%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM693^1 : 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 : n024.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 09:24:18 AM UTC 2026
% Result : Theorem 1.41s 1.26s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 92 ( 20 ~; 5 |; 1 &; 58 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 23 !; 2 ?; 25 :)
% 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,
more: nat > nat > $o ).
thf(func_def_3,type,
n_1: nat ).
thf(func_def_4,type,
suc: nat > nat ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(func_def_9,type,
sK0: nat > nat ).
thf(f35,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f34,f26]) ).
thf(f26,plain,
n_1 != x,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( n_1 != x )
& ( ( more @ x @ n_1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( ( more @ x @ n_1 )
!= $true )
=> ( n_1 = x ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( ( more @ x @ n_1 )
!= $true )
=> ( n_1 = x ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ~ ( more @ x @ n_1 )
=> ( n_1 = x ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ~ ( more @ x @ n_1 )
=> ( n_1 = x ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ~ ( more @ x @ n_1 )
=> ( n_1 = x ) ),
file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz24) ).
thf(f34,plain,
n_1 = x,
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( n_1 = x )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f32]) ).
thf(f32,plain,
! [X0: nat] :
( ( ( more @ X0 @ n_1 )
= $true )
| ( n_1 = X0 ) ),
inference(superposition,[status(thm)],[f31,f29]) ).
thf(f29,plain,
! [X0: nat] :
( ( ( suc @ ( sK0 @ X0 ) )
= X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat] :
( ( n_1 = X0 )
| ( ( suc @ ( sK0 @ X0 ) )
= X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f22]) ).
thf(f22,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
=> ( ( suc @ ( sK0 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X0: nat] :
( ( n_1 = X0 )
| ? [X1: nat] :
( ( suc @ X1 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat] :
( ( n_1 != X0 )
=> ~ ! [X1: nat] :
( ( suc @ X1 )
!= X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat] :
( ( n_1 != X1 )
=> ~ ! [X2: nat] :
( ( suc @ X2 )
!= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz3) ).
thf(f31,plain,
! [X0: nat] :
( $true
= ( more @ ( suc @ X0 ) @ n_1 ) ),
inference(superposition,[status(thm)],[f28,f27]) ).
thf(f27,plain,
! [X0: nat] :
( ( suc @ X0 )
= ( pl @ n_1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat] :
( ( suc @ X0 )
= ( pl @ n_1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat] :
( ( suc @ X1 )
= ( pl @ n_1 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz4g) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( $true
= ( more @ ( pl @ X1 @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( $true
= ( more @ ( pl @ X1 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: nat,X0: nat] :
( ( more @ ( pl @ X0 @ X1 ) @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] : ( more @ ( pl @ X0 @ X1 ) @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X3: nat] : ( more @ ( pl @ X1 @ X3 ) @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz18) ).
thf(f25,plain,
( ( more @ x @ n_1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM693^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 06:10:55 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 ---- Original DTF file ---
% 0.07/0.34 thf(spec,logic,$$dhol).
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 % File : NUM693^1 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.34 % Domain : Number Theory
% 0.07/0.34 % Problem : Landau theorem 24
% 0.07/0.34 % Version : Especial.
% 0.07/0.34 % English : ~(more x n_1) -> x = n_1
% 0.07/0.34
% 0.07/0.34 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.07/0.34 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.07/0.34 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.34 % Source : [Bro09]
% 0.07/0.34 % Names : satz24 [Lan30]
% 0.07/0.34
% 0.07/0.34 % Status : Theorem
% 0.07/0.34 % : Without extensionality : Theorem
% 0.07/0.34 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.33 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 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.07/0.34 % Syntax : Number of formulae : 11 ( 2 unt; 6 typ; 0 def)
% 0.07/0.34 % Number of atoms : 6 ( 4 equ; 0 cnn)
% 0.07/0.34 % Maximal formula atoms : 2 ( 1 avg)
% 0.07/0.34 % Number of connectives : 19 ( 6 ~; 0 |; 0 &; 10 @)
% 0.07/0.34 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.34 % Maximal formula depth : 7 ( 5 avg)
% 0.07/0.34 % Number of types : 2 ( 1 usr)
% 0.07/0.34 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.34 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.07/0.34 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.07/0.34 % SPC : TH0_THM_EQU_NAR
% 0.07/0.34
% 0.07/0.34 % Comments :
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 thf(nat_type,type,
% 0.07/0.34 nat: $tType ).
% 0.07/0.34
% 0.07/0.34 thf(x,type,
% 0.07/0.34 x: nat ).
% 0.07/0.34
% 0.07/0.34 thf(more,type,
% 0.07/0.34 more: nat > nat > $o ).
% 0.07/0.34
% 0.07/0.34 thf(n_1,type,
% 0.07/0.34 n_1: nat ).
% 0.07/0.34
% 0.07/0.34 thf(et,axiom,
% 0.07/0.34 ! [Xa: $o] :
% 0.07/0.34 ( ~ ~ Xa
% 0.07/0.34 => Xa ) ).
% 0.07/0.34
% 0.07/0.34 thf(suc,type,
% 0.07/0.34 suc: nat > nat ).
% 0.07/0.34
% 0.07/0.34 thf(satz3,axiom,
% 0.07/0.34 ! [Xx: nat] :
% 0.07/0.34 ( ( Xx != n_1 )
% 0.07/0.34 => ~ ! [Xx_0: nat] :
% 0.07/0.34 ( Xx
% 0.07/0.34 != ( suc @ Xx_0 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(pl,type,
% 0.07/0.34 pl: nat > nat > nat ).
% 0.07/0.34
% 0.07/0.34 thf(satz18,axiom,
% 0.07/0.34 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 0.07/0.34
% 0.07/0.34 thf(satz4g,axiom,
% 0.07/0.34 ! [Xx: nat] :
% 0.07/0.34 ( ( suc @ Xx )
% 0.07/0.34 = ( pl @ n_1 @ Xx ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(satz24,conjecture,
% 0.07/0.34 ( ~ ( more @ x @ n_1 )
% 0.07/0.34 => ( x = n_1 ) ) ).
% 0.07/0.34
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 ------------------------
% 1.41/1.23 ---- Embedded in THF ---
% 1.41/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.23 %%% Generated on Tue Feb 24 06:10:56 EST 2026
% 1.41/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.23 %%% Logic specification used:
% 1.41/1.23 %%% thf(spec, logic, $$dhol).
% 1.41/1.23
% 1.41/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2DTF17994.p
% See solution above
% 1.41/1.23 ------------------------
% 1.41/1.24 ---- Cleaned THF ---
% 1.41/1.24 thf(nat_type,type,
% 1.41/1.24 nat: $tType ).
% 1.41/1.24
% 1.41/1.24 thf(x,type,
% 1.41/1.24 x: nat ).
% 1.41/1.24
% 1.41/1.24 thf(more,type,
% 1.41/1.24 more: nat > nat > $o ).
% 1.41/1.24
% 1.41/1.24 thf(n_1,type,
% 1.41/1.24 n_1: nat ).
% 1.41/1.24
% 1.41/1.24 thf(et,axiom,
% 1.41/1.24 ! [Xa: $o] :
% 1.41/1.24 ( ~ ~ Xa
% 1.41/1.24 => Xa ) ).
% 1.41/1.24
% 1.41/1.24 thf(suc,type,
% 1.41/1.24 suc: nat > nat ).
% 1.41/1.24
% 1.41/1.24 thf(satz3,axiom,
% 1.41/1.24 ! [Xx: nat] :
% 1.41/1.24 ( ( Xx != n_1 )
% 1.41/1.24 => ~ ! [Xx_0: nat] :
% 1.41/1.24 ( Xx
% 1.41/1.24 != ( suc @ Xx_0 ) ) ) ).
% 1.41/1.24
% 1.41/1.24 thf(pl,type,
% 1.41/1.24 pl: nat > nat > nat ).
% 1.41/1.24
% 1.41/1.24 thf(satz18,axiom,
% 1.41/1.24 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 1.41/1.24
% 1.41/1.24 thf(satz4g,axiom,
% 1.41/1.24 ! [Xx: nat] :
% 1.41/1.24 ( ( suc @ Xx )
% 1.41/1.24 = ( pl @ n_1 @ Xx ) ) ).
% 1.41/1.24
% 1.41/1.24 thf(satz24,conjecture,
% 1.41/1.24 ( ~ ( more @ x @ n_1 )
% 1.41/1.24 => ( x = n_1 ) ) ).
% 1.41/1.24 ------------------------
% 1.41/1.26 % (18091)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/183Mi)
% 1.41/1.26 % (18092)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_17994 for (3000ds/4Mi)
% 1.41/1.26 % (18093)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_17994 for (3000ds/27Mi)
% 1.41/1.26 % (18094)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/2Mi)
% 1.41/1.26 % (18095)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_17994 for (3000ds/2Mi)
% 1.41/1.26 % (18096)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_17994 for (3000ds/275Mi)
% 1.41/1.26 % (18097)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/18Mi)
% 1.41/1.26 % (18096)Refutation not found, incomplete strategy
% 1.41/1.26 % (18096)------------------------------
% 1.41/1.26 % (18096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.26 % (18096)Termination reason: Refutation not found, incomplete strategy
% 1.41/1.26
% 1.41/1.26
% 1.41/1.26 % (18096)Memory used [KB]: 5500
% 1.41/1.26 % (18096)Time elapsed: 0.002 s
% 1.41/1.26 % (18096)Instructions burned: 1 (million)
% 1.41/1.26 % (18096)------------------------------
% 1.41/1.26 % (18096)------------------------------
% 1.41/1.26 % (18094)Instruction limit reached!
% 1.41/1.26 % (18094)------------------------------
% 1.41/1.26 % (18094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.26 % (18094)Termination reason: Unknown
% 1.41/1.26 % (18094)Termination phase: Saturation
% 1.41/1.26 % (18095)Instruction limit reached!
% 1.41/1.26 % (18095)------------------------------
% 1.41/1.26 % (18095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.26 % (18095)Termination reason: Unknown
% 1.41/1.26 % (18095)Termination phase: Saturation
% 1.41/1.26
% 1.41/1.26 % (18095)Memory used [KB]: 5500
% 1.41/1.26 % (18095)Time elapsed: 0.003 s
% 1.41/1.26 % (18095)Instructions burned: 3 (million)
% 1.41/1.26 % (18095)------------------------------
% 1.41/1.26 % (18095)------------------------------
% 1.41/1.26
% 1.41/1.26 % (18094)Memory used [KB]: 5500
% 1.41/1.26 % (18094)Time elapsed: 0.003 s
% 1.41/1.26 % (18094)Instructions burned: 2 (million)
% 1.41/1.26 % (18094)------------------------------
% 1.41/1.26 % (18094)------------------------------
% 1.41/1.26 % (18091)First to succeed.
% 1.41/1.26 % (18092)Instruction limit reached!
% 1.41/1.26 % (18092)------------------------------
% 1.41/1.26 % (18092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.26 % (18092)Termination reason: Unknown
% 1.41/1.26 % (18092)Termination phase: Saturation
% 1.41/1.26
% 1.41/1.26 % (18092)Memory used [KB]: 5500
% 1.41/1.26 % (18092)Time elapsed: 0.004 s
% 1.41/1.26 % (18092)Instructions burned: 4 (million)
% 1.41/1.26 % (18092)------------------------------
% 1.41/1.26 % (18092)------------------------------
% 1.41/1.26 % (18093)Also succeeded, but the first one will report.
% 1.41/1.26 % (18091)Refutation found. Thanks to Tanya!
% 1.41/1.26 % SZS status Theorem for DTF2THF_17994
% 1.41/1.26 % SZS output start Proof for DTF2THF_17994
% 1.41/1.26 thf(type_def_5, type, nat: $tType).
% 1.41/1.26 thf(func_def_0, type, nat: $tType).
% 1.41/1.26 thf(func_def_1, type, x: nat).
% 1.41/1.26 thf(func_def_2, type, more: nat > nat > $o).
% 1.41/1.26 thf(func_def_3, type, n_1: nat).
% 1.41/1.26 thf(func_def_4, type, suc: nat > nat).
% 1.41/1.26 thf(func_def_6, type, pl: nat > nat > nat).
% 1.41/1.26 thf(func_def_9, type, sK0: nat > nat).
% 1.41/1.26 thf(f35,plain,(
% 1.41/1.26 $false),
% 1.41/1.26 inference(subsumption_resolution,[status(thm)],[f34,f26])).
% 1.41/1.26 thf(f26,plain,(
% 1.41/1.26 (n_1 != x)),
% 1.41/1.26 inference(cnf_transformation,[status(thm)],[f20])).
% 1.41/1.26 thf(f20,plain,(
% 1.41/1.26 (n_1 != x) & ((more @ x @ n_1) != $true)),
% 1.41/1.26 inference(ennf_transformation,[status(thm)],[f17])).
% 1.41/1.26 thf(f17,plain,(
% 1.41/1.26 ~(((more @ x @ n_1) != $true) => (n_1 = x))),
% 1.41/1.26 inference(flattening,[status(thm)],[f13])).
% 1.41/1.26 thf(f13,plain,(
% 1.41/1.26 ~(~((more @ x @ n_1) = $true) => (n_1 = x))),
% 1.41/1.26 inference(fool_elimination,[status(thm)],[f12])).
% 1.41/1.26 thf(f12,plain,(
% 1.41/1.26 ~(~(more @ x @ n_1) => (n_1 = x))),
% 1.41/1.26 inference(rectify,[status(thm)],[f6])).
% 1.41/1.26 thf(f6,negated_conjecture,(
% 1.41/1.26 ~(~(more @ x @ n_1) => (n_1 = x))),
% 1.41/1.26 inference(negated_conjecture,[status(cth)],[f5])).
% 1.41/1.26 thf(f5,conjecture,(
% 1.41/1.26 ~(more @ x @ n_1) => (n_1 = x)),
% 1.41/1.26 file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz24)).
% 1.41/1.26 thf(f34,plain,(
% 1.41/1.26 (n_1 = x)),
% 1.41/1.26 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.41/1.26 thf(f33,plain,(
% 1.41/1.26 (n_1 = x) | ($true != $true)),
% 1.41/1.26 inference(superposition,[status(thm)],[f25,f32])).
% 1.41/1.26 thf(f32,plain,(
% 1.41/1.26 ( ! [X0 : nat] : (((more @ X0 @ n_1) = $true) | (n_1 = X0)) )),
% 1.41/1.26 inference(superposition,[status(thm)],[f31,f29])).
% 1.41/1.26 thf(f29,plain,(
% 1.41/1.26 ( ! [X0 : nat] : (((suc @ (sK0 @ X0)) = X0) | (n_1 = X0)) )),
% 1.41/1.26 inference(cnf_transformation,[status(thm)],[f23])).
% 1.41/1.26 thf(f23,plain,(
% 1.41/1.26 ! [X0 : nat] : ((n_1 = X0) | ((suc @ (sK0 @ X0)) = X0))),
% 1.41/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f22])).
% 1.41/1.26 thf(f22,plain,(
% 1.41/1.26 ! [X0 : nat] : (? [X1 : nat] : ((suc @ X1) = X0) => ((suc @ (sK0 @ X0)) = X0))),
% 1.41/1.26 introduced(definition,[],[choice_axiom])).
% 1.41/1.26 thf(f19,plain,(
% 1.41/1.26 ! [X0 : nat] : ((n_1 = X0) | ? [X1 : nat] : ((suc @ X1) = X0))),
% 1.41/1.26 inference(ennf_transformation,[status(thm)],[f14])).
% 1.41/1.26 thf(f14,plain,(
% 1.41/1.26 ! [X0 : nat] : ((n_1 != X0) => ~! [X1 : nat] : ((suc @ X1) != X0))),
% 1.41/1.26 inference(rectify,[status(thm)],[f2])).
% 1.41/1.26 thf(f2,axiom,(
% 1.41/1.26 ! [X1 : nat] : ((n_1 != X1) => ~! [X2 : nat] : ((suc @ X2) != X1))),
% 1.41/1.26 file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz3)).
% 1.41/1.26 thf(f31,plain,(
% 1.41/1.26 ( ! [X0 : nat] : (($true = (more @ (suc @ X0) @ n_1))) )),
% 1.41/1.26 inference(superposition,[status(thm)],[f28,f27])).
% 1.41/1.26 thf(f27,plain,(
% 1.41/1.26 ( ! [X0 : nat] : (((suc @ X0) = (pl @ n_1 @ X0))) )),
% 1.41/1.26 inference(cnf_transformation,[status(thm)],[f15])).
% 1.41/1.26 thf(f15,plain,(
% 1.41/1.26 ! [X0 : nat] : ((suc @ X0) = (pl @ n_1 @ X0))),
% 1.41/1.26 inference(rectify,[status(thm)],[f4])).
% 1.41/1.26 thf(f4,axiom,(
% 1.41/1.26 ! [X1 : nat] : ((suc @ X1) = (pl @ n_1 @ X1))),
% 1.41/1.26 file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz4g)).
% 1.41/1.26 thf(f28,plain,(
% 1.41/1.26 ( ! [X0 : nat,X1 : nat] : (($true = (more @ (pl @ X1 @ X0) @ X1))) )),
% 1.41/1.26 inference(cnf_transformation,[status(thm)],[f21])).
% 1.41/1.26 thf(f21,plain,(
% 1.41/1.26 ! [X0 : nat,X1 : nat] : ($true = (more @ (pl @ X1 @ X0) @ X1))),
% 1.41/1.26 inference(rectify,[status(thm)],[f9])).
% 1.41/1.26 thf(f9,plain,(
% 1.41/1.26 ! [X1 : nat,X0 : nat] : ((more @ (pl @ X0 @ X1) @ X0) = $true)),
% 1.41/1.26 inference(fool_elimination,[status(thm)],[f8])).
% 1.41/1.26 thf(f8,plain,(
% 1.41/1.26 ! [X0 : nat,X1 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 1.41/1.26 inference(rectify,[status(thm)],[f3])).
% 1.41/1.26 thf(f3,axiom,(
% 1.41/1.26 ! [X1 : nat,X3 : nat] : (more @ (pl @ X1 @ X3) @ X1)),
% 1.41/1.26 file('/export/starexec/sandbox/tmp/tmp.ubFcHcYU5C/DTF2THF_17994.p',satz18)).
% 1.41/1.26 thf(f25,plain,(
% 1.41/1.26 ((more @ x @ n_1) != $true)),
% 1.41/1.26 inference(cnf_transformation,[status(thm)],[f20])).
% 1.41/1.26 % SZS output end Proof for DTF2THF_17994
% 1.41/1.26 % (18091)------------------------------
% 1.41/1.26 % (18091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.26 % (18091)Termination reason: Refutation
% 1.41/1.26
% 1.41/1.26 % (18091)Memory used [KB]: 5500
% 1.41/1.26 % (18091)Time elapsed: 0.004 s
% 1.41/1.26 % (18091)Instructions burned: 2 (million)
% 1.41/1.26 % (18091)------------------------------
% 1.41/1.26 % (18091)------------------------------
% 1.41/1.26 % (18090)Success in time 0.017 s
%------------------------------------------------------------------------------