%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM673^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 09:24:13 AM UTC 2026
% Result : Theorem 1.60s 1.30s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 144 ( 13 ~; 4 |; 0 &; 124 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% 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,
more: nat > nat > $o ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(f26,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f18]) ).
thf(f18,plain,
( ( more @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( more @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
more @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
more @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',m) ).
thf(f25,plain,
( ( more @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true != $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f23,f19]) ).
thf(f19,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) )
| ( $true
!= ( more @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) )
| ( $true
!= ( more @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) )
| ( $true
!= ( more @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X1 @ X0 )
=> ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat,X2: nat] :
( ( more @ X0 @ X1 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz19a) ).
thf(f23,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f22,f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz6) ).
thf(f22,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ z @ y ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f20,f21]) ).
thf(f20,plain,
( ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
more @ ( pl @ z @ x ) @ ( pl @ z @ y ),
file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz19d) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM673^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:10:26 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : NUM673^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 19d
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : more (pl z x) (pl z y)
% 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 : [Bro09]
% 0.29/0.46 % Names : satz19d [Lan30]
% 0.29/0.46 % : satz32d [Lan30]
% 0.29/0.46 % : satz19f [Lan30]
% 0.29/0.46 % : satz96f [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 0 def)
% 0.29/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.29/0.46 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 20 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 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(nat_type,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(x,type,
% 0.29/0.46 x: nat ).
% 0.29/0.46
% 0.29/0.46 thf(y,type,
% 0.29/0.46 y: nat ).
% 0.29/0.46
% 0.29/0.46 thf(z,type,
% 0.29/0.46 z: nat ).
% 0.29/0.46
% 0.29/0.46 thf(more,type,
% 0.29/0.46 more: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(m,axiom,
% 0.29/0.46 more @ x @ y ).
% 0.29/0.46
% 0.29/0.46 thf(pl,type,
% 0.29/0.46 pl: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(satz19a,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.29/0.46 ( ( more @ Xx @ Xy )
% 0.29/0.46 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz6,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat] :
% 0.29/0.46 ( ( pl @ Xx @ Xy )
% 0.29/0.46 = ( pl @ Xy @ Xx ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz19d,conjecture,
% 0.29/0.46 more @ ( pl @ z @ x ) @ ( pl @ z @ y ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 11:10:26 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2DTF8680.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(nat_type,type,
% 1.46/1.27 nat: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(x,type,
% 1.46/1.27 x: nat ).
% 1.46/1.27
% 1.46/1.27 thf(y,type,
% 1.46/1.27 y: nat ).
% 1.46/1.27
% 1.46/1.27 thf(z,type,
% 1.46/1.27 z: nat ).
% 1.46/1.27
% 1.46/1.27 thf(more,type,
% 1.46/1.27 more: nat > nat > $o ).
% 1.46/1.27
% 1.46/1.27 thf(m,axiom,
% 1.46/1.27 more @ x @ y ).
% 1.46/1.27
% 1.46/1.27 thf(pl,type,
% 1.46/1.27 pl: nat > nat > nat ).
% 1.46/1.27
% 1.46/1.27 thf(satz19a,axiom,
% 1.46/1.27 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.46/1.27 ( ( more @ Xx @ Xy )
% 1.46/1.27 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(satz6,axiom,
% 1.46/1.27 ! [Xx: nat,Xy: nat] :
% 1.46/1.27 ( ( pl @ Xx @ Xy )
% 1.46/1.27 = ( pl @ Xy @ Xx ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(satz19d,conjecture,
% 1.46/1.27 more @ ( pl @ z @ x ) @ ( pl @ z @ y ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (8963)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8680 for (2999ds/2Mi)
% 1.46/1.29 % (8963)Instruction limit reached!
% 1.46/1.29 % (8963)------------------------------
% 1.46/1.29 % (8963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (8963)Termination reason: Unknown
% 1.46/1.29 % (8963)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (8963)Memory used [KB]: 5500
% 1.46/1.29 % (8963)Time elapsed: 0.002 s
% 1.46/1.29 % (8963)Instructions burned: 2 (million)
% 1.46/1.29 % (8963)------------------------------
% 1.46/1.29 % (8963)------------------------------
% 1.46/1.30 % (8960)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8680 for (2999ds/183Mi)
% 1.46/1.30 % (8961)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_8680 for (2999ds/4Mi)
% 1.60/1.30 % (8962)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_8680 for (2999ds/27Mi)
% 1.60/1.30 % (8964)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_8680 for (2999ds/2Mi)
% 1.60/1.30 % (8965)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_8680 for (2999ds/275Mi)
% 1.60/1.30 % (8966)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8680 for (2999ds/18Mi)
% 1.60/1.30 % (8964)Instruction limit reached!
% 1.60/1.30 % (8964)------------------------------
% 1.60/1.30 % (8964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (8964)Termination reason: Unknown
% 1.60/1.30 % (8964)Termination phase: Property scanning
% 1.60/1.30
% 1.60/1.30 % (8964)Memory used [KB]: 895
% 1.60/1.30 % (8964)Time elapsed: 0.003 s
% 1.60/1.30 % (8964)Instructions burned: 2 (million)
% 1.60/1.30 % (8964)------------------------------
% 1.60/1.30 % (8964)------------------------------
% 1.60/1.30 % (8967)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8680 for (2999ds/3Mi)
% 1.60/1.30 % (8965)First to succeed.
% 1.60/1.30 % (8961)Instruction limit reached!
% 1.60/1.30 % (8961)------------------------------
% 1.60/1.30 % (8961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (8961)Termination reason: Unknown
% 1.60/1.30 % (8961)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (8961)Memory used [KB]: 5500
% 1.60/1.30 % (8961)Time elapsed: 0.005 s
% 1.60/1.30 % (8961)Instructions burned: 4 (million)
% 1.60/1.30 % (8961)------------------------------
% 1.60/1.30 % (8961)------------------------------
% 1.60/1.30 % (8967)Instruction limit reached!
% 1.60/1.30 % (8967)------------------------------
% 1.60/1.30 % (8967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (8967)Termination reason: Unknown
% 1.60/1.30 % (8967)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (8967)Memory used [KB]: 5500
% 1.60/1.30 % (8967)Time elapsed: 0.002 s
% 1.60/1.30 % (8967)Instructions burned: 3 (million)
% 1.60/1.30 % (8967)------------------------------
% 1.60/1.30 % (8967)------------------------------
% 1.60/1.30 % (8962)Also succeeded, but the first one will report.
% 1.60/1.30 % (8965)Refutation found. Thanks to Tanya!
% 1.60/1.30 % SZS status Theorem for DTF2THF_8680
% 1.60/1.30 % SZS output start Proof for DTF2THF_8680
% 1.60/1.30 thf(type_def_5, type, nat: $tType).
% 1.60/1.30 thf(func_def_0, type, nat: $tType).
% 1.60/1.30 thf(func_def_1, type, x: nat).
% 1.60/1.30 thf(func_def_2, type, y: nat).
% 1.60/1.30 thf(func_def_3, type, z: nat).
% 1.60/1.30 thf(func_def_4, type, more: nat > nat > $o).
% 1.60/1.30 thf(func_def_6, type, pl: nat > nat > nat).
% 1.60/1.30 thf(f26,plain,(
% 1.60/1.30 $false),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f25,f18])).
% 1.60/1.30 thf(f18,plain,(
% 1.60/1.30 ((more @ x @ y) = $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.60/1.30 thf(f12,plain,(
% 1.60/1.30 ((more @ x @ y) = $true)),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.60/1.30 thf(f11,plain,(
% 1.60/1.30 (more @ x @ y)),
% 1.60/1.30 inference(rectify,[status(thm)],[f1])).
% 1.60/1.30 thf(f1,axiom,(
% 1.60/1.30 (more @ x @ y)),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',m)).
% 1.60/1.30 thf(f25,plain,(
% 1.60/1.30 ((more @ x @ y) != $true)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.60/1.30 thf(f24,plain,(
% 1.60/1.30 ($true != $true) | ((more @ x @ y) != $true)),
% 1.60/1.30 inference(superposition,[status(thm)],[f23,f19])).
% 1.60/1.30 thf(f19,plain,(
% 1.60/1.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X2 @ X0) @ (pl @ X1 @ X0))) | ($true != (more @ X2 @ X1))) )),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.30 thf(f16,plain,(
% 1.60/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (more @ (pl @ X2 @ X0) @ (pl @ X1 @ X0))) | ($true != (more @ X2 @ X1)))),
% 1.60/1.30 inference(rectify,[status(thm)],[f15])).
% 1.60/1.30 thf(f15,plain,(
% 1.60/1.30 ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X2))) | ($true != (more @ X1 @ X0)))),
% 1.60/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.60/1.30 thf(f8,plain,(
% 1.60/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (more @ X1 @ X0)) => ($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X2))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.60/1.30 thf(f7,plain,(
% 1.60/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X1 @ X0) => (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X2)))),
% 1.60/1.30 inference(rectify,[status(thm)],[f2])).
% 1.60/1.30 thf(f2,axiom,(
% 1.60/1.30 ! [X1 : nat,X0 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz19a)).
% 1.60/1.30 thf(f23,plain,(
% 1.60/1.30 ((more @ (pl @ x @ z) @ (pl @ y @ z)) != $true)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f22,f21])).
% 1.60/1.30 thf(f21,plain,(
% 1.60/1.30 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X1 @ X0))) )),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f17])).
% 1.60/1.30 thf(f17,plain,(
% 1.60/1.30 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.60/1.30 inference(rectify,[status(thm)],[f14])).
% 1.60/1.30 thf(f14,plain,(
% 1.60/1.30 ! [X1 : nat,X0 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.60/1.30 inference(rectify,[status(thm)],[f3])).
% 1.60/1.30 thf(f3,axiom,(
% 1.60/1.30 ! [X1 : nat,X0 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz6)).
% 1.60/1.30 thf(f22,plain,(
% 1.60/1.30 ((more @ (pl @ x @ z) @ (pl @ z @ y)) != $true)),
% 1.60/1.30 inference(forward_demodulation,[status(thm)],[f20,f21])).
% 1.60/1.30 thf(f20,plain,(
% 1.60/1.30 ((more @ (pl @ z @ x) @ (pl @ z @ y)) != $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.60/1.30 thf(f13,plain,(
% 1.60/1.30 ((more @ (pl @ z @ x) @ (pl @ z @ y)) != $true)),
% 1.60/1.30 inference(flattening,[status(thm)],[f10])).
% 1.60/1.30 thf(f10,plain,(
% 1.60/1.30 ~((more @ (pl @ z @ x) @ (pl @ z @ y)) = $true)),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.60/1.30 thf(f9,plain,(
% 1.60/1.30 ~(more @ (pl @ z @ x) @ (pl @ z @ y))),
% 1.60/1.30 inference(rectify,[status(thm)],[f5])).
% 1.60/1.30 thf(f5,negated_conjecture,(
% 1.60/1.30 ~(more @ (pl @ z @ x) @ (pl @ z @ y))),
% 1.60/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.60/1.30 thf(f4,conjecture,(
% 1.60/1.30 (more @ (pl @ z @ x) @ (pl @ z @ y))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.WMmry1SZQ6/DTF2THF_8680.p',satz19d)).
% 1.60/1.30 % SZS output end Proof for DTF2THF_8680
% 1.60/1.30 % (8965)------------------------------
% 1.60/1.30 % (8965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (8965)Termination reason: Refutation
% 1.60/1.30
% 1.60/1.30 % (8965)Memory used [KB]: 5500
% 1.60/1.30 % (8965)Time elapsed: 0.005 s
% 1.60/1.30 % (8965)Instructions burned: 2 (million)
% 1.60/1.30 % (8965)------------------------------
% 1.60/1.30 % (8965)------------------------------
% 1.60/1.30 % (8959)Success in time 0.02 s
%------------------------------------------------------------------------------