0)) & (x = (pl @ y @ sK1)) & (sK1 != sK0)),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ? [X0 : nat,X1 : nat] : ((x = (pl @ y @ X0)) & (x = (pl @ y @ X1)) & (X0 != X1)) => ((x = (pl @ y @ sK0)) & (x = (pl @ y @ sK1)) & (sK1 != sK0))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 ? [X0 : nat,X1 : nat] : ((x = (pl @ y @ X0)) & (x = (pl @ y @ X1)) & (X0 != X1))),
% 1.48/1.27 inference(flattening,[status(thm)],[f8])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 ? [X0 : nat,X1 : nat] : (((X0 != X1) & (x = (pl @ y @ X1))) & (x = (pl @ y @ X0)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.27 thf(f6,plain,(
% 1.48/1.27 ~! [X0 : nat,X1 : nat] : ((x = (pl @ y @ X0)) => ((x = (pl @ y @ X1)) => (X0 = X1)))),
% 1.48/1.27 inference(rectify,[status(thm)],[f3])).
% 1.48/1.27 thf(f3,negated_conjecture,(
% 1.48/1.27 ~! [X3 : nat,X4 : nat] : ((x = (pl @ y @ X3)) => ((x = (pl @ y @ X4)) => (X3 = X4)))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.27 thf(f2,conjecture,(
% 1.48/1.27 ! [X3 : nat,X4 : nat] : ((x = (pl @ y @ X3)) => ((x = (pl @ y @ X4)) => (X3 = X4)))),
% 1.48/1.27 file('/export/starexec/sandbox/tmp/tmp.xQ32FlDi69/DTF2THF_30480.p',satz8b)).
% 1.48/1.27 thf(f22,plain,(
% 1.48/1.27 (sK1 = sK0)),
% 1.48/1.27 inference(equality_resolution,[status(thm)],[f19])).
% 1.48/1.27 thf(f19,plain,(
% 1.48/1.27 ( ! [X0 : nat] : (((pl @ y @ sK0) != (pl @ y @ X0)) | (sK1 = X0)) )),
% 1.48/1.27 inference(superposition,[status(thm)],[f13,f17])).
% 1.48/1.27 thf(f17,plain,(
% 1.48/1.27 ((pl @ y @ sK1) = (pl @ y @ sK0))),
% 1.48/1.27 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.48/1.27 thf(f16,plain,(
% 1.48/1.27 (x = (pl @ y @ sK0))),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 (x = (pl @ y @ sK1))),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 thf(f13,plain,(
% 1.48/1.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ X1 @ X0) != (pl @ X1 @ X2)) | (X0 = X2)) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((X0 = X2) | ((pl @ X1 @ X0) != (pl @ X1 @ X2)))),
% 1.48/1.27 inference(rectify,[status(thm)],[f7])).
% 1.48/1.27 thf(f7,plain,(
% 1.48/1.27 ! [X1 : nat,X0 : nat,X2 : nat] : ((X1 = X2) | ((pl @ X0 @ X1) != (pl @ X0 @ X2)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.27 thf(f5,plain,(
% 1.48/1.27 ! [X2 : nat,X1 : nat,X0 : nat] : (((pl @ X0 @ X1) = (pl @ X0 @ X2)) => (X1 = X2))),
% 1.48/1.27 inference(rectify,[status(thm)],[f1])).
% 1.48/1.27 thf(f1,axiom,(
% 1.48/1.27 ! [X0 : nat,X2 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X0 @ X2)) => (X1 = X2))),
% 1.48/1.27 file('/export/starexec/sandbox/tmp/tmp.xQ32FlDi69/DTF2THF_30480.p',satz8a)).
% 1.48/1.27 % SZS output end Proof for DTF2THF_30480
% 1.48/1.27 % (30592)------------------------------
% 1.48/1.27 % (30592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (30592)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (30592)Memory used [KB]: 5500
% 1.48/1.27 % (30592)Time elapsed: 0.003 s
% 1.48/1.27 % (30592)Instructions burned: 1 (million)
% 1.48/1.27 % (30592)------------------------------
% 1.48/1.27 % (30592)------------------------------
% 1.48/1.27 % (30585)Success in time 0.012 s
%------------------------------------------------------------------------------