%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM642^1 : 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 : n014.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 09:24:03 AM UTC 2026
% Result : Theorem 1.45s 1.26s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 20 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 108 ( 4 ~; 0 |; 0 &; 98 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 20 ( 8 ^; 12 !; 0 ?; 20 :)
% 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(func_def_4,type,
pl: nat > nat > nat ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( suc @ ( pl @ x @ y ) ) ),
inference(superposition,[status(thm)],[f8,f14]) ).
thf(f14,plain,
! [X2: nat,X1: nat] :
( ( suc @ ( pl @ X1 @ X2 ) )
= ( pl @ ( suc @ X1 ) @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( suc @ ( pl @ X1 @ X2 ) )
= ( pl @ ( suc @ X1 ) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( suc @ ( pl @ X1 @ Y0 ) )
= ( pl @ ( suc @ X1 ) @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ ( pl @ X1 @ Y0 ) )
= ( pl @ ( suc @ X1 ) @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: nat,X1: nat] :
( ( suc @ ( pl @ X1 @ X0 ) )
= ( pl @ ( suc @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( ( pl @ ( suc @ X0 ) @ X1 )
= ( suc @ ( pl @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uIXNJiVjmr/DTF2THF_8773.p',satz4d) ).
thf(f8,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( suc @ ( pl @ x @ y ) )
= ( pl @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.uIXNJiVjmr/DTF2THF_8773.p',satz4h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM642^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n014.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:08:57 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM642^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 4h
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : suc (pl x y) = pl (suc x) y
% 0.20/0.46
% 0.20/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : satz4h [Lan30]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without extensionality : Theorem
% 0.20/0.46 % 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 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 7 ( 2 unt; 5 typ; 0 def)
% 0.20/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 0 &; 12 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 3 ( 2 avg)
% 0.20/0.46 % Number of types : 1 ( 1 usr)
% 0.20/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(nat_type,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(x,type,
% 0.20/0.46 x: nat ).
% 0.20/0.46
% 0.20/0.46 thf(y,type,
% 0.20/0.46 y: nat ).
% 0.20/0.46
% 0.20/0.46 thf(suc,type,
% 0.20/0.46 suc: nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(pl,type,
% 0.20/0.46 pl: nat > nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(satz4d,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] :
% 0.20/0.46 ( ( pl @ ( suc @ Xx ) @ Xy )
% 0.20/0.46 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4h,conjecture,
% 0.20/0.46 ( ( suc @ ( pl @ x @ y ) )
% 0.20/0.46 = ( pl @ ( suc @ x ) @ y ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.45/1.23 ---- Embedded in THF ---
% 1.45/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.23 %%% Generated on Tue Feb 24 11:08:58 EST 2026
% 1.45/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.23 %%% Logic specification used:
% 1.45/1.23 %%% thf(spec, logic, $$dhol).
% 1.45/1.23
% 1.45/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uIXNJiVjmr/DTF2DTF8773.p
% See solution above
% 1.45/1.23 ------------------------
% 1.45/1.24 ---- Cleaned THF ---
% 1.45/1.24 thf(nat_type,type,
% 1.45/1.24 nat: $tType ).
% 1.45/1.24
% 1.45/1.24 thf(x,type,
% 1.45/1.24 x: nat ).
% 1.45/1.24
% 1.45/1.24 thf(y,type,
% 1.45/1.24 y: nat ).
% 1.45/1.24
% 1.45/1.24 thf(suc,type,
% 1.45/1.24 suc: nat > nat ).
% 1.45/1.24
% 1.45/1.24 thf(pl,type,
% 1.45/1.24 pl: nat > nat > nat ).
% 1.45/1.24
% 1.45/1.24 thf(satz4d,axiom,
% 1.45/1.24 ! [Xx: nat,Xy: nat] :
% 1.45/1.24 ( ( pl @ ( suc @ Xx ) @ Xy )
% 1.45/1.24 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(satz4h,conjecture,
% 1.45/1.24 ( ( suc @ ( pl @ x @ y ) )
% 1.45/1.24 = ( pl @ ( suc @ x ) @ y ) ) ).
% 1.45/1.24 ------------------------
% 1.45/1.26 % (8963)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_8773 for (3000ds/4Mi)
% 1.45/1.26 % (8966)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_8773 for (3000ds/2Mi)
% 1.45/1.26 % (8966)Instruction limit reached!
% 1.45/1.26 % (8966)------------------------------
% 1.45/1.26 % (8966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (8966)Termination reason: Unknown
% 1.45/1.26 % (8966)Termination phase: Saturation
% 1.45/1.26
% 1.45/1.26 % (8966)Memory used [KB]: 5500
% 1.45/1.26 % (8966)Time elapsed: 0.002 s
% 1.45/1.26 % (8966)Instructions burned: 2 (million)
% 1.45/1.26 % (8966)------------------------------
% 1.45/1.26 % (8966)------------------------------
% 1.45/1.26 % (8963)First to succeed.
% 1.45/1.26 % (8963)Refutation found. Thanks to Tanya!
% 1.45/1.26 % SZS status Theorem for DTF2THF_8773
% 1.45/1.26 % SZS output start Proof for DTF2THF_8773
% 1.45/1.26 thf(type_def_5, type, nat: $tType).
% 1.45/1.26 thf(func_def_0, type, nat: $tType).
% 1.45/1.26 thf(func_def_1, type, x: nat).
% 1.45/1.26 thf(func_def_2, type, y: nat).
% 1.45/1.26 thf(func_def_3, type, suc: nat > nat).
% 1.45/1.26 thf(func_def_4, type, pl: nat > nat > nat).
% 1.45/1.26 thf(f16,plain,(
% 1.45/1.26 $false),
% 1.45/1.26 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.45/1.26 thf(f15,plain,(
% 1.45/1.26 ((suc @ (pl @ x @ y)) != (suc @ (pl @ x @ y)))),
% 1.45/1.26 inference(superposition,[status(thm)],[f8,f14])).
% 1.45/1.26 thf(f14,plain,(
% 1.45/1.26 ( ! [X2 : nat,X1 : nat] : (((suc @ (pl @ X1 @ X2)) = (pl @ (suc @ X1) @ X2))) )),
% 1.45/1.26 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.45/1.26 thf(f13,plain,(
% 1.45/1.26 ( ! [X2 : nat,X1 : nat] : (($true = ((suc @ (pl @ X1 @ X2)) = (pl @ (suc @ X1) @ X2)))) )),
% 1.45/1.26 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.45/1.26 thf(f12,plain,(
% 1.45/1.26 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((suc @ (pl @ X1 @ Y0)) = (pl @ (suc @ X1) @ Y0))) @ X2))) )),
% 1.45/1.26 inference(pi_clausification,[status(thm)],[f11])).
% 1.45/1.26 thf(f11,plain,(
% 1.45/1.26 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((suc @ (pl @ X1 @ Y0)) = (pl @ (suc @ X1) @ Y0)))))) )),
% 1.45/1.26 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.45/1.26 thf(f10,plain,(
% 1.45/1.26 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1))))) @ X1))) )),
% 1.45/1.26 inference(pi_clausification,[status(thm)],[f9])).
% 1.45/1.26 thf(f9,plain,(
% 1.45/1.26 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1)))))))),
% 1.45/1.26 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.26 thf(f6,plain,(
% 1.45/1.26 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1)))))))),
% 1.45/1.26 inference(fool_elimination,[status(thm)],[f5])).
% 1.45/1.26 thf(f5,plain,(
% 1.45/1.26 ! [X0 : nat,X1 : nat] : ((suc @ (pl @ X1 @ X0)) = (pl @ (suc @ X1) @ X0))),
% 1.45/1.26 inference(rectify,[status(thm)],[f1])).
% 1.45/1.26 thf(f1,axiom,(
% 1.45/1.26 ! [X1 : nat,X0 : nat] : ((pl @ (suc @ X0) @ X1) = (suc @ (pl @ X0 @ X1)))),
% 1.45/1.26 file('/export/starexec/sandbox/tmp/tmp.uIXNJiVjmr/DTF2THF_8773.p',satz4d)).
% 1.45/1.26 thf(f8,plain,(
% 1.45/1.26 ((suc @ (pl @ x @ y)) != (pl @ (suc @ x) @ y))),
% 1.45/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.26 thf(f7,plain,(
% 1.45/1.26 ((suc @ (pl @ x @ y)) != (pl @ (suc @ x) @ y))),
% 1.45/1.26 inference(flattening,[status(thm)],[f3])).
% 1.45/1.26 thf(f3,negated_conjecture,(
% 1.45/1.26 ~((suc @ (pl @ x @ y)) = (pl @ (suc @ x) @ y))),
% 1.45/1.26 inference(negated_conjecture,[status(cth)],[f2])).
% 1.45/1.26 thf(f2,conjecture,(
% 1.45/1.26 ((suc @ (pl @ x @ y)) = (pl @ (suc @ x) @ y))),
% 1.45/1.26 file('/export/starexec/sandbox/tmp/tmp.uIXNJiVjmr/DTF2THF_8773.p',satz4h)).
% 1.45/1.26 % SZS output end Proof for DTF2THF_8773
% 1.45/1.26 % (8963)------------------------------
% 1.45/1.26 % (8963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (8963)Termination reason: Refutation
% 1.45/1.26
% 1.45/1.26 % (8963)Memory used [KB]: 5500
% 1.45/1.26 % (8963)Time elapsed: 0.002 s
% 1.45/1.26 % (8963)Instructions burned: 1 (million)
% 1.45/1.26 % (8963)------------------------------
% 1.45/1.26 % (8963)------------------------------
% 1.45/1.26 % (8961)Success in time 0.009 s
%------------------------------------------------------------------------------