%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM713^1 : 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 : 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 09:24:25 AM UTC 2026
% Result : Theorem 1.67s 1.46s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 139 ( 12 ~; 0 |; 0 &; 126 @)
% ( 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 : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 31 !; 2 ?; 33 :)
% 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,
z: nat ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_6,type,
ts: nat > nat > nat ).
thf(func_def_9,type,
sK0: nat ).
thf(f51,plain,
$false,
inference(equality_resolution,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: nat] :
( ( ts @ z @ ( pl @ y @ sK0 ) )
!= ( ts @ z @ ( pl @ y @ X0 ) ) ),
inference(superposition,[status(thm)],[f27,f31]) ).
thf(f31,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( ts @ X1 @ X0 ) @ ( ts @ X0 @ X2 ) )
= ( ts @ X0 @ ( pl @ X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f22,f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: nat,X3: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz29) ).
thf(f22,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X2 @ ( pl @ X1 @ X0 ) )
= ( pl @ ( ts @ X2 @ X1 ) @ ( ts @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ts @ X2 @ ( pl @ X1 @ X0 ) )
= ( pl @ ( ts @ X2 @ X1 ) @ ( ts @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( pl @ ( ts @ X0 @ X2 ) @ ( ts @ X0 @ X1 ) )
= ( ts @ X0 @ ( pl @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X4: nat,X3: nat] :
( ( ts @ X2 @ ( pl @ X3 @ X4 ) )
= ( pl @ ( ts @ X2 @ X3 ) @ ( ts @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz30) ).
thf(f27,plain,
! [X0: nat] :
( ( pl @ ( ts @ y @ z ) @ X0 )
!= ( ts @ z @ ( pl @ y @ sK0 ) ) ),
inference(superposition,[status(thm)],[f25,f21]) ).
thf(f25,plain,
! [X0: nat] :
( ( pl @ ( ts @ y @ z ) @ X0 )
!= ( ts @ ( pl @ y @ sK0 ) @ z ) ),
inference(definition_unfolding,[status(thm)],[f24,f23]) ).
thf(f23,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f18]) ).
thf(f18,plain,
( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: nat] :
( x
= ( pl @ y @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',m) ).
thf(f24,plain,
! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ~ ! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
~ ! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz32a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM713^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:12:49 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : NUM713^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Number Theory
% 0.20/0.47 % Problem : Landau theorem 32a
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : ~(forall x_0:nat.~(ts x z = pl (ts y z) x_0))
% 0.20/0.47
% 0.20/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : satz32a [Lan30]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % : Without extensionality : Theorem
% 0.20/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 11 ( 4 unt; 6 typ; 0 def)
% 0.20/0.47 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 1 ( 0 avg)
% 0.20/0.47 % Number of connectives : 29 ( 6 ~; 0 |; 0 &; 22 @)
% 0.20/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 5 ( 4 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments :
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(nat_type,type,
% 0.20/0.47 nat: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(x,type,
% 0.20/0.47 x: nat ).
% 0.20/0.47
% 0.20/0.47 thf(y,type,
% 0.20/0.47 y: nat ).
% 0.20/0.47
% 0.20/0.47 thf(z,type,
% 0.20/0.47 z: nat ).
% 0.20/0.47
% 0.20/0.47 thf(pl,type,
% 0.20/0.47 pl: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(m,axiom,
% 0.20/0.47 ~ ! [Xx_0: nat] :
% 0.20/0.47 ( x
% 0.20/0.47 != ( pl @ y @ Xx_0 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ts,type,
% 0.20/0.47 ts: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(et,axiom,
% 0.20/0.47 ! [Xa: $o] :
% 0.20/0.47 ( ~ ~ Xa
% 0.20/0.47 => Xa ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz29,axiom,
% 0.20/0.47 ! [Xx: nat,Xy: nat] :
% 0.20/0.47 ( ( ts @ Xx @ Xy )
% 0.20/0.47 = ( ts @ Xy @ Xx ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz30,axiom,
% 0.20/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.47 ( ( ts @ Xx @ ( pl @ Xy @ Xz ) )
% 0.20/0.47 = ( pl @ ( ts @ Xx @ Xy ) @ ( ts @ Xx @ Xz ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz32a,conjecture,
% 0.20/0.47 ~ ! [Xx_0: nat] :
% 0.20/0.47 ( ( ts @ x @ z )
% 0.20/0.47 != ( pl @ ( ts @ y @ z ) @ Xx_0 ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.67/1.42 ---- Embedded in THF ---
% 1.67/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.42 %%% Generated on Tue Feb 24 11:12:50 EST 2026
% 1.67/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.42 %%% Logic specification used:
% 1.67/1.42 %%% thf(spec, logic, $$dhol).
% 1.67/1.42
% 1.67/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2DTF1056.p
% See solution above
% 1.67/1.42 ------------------------
% 1.67/1.43 ---- Cleaned THF ---
% 1.67/1.43 thf(nat_type,type,
% 1.67/1.43 nat: $tType ).
% 1.67/1.43
% 1.67/1.43 thf(x,type,
% 1.67/1.43 x: nat ).
% 1.67/1.43
% 1.67/1.43 thf(y,type,
% 1.67/1.43 y: nat ).
% 1.67/1.43
% 1.67/1.43 thf(z,type,
% 1.67/1.43 z: nat ).
% 1.67/1.43
% 1.67/1.43 thf(pl,type,
% 1.67/1.43 pl: nat > nat > nat ).
% 1.67/1.43
% 1.67/1.43 thf(m,axiom,
% 1.67/1.43 ~ ! [Xx_0: nat] :
% 1.67/1.43 ( x
% 1.67/1.43 != ( pl @ y @ Xx_0 ) ) ).
% 1.67/1.43
% 1.67/1.43 thf(ts,type,
% 1.67/1.43 ts: nat > nat > nat ).
% 1.67/1.43
% 1.67/1.43 thf(et,axiom,
% 1.67/1.43 ! [Xa: $o] :
% 1.67/1.43 ( ~ ~ Xa
% 1.67/1.43 => Xa ) ).
% 1.67/1.43
% 1.67/1.43 thf(satz29,axiom,
% 1.67/1.43 ! [Xx: nat,Xy: nat] :
% 1.67/1.43 ( ( ts @ Xx @ Xy )
% 1.67/1.43 = ( ts @ Xy @ Xx ) ) ).
% 1.67/1.43
% 1.67/1.43 thf(satz30,axiom,
% 1.67/1.43 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.67/1.43 ( ( ts @ Xx @ ( pl @ Xy @ Xz ) )
% 1.67/1.43 = ( pl @ ( ts @ Xx @ Xy ) @ ( ts @ Xx @ Xz ) ) ) ).
% 1.67/1.43
% 1.67/1.43 thf(satz32a,conjecture,
% 1.67/1.43 ~ ! [Xx_0: nat] :
% 1.67/1.43 ( ( ts @ x @ z )
% 1.67/1.43 != ( pl @ ( ts @ y @ z ) @ Xx_0 ) ) ).
% 1.67/1.43 ------------------------
% 1.67/1.45 % (1166)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1056 for (2999ds/18Mi)
% 1.67/1.45 % (1161)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_1056 for (2999ds/4Mi)
% 1.67/1.45 % (1164)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_1056 for (2999ds/2Mi)
% 1.67/1.45 % (1162)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_1056 for (2999ds/27Mi)
% 1.67/1.45 % (1163)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1056 for (2999ds/2Mi)
% 1.67/1.45 % (1165)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_1056 for (2999ds/275Mi)
% 1.67/1.45 % (1160)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1056 for (2999ds/183Mi)
% 1.67/1.45 % (1163)Instruction limit reached!
% 1.67/1.45 % (1163)------------------------------
% 1.67/1.45 % (1163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (1163)Termination reason: Unknown
% 1.67/1.45 % (1163)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (1163)Memory used [KB]: 5373
% 1.67/1.45 % (1163)Time elapsed: 0.003 s
% 1.67/1.45 % (1163)Instructions burned: 2 (million)
% 1.67/1.45 % (1163)------------------------------
% 1.67/1.45 % (1163)------------------------------
% 1.67/1.45 % (1164)Instruction limit reached!
% 1.67/1.45 % (1164)------------------------------
% 1.67/1.45 % (1164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (1164)Termination reason: Unknown
% 1.67/1.45 % (1164)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (1164)Memory used [KB]: 895
% 1.67/1.45 % (1164)Time elapsed: 0.003 s
% 1.67/1.45 % (1164)Instructions burned: 2 (million)
% 1.67/1.45 % (1164)------------------------------
% 1.67/1.45 % (1164)------------------------------
% 1.67/1.45 % (1165)Refutation not found, incomplete strategy
% 1.67/1.45 % (1165)------------------------------
% 1.67/1.45 % (1165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (1165)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.45
% 1.67/1.45
% 1.67/1.45 % (1165)Memory used [KB]: 5500
% 1.67/1.45 % (1165)Time elapsed: 0.003 s
% 1.67/1.45 % (1165)Instructions burned: 2 (million)
% 1.67/1.45 % (1165)------------------------------
% 1.67/1.45 % (1165)------------------------------
% 1.67/1.45 % (1161)Instruction limit reached!
% 1.67/1.45 % (1161)------------------------------
% 1.67/1.45 % (1161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (1161)Termination reason: Unknown
% 1.67/1.45 % (1161)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (1161)Memory used [KB]: 5500
% 1.67/1.45 % (1161)Time elapsed: 0.005 s
% 1.67/1.45 % (1161)Instructions burned: 5 (million)
% 1.67/1.45 % (1161)------------------------------
% 1.67/1.45 % (1161)------------------------------
% 1.67/1.45 % (1160)First to succeed.
% 1.67/1.45 % (1162)Also succeeded, but the first one will report.
% 1.67/1.45 % (1166)Also succeeded, but the first one will report.
% 1.67/1.46 % (1160)Refutation found. Thanks to Tanya!
% 1.67/1.46 % SZS status Theorem for DTF2THF_1056
% 1.67/1.46 % SZS output start Proof for DTF2THF_1056
% 1.67/1.46 thf(type_def_5, type, nat: $tType).
% 1.67/1.46 thf(func_def_0, type, nat: $tType).
% 1.67/1.46 thf(func_def_1, type, x: nat).
% 1.67/1.46 thf(func_def_2, type, y: nat).
% 1.67/1.46 thf(func_def_3, type, z: nat).
% 1.67/1.46 thf(func_def_4, type, pl: nat > nat > nat).
% 1.67/1.46 thf(func_def_6, type, ts: nat > nat > nat).
% 1.67/1.46 thf(func_def_9, type, sK0: nat).
% 1.67/1.46 thf(f51,plain,(
% 1.67/1.46 $false),
% 1.67/1.46 inference(equality_resolution,[status(thm)],[f49])).
% 1.67/1.46 thf(f49,plain,(
% 1.67/1.46 ( ! [X0 : nat] : (((ts @ z @ (pl @ y @ sK0)) != (ts @ z @ (pl @ y @ X0)))) )),
% 1.67/1.46 inference(superposition,[status(thm)],[f27,f31])).
% 1.67/1.46 thf(f31,plain,(
% 1.67/1.46 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ (ts @ X1 @ X0) @ (ts @ X0 @ X2)) = (ts @ X0 @ (pl @ X1 @ X2)))) )),
% 1.67/1.46 inference(superposition,[status(thm)],[f22,f21])).
% 1.67/1.46 thf(f21,plain,(
% 1.67/1.46 ( ! [X0 : nat,X1 : nat] : (((ts @ X0 @ X1) = (ts @ X1 @ X0))) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.46 thf(f16,plain,(
% 1.67/1.46 ! [X0 : nat,X1 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.67/1.46 inference(rectify,[status(thm)],[f10])).
% 1.67/1.46 thf(f10,plain,(
% 1.67/1.46 ! [X1 : nat,X0 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.67/1.46 inference(rectify,[status(thm)],[f3])).
% 1.67/1.46 thf(f3,axiom,(
% 1.67/1.46 ! [X2 : nat,X3 : nat] : ((ts @ X2 @ X3) = (ts @ X3 @ X2))),
% 1.67/1.46 file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz29)).
% 1.67/1.46 thf(f22,plain,(
% 1.67/1.46 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ts @ X2 @ (pl @ X1 @ X0)) = (pl @ (ts @ X2 @ X1) @ (ts @ X2 @ X0)))) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.46 thf(f17,plain,(
% 1.67/1.46 ! [X0 : nat,X1 : nat,X2 : nat] : ((ts @ X2 @ (pl @ X1 @ X0)) = (pl @ (ts @ X2 @ X1) @ (ts @ X2 @ X0)))),
% 1.67/1.46 inference(rectify,[status(thm)],[f13])).
% 1.67/1.46 thf(f13,plain,(
% 1.67/1.46 ! [X1 : nat,X2 : nat,X0 : nat] : ((pl @ (ts @ X0 @ X2) @ (ts @ X0 @ X1)) = (ts @ X0 @ (pl @ X2 @ X1)))),
% 1.67/1.46 inference(rectify,[status(thm)],[f4])).
% 1.67/1.46 thf(f4,axiom,(
% 1.67/1.46 ! [X2 : nat,X4 : nat,X3 : nat] : ((ts @ X2 @ (pl @ X3 @ X4)) = (pl @ (ts @ X2 @ X3) @ (ts @ X2 @ X4)))),
% 1.67/1.46 file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz30)).
% 1.67/1.46 thf(f27,plain,(
% 1.67/1.46 ( ! [X0 : nat] : (((pl @ (ts @ y @ z) @ X0) != (ts @ z @ (pl @ y @ sK0)))) )),
% 1.67/1.46 inference(superposition,[status(thm)],[f25,f21])).
% 1.67/1.46 thf(f25,plain,(
% 1.67/1.46 ( ! [X0 : nat] : (((pl @ (ts @ y @ z) @ X0) != (ts @ (pl @ y @ sK0) @ z))) )),
% 1.67/1.46 inference(definition_unfolding,[status(thm)],[f24,f23])).
% 1.67/1.46 thf(f23,plain,(
% 1.67/1.46 (x = (pl @ y @ sK0))),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.46 thf(f19,plain,(
% 1.67/1.46 (x = (pl @ y @ sK0))),
% 1.67/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f18])).
% 1.67/1.46 thf(f18,plain,(
% 1.67/1.46 ? [X0 : nat] : (x = (pl @ y @ X0)) => (x = (pl @ y @ sK0))),
% 1.67/1.46 introduced(definition,[],[choice_axiom])).
% 1.67/1.46 thf(f15,plain,(
% 1.67/1.46 ? [X0 : nat] : (x = (pl @ y @ X0))),
% 1.67/1.46 inference(ennf_transformation,[status(thm)],[f1])).
% 1.67/1.46 thf(f1,axiom,(
% 1.67/1.46 ~! [X0 : nat] : (x != (pl @ y @ X0))),
% 1.67/1.46 file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',m)).
% 1.67/1.46 thf(f24,plain,(
% 1.67/1.46 ( ! [X0 : nat] : (((ts @ x @ z) != (pl @ (ts @ y @ z) @ X0))) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.46 thf(f12,plain,(
% 1.67/1.46 ! [X0 : nat] : ((ts @ x @ z) != (pl @ (ts @ y @ z) @ X0))),
% 1.67/1.46 inference(flattening,[status(thm)],[f6])).
% 1.67/1.46 thf(f6,negated_conjecture,(
% 1.67/1.46 ~~! [X0 : nat] : ((ts @ x @ z) != (pl @ (ts @ y @ z) @ X0))),
% 1.67/1.46 inference(negated_conjecture,[status(cth)],[f5])).
% 1.67/1.46 thf(f5,conjecture,(
% 1.67/1.46 ~! [X0 : nat] : ((ts @ x @ z) != (pl @ (ts @ y @ z) @ X0))),
% 1.67/1.46 file('/export/starexec/sandbox/tmp/tmp.BWhPFMwNSR/DTF2THF_1056.p',satz32a)).
% 1.67/1.46 % SZS output end Proof for DTF2THF_1056
% 1.67/1.46 % (1160)------------------------------
% 1.67/1.46 % (1160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (1160)Termination reason: Refutation
% 1.67/1.46
% 1.67/1.46 % (1160)Memory used [KB]: 5500
% 1.67/1.46 % (1160)Time elapsed: 0.008 s
% 1.67/1.46 % (1160)Instructions burned: 8 (million)
% 1.67/1.46 % (1160)------------------------------
% 1.67/1.46 % (1160)------------------------------
% 1.67/1.46 % (1159)Success in time 0.021 s
%------------------------------------------------------------------------------