%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM688^1 : 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 : n006.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 09:24:16 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 62 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 287 ( 37 ~; 24 |; 0 &; 210 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% 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,
u: nat ).
thf(func_def_5,type,
more: nat > nat > $o ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(f52,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f51,f37]) ).
thf(f37,plain,
( ( more @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( more @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
more @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
more @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',m) ).
thf(f51,plain,
( ( more @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f46,f39]) ).
thf(f39,plain,
! [X3: nat,X0: nat,X1: nat] :
( ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X0 @ X3 ) )
= $true )
| ( $true
!= ( more @ X1 @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( X2 != X3 )
| ( $true
!= ( more @ X1 @ X0 ) )
| ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X2 != X3 )
| ( $true
!= ( more @ X1 @ X0 ) )
| ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: nat,X1: nat,X3: nat,X0: nat] :
( ( X0 != X3 )
| ( ( more @ X1 @ X2 )
!= $true )
| ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true )
| ( ( more @ X1 @ X2 )
!= $true )
| ( X0 != X3 ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( X0 = X3 )
=> ( ( ( more @ X1 @ X2 )
= $true )
=> ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X0 = X3 )
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X3: nat,X4: nat,X1: nat] :
( ( X1 = X2 )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz19h) ).
thf(f46,plain,
( $true
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ),
inference(superposition,[status(thm)],[f33,f44]) ).
thf(f44,plain,
z = u,
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( z = u ) ),
inference(superposition,[status(thm)],[f42,f34]) ).
thf(f34,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',n) ).
thf(f42,plain,
( ( more @ z @ u )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f41,f37]) ).
thf(f41,plain,
( ( ( more @ x @ y )
!= $true )
| ( ( more @ z @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( more @ z @ u )
!= $true )
| ( $true != $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f33,f32]) ).
thf(f32,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) )
= $true )
| ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( more @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( more @ X2 @ X3 ) )
| ( ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) )
= $true ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: nat,X2: nat,X3: nat,X0: nat] :
( ( ( more @ X1 @ X2 )
!= $true )
| ( $true
!= ( more @ X3 @ X0 ) )
| ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: nat,X3: nat,X0: nat,X2: nat] :
( ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true )
| ( $true
!= ( more @ X3 @ X0 ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: nat,X3: nat,X0: nat,X2: nat] :
( ( ( more @ X1 @ X2 )
= $true )
=> ( ( $true
= ( more @ X3 @ X0 ) )
=> ( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( ( more @ X3 @ X0 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz21) ).
thf(f33,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz22b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM688^1 : 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
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:10:45 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUM688^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Number Theory
% 0.30/0.46 % Problem : Landau theorem 22b
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : more (pl x z) (pl y u)
% 0.30/0.46
% 0.30/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : satz22b [Lan30]
% 0.30/0.46 % : satz35b [Lan30]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % : Without extensionality : Theorem
% 0.30/0.46 % 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, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 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, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 13 ( 2 unt; 7 typ; 0 def)
% 0.30/0.46 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 3 ( 1 avg)
% 0.30/0.46 % Number of connectives : 37 ( 3 ~; 0 |; 0 &; 28 @)
% 0.30/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(nat_type,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(x,type,
% 0.30/0.46 x: nat ).
% 0.30/0.46
% 0.30/0.46 thf(y,type,
% 0.30/0.46 y: nat ).
% 0.30/0.46
% 0.30/0.46 thf(z,type,
% 0.30/0.46 z: nat ).
% 0.30/0.46
% 0.30/0.46 thf(u,type,
% 0.30/0.46 u: nat ).
% 0.30/0.46
% 0.30/0.46 thf(more,type,
% 0.30/0.46 more: nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(m,axiom,
% 0.30/0.46 more @ x @ y ).
% 0.30/0.46
% 0.30/0.46 thf(n,axiom,
% 0.30/0.46 ( ~ ( more @ z @ u )
% 0.30/0.46 => ( z = u ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(pl,type,
% 0.30/0.46 pl: nat > nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(et,axiom,
% 0.30/0.46 ! [Xa: $o] :
% 0.30/0.46 ( ~ ~ Xa
% 0.30/0.46 => Xa ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz19h,axiom,
% 0.30/0.46 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( more @ Xz @ Xu )
% 0.30/0.46 => ( more @ ( pl @ Xz @ Xx ) @ ( pl @ Xu @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz21,axiom,
% 0.30/0.46 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.30/0.46 ( ( more @ Xx @ Xy )
% 0.30/0.46 => ( ( more @ Xz @ Xu )
% 0.30/0.46 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz22b,conjecture,
% 0.30/0.46 more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 11:10:46 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2DTF29525.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(nat_type,type,
% 1.49/1.25 nat: $tType ).
% 1.49/1.25
% 1.49/1.25 thf(x,type,
% 1.49/1.25 x: nat ).
% 1.49/1.25
% 1.49/1.25 thf(y,type,
% 1.49/1.25 y: nat ).
% 1.49/1.25
% 1.49/1.25 thf(z,type,
% 1.49/1.25 z: nat ).
% 1.49/1.25
% 1.49/1.25 thf(u,type,
% 1.49/1.25 u: nat ).
% 1.49/1.25
% 1.49/1.25 thf(more,type,
% 1.49/1.25 more: nat > nat > $o ).
% 1.49/1.25
% 1.49/1.25 thf(m,axiom,
% 1.49/1.25 more @ x @ y ).
% 1.49/1.25
% 1.49/1.25 thf(n,axiom,
% 1.49/1.25 ( ~ ( more @ z @ u )
% 1.49/1.25 => ( z = u ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(pl,type,
% 1.49/1.25 pl: nat > nat > nat ).
% 1.49/1.25
% 1.49/1.25 thf(et,axiom,
% 1.49/1.25 ! [Xa: $o] :
% 1.49/1.25 ( ~ ~ Xa
% 1.49/1.25 => Xa ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz19h,axiom,
% 1.49/1.25 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.49/1.25 ( ( Xx = Xy )
% 1.49/1.25 => ( ( more @ Xz @ Xu )
% 1.49/1.25 => ( more @ ( pl @ Xz @ Xx ) @ ( pl @ Xu @ Xy ) ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz21,axiom,
% 1.49/1.25 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.49/1.25 ( ( more @ Xx @ Xy )
% 1.49/1.25 => ( ( more @ Xz @ Xu )
% 1.49/1.25 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz22b,conjecture,
% 1.49/1.25 more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (29813)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_29525 for (2999ds/275Mi)
% 1.49/1.26 % (29809)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_29525 for (2999ds/4Mi)
% 1.49/1.27 % (29813)First to succeed.
% 1.49/1.27 % (29809)Instruction limit reached!
% 1.49/1.27 % (29809)------------------------------
% 1.49/1.27 % (29809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (29809)Termination reason: Unknown
% 1.49/1.27 % (29809)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (29809)Memory used [KB]: 5500
% 1.49/1.27 % (29809)Time elapsed: 0.003 s
% 1.49/1.27 % (29809)Instructions burned: 5 (million)
% 1.49/1.27 % (29809)------------------------------
% 1.49/1.27 % (29809)------------------------------
% 1.49/1.27 % (29813)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_29525
% 1.49/1.27 % SZS output start Proof for DTF2THF_29525
% 1.49/1.27 thf(type_def_5, type, nat: $tType).
% 1.49/1.27 thf(func_def_0, type, nat: $tType).
% 1.49/1.27 thf(func_def_1, type, x: nat).
% 1.49/1.27 thf(func_def_2, type, y: nat).
% 1.49/1.27 thf(func_def_3, type, z: nat).
% 1.49/1.27 thf(func_def_4, type, u: nat).
% 1.49/1.27 thf(func_def_5, type, more: nat > nat > $o).
% 1.49/1.27 thf(func_def_7, type, pl: nat > nat > nat).
% 1.49/1.27 thf(f52,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f51,f37])).
% 1.49/1.27 thf(f37,plain,(
% 1.49/1.27 ((more @ x @ y) = $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 ((more @ x @ y) = $true)),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f13])).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 (more @ x @ y)),
% 1.49/1.27 inference(rectify,[status(thm)],[f1])).
% 1.49/1.27 thf(f1,axiom,(
% 1.49/1.27 (more @ x @ y)),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',m)).
% 1.49/1.27 thf(f51,plain,(
% 1.49/1.27 ((more @ x @ y) != $true)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.49/1.27 thf(f49,plain,(
% 1.49/1.27 ((more @ x @ y) != $true) | ($true != $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f46,f39])).
% 1.49/1.27 thf(f39,plain,(
% 1.49/1.27 ( ! [X3 : nat,X0 : nat,X1 : nat] : (((more @ (pl @ X1 @ X3) @ (pl @ X0 @ X3)) = $true) | ($true != (more @ X1 @ X0))) )),
% 1.49/1.27 inference(equality_resolution,[status(thm)],[f36])).
% 1.49/1.27 thf(f36,plain,(
% 1.49/1.27 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((X2 != X3) | ($true != (more @ X1 @ X0)) | ((more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3)) = $true)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f31])).
% 1.49/1.27 thf(f31,plain,(
% 1.49/1.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((X2 != X3) | ($true != (more @ X1 @ X0)) | ((more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3)) = $true))),
% 1.49/1.27 inference(rectify,[status(thm)],[f25])).
% 1.49/1.27 thf(f25,plain,(
% 1.49/1.27 ! [X2 : nat,X1 : nat,X3 : nat,X0 : nat] : ((X0 != X3) | ((more @ X1 @ X2) != $true) | ((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true))),
% 1.49/1.27 inference(flattening,[status(thm)],[f24])).
% 1.49/1.27 thf(f24,plain,(
% 1.49/1.27 ! [X2 : nat,X0 : nat,X1 : nat,X3 : nat] : ((((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true) | ((more @ X1 @ X2) != $true)) | (X0 != X3))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f20])).
% 1.49/1.27 thf(f20,plain,(
% 1.49/1.27 ! [X2 : nat,X0 : nat,X1 : nat,X3 : nat] : ((X0 = X3) => (((more @ X1 @ X2) = $true) => ((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f19])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((X0 = X3) => ((more @ X1 @ X2) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f4])).
% 1.49/1.27 thf(f4,axiom,(
% 1.49/1.27 ! [X2 : nat,X3 : nat,X4 : nat,X1 : nat] : ((X1 = X2) => ((more @ X3 @ X4) => (more @ (pl @ X3 @ X1) @ (pl @ X4 @ X2))))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz19h)).
% 1.49/1.27 thf(f46,plain,(
% 1.49/1.27 ($true != (more @ (pl @ x @ z) @ (pl @ y @ z)))),
% 1.49/1.27 inference(superposition,[status(thm)],[f33,f44])).
% 1.49/1.27 thf(f44,plain,(
% 1.49/1.27 (z = u)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.49/1.27 thf(f43,plain,(
% 1.49/1.27 ($true != $true) | (z = u)),
% 1.49/1.27 inference(superposition,[status(thm)],[f42,f34])).
% 1.49/1.27 thf(f34,plain,(
% 1.49/1.27 ((more @ z @ u) = $true) | (z = u)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f29])).
% 1.49/1.27 thf(f29,plain,(
% 1.49/1.27 ((more @ z @ u) = $true) | (z = u)),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f23])).
% 1.49/1.27 thf(f23,plain,(
% 1.49/1.27 ((more @ z @ u) != $true) => (z = u)),
% 1.49/1.27 inference(flattening,[status(thm)],[f18])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 ~((more @ z @ u) = $true) => (z = u)),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f17])).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 ~(more @ z @ u) => (z = u)),
% 1.49/1.27 inference(rectify,[status(thm)],[f2])).
% 1.49/1.27 thf(f2,axiom,(
% 1.49/1.27 ~(more @ z @ u) => (z = u)),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',n)).
% 1.49/1.27 thf(f42,plain,(
% 1.49/1.27 ((more @ z @ u) != $true)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f41,f37])).
% 1.49/1.27 thf(f41,plain,(
% 1.49/1.27 ((more @ x @ y) != $true) | ((more @ z @ u) != $true)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.49/1.27 thf(f40,plain,(
% 1.49/1.27 ((more @ z @ u) != $true) | ($true != $true) | ((more @ x @ y) != $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f33,f32])).
% 1.49/1.27 thf(f32,plain,(
% 1.49/1.27 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3)) = $true) | ($true != (more @ X0 @ X1)) | ($true != (more @ X2 @ X3))) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.27 thf(f30,plain,(
% 1.49/1.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true != (more @ X0 @ X1)) | ($true != (more @ X2 @ X3)) | ((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3)) = $true))),
% 1.49/1.27 inference(rectify,[status(thm)],[f27])).
% 1.49/1.27 thf(f27,plain,(
% 1.49/1.27 ! [X1 : nat,X2 : nat,X3 : nat,X0 : nat] : (((more @ X1 @ X2) != $true) | ($true != (more @ X3 @ X0)) | ((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true))),
% 1.49/1.27 inference(flattening,[status(thm)],[f26])).
% 1.49/1.27 thf(f26,plain,(
% 1.49/1.27 ! [X1 : nat,X3 : nat,X0 : nat,X2 : nat] : ((((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true) | ($true != (more @ X3 @ X0))) | ((more @ X1 @ X2) != $true))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f16])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 ! [X1 : nat,X3 : nat,X0 : nat,X2 : nat] : (((more @ X1 @ X2) = $true) => (($true = (more @ X3 @ X0)) => ((more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)) = $true)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f15])).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X1 @ X2) => ((more @ X3 @ X0) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,axiom,(
% 1.49/1.27 ! [X4 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X1 @ X2) => ((more @ X3 @ X4) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X4))))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz21)).
% 1.49/1.27 thf(f33,plain,(
% 1.49/1.27 ((more @ (pl @ x @ z) @ (pl @ y @ u)) != $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f21])).
% 1.49/1.27 thf(f21,plain,(
% 1.49/1.27 ((more @ (pl @ x @ z) @ (pl @ y @ u)) != $true)),
% 1.49/1.27 inference(flattening,[status(thm)],[f12])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 ~((more @ (pl @ x @ z) @ (pl @ y @ u)) = $true)),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f11])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 ~(more @ (pl @ x @ z) @ (pl @ y @ u))),
% 1.49/1.27 inference(rectify,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,negated_conjecture,(
% 1.49/1.27 ~(more @ (pl @ x @ z) @ (pl @ y @ u))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f6])).
% 1.49/1.27 thf(f6,conjecture,(
% 1.49/1.27 (more @ (pl @ x @ z) @ (pl @ y @ u))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.Ih9gvY7kJK/DTF2THF_29525.p',satz22b)).
% 1.49/1.27 % SZS output end Proof for DTF2THF_29525
% 1.49/1.27 % (29813)------------------------------
% 1.49/1.27 % (29813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (29813)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (29813)Memory used [KB]: 5500
% 1.49/1.27 % (29813)Time elapsed: 0.003 s
% 1.49/1.27 % (29813)Instructions burned: 3 (million)
% 1.49/1.27 % (29813)------------------------------
% 1.49/1.27 % (29813)------------------------------
% 1.49/1.27 % (29807)Success in time 0.013 s
%------------------------------------------------------------------------------