%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM681^1 : 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 : n010.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 09:24:14 AM UTC 2026
% Result : Theorem 1.69s 1.33s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 90 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 349 ( 69 ~; 28 |; 4 &; 214 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% 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,
less: nat > nat > $o ).
thf(func_def_7,type,
more: nat > nat > $o ).
thf(f80,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f79,f60]) ).
thf(f60,plain,
( $true
!= ( less @ x @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ( $true
!= ( less @ x @ y ) ) ),
inference(superposition,[status(thm)],[f43,f46]) ).
thf(f46,plain,
! [X0: nat] :
( ( $true
= ( less @ ( pl @ X0 @ z ) @ ( pl @ x @ z ) ) )
| ( $true
!= ( less @ X0 @ y ) ) ),
inference(superposition,[status(thm)],[f33,f37]) ).
thf(f37,plain,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',i) ).
thf(f33,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( less @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) )
| ( $true
!= ( less @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( less @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) )
| ( $true
!= ( less @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( $true
= ( less @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) )
| ( $true
!= ( less @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
=> ( $true
= ( less @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X1 @ X0 )
=> ( less @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X1: nat,X3: nat] :
( ( less @ X1 @ X2 )
=> ( less @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz19c) ).
thf(f43,plain,
! [X1: nat] :
( $true
!= ( less @ X1 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( less @ X0 @ X1 ) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: nat,X1: nat] :
( ( ( $true
!= ( less @ X0 @ X1 ) )
| ( X0 != X1 ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( X0 != X1 )
| ( ( more @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( ( $true
!= ( less @ X0 @ X1 ) )
| ( X0 != X1 ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( X0 != X1 )
| ( ( more @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat] :
~ ( ( ( X1 = X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ~ ~ ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ( X1 != X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz10b) ).
thf(f79,plain,
( $true
= ( less @ x @ y ) ),
inference(subsumption_resolution,[status(thm)],[f78,f35]) ).
thf(f35,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
x != y,
inference(flattening,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
x != y,
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
x = y,
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz20b) ).
thf(f78,plain,
( ( x = y )
| ( $true
= ( less @ x @ y ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( x = y )
| ( $true != $true )
| ( $true
= ( less @ x @ y ) ) ),
inference(superposition,[status(thm)],[f76,f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
| ( $true
= ( more @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: nat,X0: nat] :
( ( $true
= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: nat,X0: nat] :
( ( $true
= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ~ ( more @ X1 @ X2 )
=> ( less @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz10a) ).
thf(f76,plain,
( $true
!= ( more @ x @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true
!= ( more @ x @ y ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f44,f52]) ).
thf(f52,plain,
! [X0: nat] :
( ( $true
= ( more @ ( pl @ X0 @ z ) @ ( pl @ x @ z ) ) )
| ( $true
!= ( more @ X0 @ y ) ) ),
inference(superposition,[status(thm)],[f41,f37]) ).
thf(f41,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) )
| ( $true
!= ( more @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
!= ( more @ X2 @ X0 ) )
| ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( $true
= ( more @ X2 @ X0 ) )
=> ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X2 @ X0 )
=> ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: nat,X3: nat,X1: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz19a) ).
thf(f44,plain,
! [X1: nat] :
( $true
!= ( more @ X1 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM681^1 : 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 : n010.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 11:10:18 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
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : NUM681^1 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.47 % Domain : Number Theory
% 0.32/0.47 % Problem : Landau theorem 20b
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English : x = y
% 0.32/0.47
% 0.32/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.32/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.32/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.47 % Source : [Bro09]
% 0.32/0.47 % Names : satz20b [Lan30]
% 0.32/0.47 % : satz33b [Lan30]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % : Without extensionality : Theorem
% 0.32/0.47 % 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, 0.25 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 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.00 v3.7.0
% 0.32/0.47 % Syntax : Number of formulae : 14 ( 2 unt; 7 typ; 0 def)
% 0.32/0.47 % Number of atoms : 15 ( 5 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 6 ( 2 avg)
% 0.32/0.47 % Number of connectives : 53 ( 11 ~; 0 |; 0 &; 32 @)
% 0.32/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 12 ( 6 avg)
% 0.32/0.47 % Number of types : 2 ( 1 usr)
% 0.32/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.32/0.47 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.32/0.47 % SPC : TH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments :
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf(nat_type,type,
% 0.32/0.47 nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(x,type,
% 0.32/0.47 x: nat ).
% 0.32/0.47
% 0.32/0.47 thf(y,type,
% 0.32/0.47 y: nat ).
% 0.32/0.47
% 0.32/0.47 thf(z,type,
% 0.32/0.47 z: nat ).
% 0.32/0.47
% 0.32/0.47 thf(pl,type,
% 0.32/0.47 pl: nat > nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(i,axiom,
% 0.32/0.47 ( ( pl @ x @ z )
% 0.32/0.47 = ( pl @ y @ z ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(et,axiom,
% 0.32/0.47 ! [Xa: $o] :
% 0.32/0.47 ( ~ ~ Xa
% 0.32/0.47 => Xa ) ).
% 0.32/0.47
% 0.32/0.47 thf(less,type,
% 0.32/0.47 less: nat > nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(more,type,
% 0.32/0.47 more: nat > nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(satz10b,axiom,
% 0.32/0.47 ! [Xx: nat,Xy: nat] :
% 0.32/0.47 ~ ( ( ( Xx = Xy )
% 0.32/0.47 => ~ ( more @ Xx @ Xy ) )
% 0.32/0.47 => ~ ~ ( ( ( more @ Xx @ Xy )
% 0.32/0.47 => ~ ( less @ Xx @ Xy ) )
% 0.32/0.47 => ~ ( ( less @ Xx @ Xy )
% 0.32/0.47 => ( Xx != Xy ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(satz19c,axiom,
% 0.32/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.32/0.47 ( ( less @ Xx @ Xy )
% 0.32/0.47 => ( less @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(satz10a,axiom,
% 0.32/0.47 ! [Xx: nat,Xy: nat] :
% 0.32/0.47 ( ( Xx != Xy )
% 0.32/0.47 => ( ~ ( more @ Xx @ Xy )
% 0.32/0.47 => ( less @ Xx @ Xy ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(satz19a,axiom,
% 0.32/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.32/0.47 ( ( more @ Xx @ Xy )
% 0.32/0.47 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(satz20b,conjecture,
% 0.32/0.47 x = y ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 11:10:19 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2DTF16696.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(nat_type,type,
% 1.69/1.30 nat: $tType ).
% 1.69/1.30
% 1.69/1.30 thf(x,type,
% 1.69/1.30 x: nat ).
% 1.69/1.30
% 1.69/1.30 thf(y,type,
% 1.69/1.30 y: nat ).
% 1.69/1.30
% 1.69/1.30 thf(z,type,
% 1.69/1.30 z: nat ).
% 1.69/1.30
% 1.69/1.30 thf(pl,type,
% 1.69/1.30 pl: nat > nat > nat ).
% 1.69/1.30
% 1.69/1.30 thf(i,axiom,
% 1.69/1.30 ( ( pl @ x @ z )
% 1.69/1.30 = ( pl @ y @ z ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(et,axiom,
% 1.69/1.30 ! [Xa: $o] :
% 1.69/1.30 ( ~ ~ Xa
% 1.69/1.30 => Xa ) ).
% 1.69/1.30
% 1.69/1.30 thf(less,type,
% 1.69/1.30 less: nat > nat > $o ).
% 1.69/1.30
% 1.69/1.30 thf(more,type,
% 1.69/1.30 more: nat > nat > $o ).
% 1.69/1.30
% 1.69/1.30 thf(satz10b,axiom,
% 1.69/1.30 ! [Xx: nat,Xy: nat] :
% 1.69/1.30 ~ ( ( ( Xx = Xy )
% 1.69/1.30 => ~ ( more @ Xx @ Xy ) )
% 1.69/1.30 => ~ ~ ( ( ( more @ Xx @ Xy )
% 1.69/1.30 => ~ ( less @ Xx @ Xy ) )
% 1.69/1.30 => ~ ( ( less @ Xx @ Xy )
% 1.69/1.30 => ( Xx != Xy ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(satz19c,axiom,
% 1.69/1.30 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.69/1.30 ( ( less @ Xx @ Xy )
% 1.69/1.30 => ( less @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(satz10a,axiom,
% 1.69/1.30 ! [Xx: nat,Xy: nat] :
% 1.69/1.30 ( ( Xx != Xy )
% 1.69/1.30 => ( ~ ( more @ Xx @ Xy )
% 1.69/1.30 => ( less @ Xx @ Xy ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(satz19a,axiom,
% 1.69/1.30 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.69/1.30 ( ( more @ Xx @ Xy )
% 1.69/1.30 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(satz20b,conjecture,
% 1.69/1.30 x = y ).
% 1.69/1.30 ------------------------
% 1.69/1.31 % (17027)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16696 for (2999ds/2Mi)
% 1.69/1.31 % (17027)Instruction limit reached!
% 1.69/1.31 % (17027)------------------------------
% 1.69/1.31 % (17027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (17027)Termination reason: Unknown
% 1.69/1.31 % (17027)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (17027)Memory used [KB]: 5500
% 1.69/1.31 % (17027)Time elapsed: 0.003 s
% 1.69/1.31 % (17027)Instructions burned: 3 (million)
% 1.69/1.31 % (17027)------------------------------
% 1.69/1.31 % (17027)------------------------------
% 1.69/1.32 % (17024)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16696 for (2999ds/183Mi)
% 1.69/1.32 % (17025)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_16696 for (2999ds/4Mi)
% 1.69/1.32 % (17026)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_16696 for (2999ds/27Mi)
% 1.69/1.32 % (17028)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_16696 for (2999ds/2Mi)
% 1.69/1.32 % (17029)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_16696 for (2999ds/275Mi)
% 1.69/1.32 % (17030)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16696 for (2999ds/18Mi)
% 1.69/1.32 % (17028)Instruction limit reached!
% 1.69/1.32 % (17028)------------------------------
% 1.69/1.32 % (17028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (17028)Termination reason: Unknown
% 1.69/1.32 % (17028)Termination phase: shuffling
% 1.69/1.32
% 1.69/1.32 % (17028)Memory used [KB]: 895
% 1.69/1.32 % (17028)Time elapsed: 0.003 s
% 1.69/1.32 % (17028)Instructions burned: 2 (million)
% 1.69/1.32 % (17028)------------------------------
% 1.69/1.32 % (17028)------------------------------
% 1.69/1.32 % (17029)Refutation not found, incomplete strategy
% 1.69/1.32 % (17029)------------------------------
% 1.69/1.32 % (17029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (17029)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.32
% 1.69/1.32
% 1.69/1.32 % (17029)Memory used [KB]: 5373
% 1.69/1.32 % (17029)Time elapsed: 0.003 s
% 1.69/1.32 % (17029)Instructions burned: 2 (million)
% 1.69/1.32 % (17029)------------------------------
% 1.69/1.32 % (17029)------------------------------
% 1.69/1.32 % (17025)Instruction limit reached!
% 1.69/1.32 % (17025)------------------------------
% 1.69/1.32 % (17025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (17025)Termination reason: Unknown
% 1.69/1.32 % (17025)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (17025)Memory used [KB]: 5500
% 1.69/1.32 % (17025)Time elapsed: 0.005 s
% 1.69/1.32 % (17025)Instructions burned: 5 (million)
% 1.69/1.32 % (17025)------------------------------
% 1.69/1.32 % (17025)------------------------------
% 1.69/1.32 % (17031)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16696 for (2999ds/3Mi)
% 1.69/1.32 % (17031)Instruction limit reached!
% 1.69/1.32 % (17031)------------------------------
% 1.69/1.32 % (17031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (17031)Termination reason: Unknown
% 1.69/1.32 % (17031)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (17031)Memory used [KB]: 5500
% 1.69/1.32 % (17031)Time elapsed: 0.002 s
% 1.69/1.32 % (17031)Instructions burned: 3 (million)
% 1.69/1.32 % (17031)------------------------------
% 1.69/1.32 % (17031)------------------------------
% 1.69/1.33 % (17024)First to succeed.
% 1.69/1.33 % (17030)Also succeeded, but the first one will report.
% 1.69/1.33 % (17024)Refutation found. Thanks to Tanya!
% 1.69/1.33 % SZS status Theorem for DTF2THF_16696
% 1.69/1.33 % SZS output start Proof for DTF2THF_16696
% 1.69/1.33 thf(type_def_5, type, nat: $tType).
% 1.69/1.33 thf(func_def_0, type, nat: $tType).
% 1.69/1.33 thf(func_def_1, type, x: nat).
% 1.69/1.33 thf(func_def_2, type, y: nat).
% 1.69/1.33 thf(func_def_3, type, z: nat).
% 1.69/1.33 thf(func_def_4, type, pl: nat > nat > nat).
% 1.69/1.33 thf(func_def_6, type, less: nat > nat > $o).
% 1.69/1.33 thf(func_def_7, type, more: nat > nat > $o).
% 1.69/1.33 thf(f80,plain,(
% 1.69/1.33 $false),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f79,f60])).
% 1.69/1.33 thf(f60,plain,(
% 1.69/1.33 ($true != (less @ x @ y))),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.69/1.33 thf(f57,plain,(
% 1.69/1.33 ($true != $true) | ($true != (less @ x @ y))),
% 1.69/1.33 inference(superposition,[status(thm)],[f43,f46])).
% 1.69/1.33 thf(f46,plain,(
% 1.69/1.33 ( ! [X0 : nat] : (($true = (less @ (pl @ X0 @ z) @ (pl @ x @ z))) | ($true != (less @ X0 @ y))) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f33,f37])).
% 1.69/1.33 thf(f37,plain,(
% 1.69/1.33 ((pl @ x @ z) = (pl @ y @ z))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f1])).
% 1.69/1.33 thf(f1,axiom,(
% 1.69/1.33 ((pl @ x @ z) = (pl @ y @ z))),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',i)).
% 1.69/1.33 thf(f33,plain,(
% 1.69/1.33 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (less @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))) | ($true != (less @ X2 @ X0))) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f31])).
% 1.69/1.33 thf(f31,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (less @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))) | ($true != (less @ X2 @ X0)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f30])).
% 1.69/1.33 thf(f30,plain,(
% 1.69/1.33 ! [X0 : nat,X2 : nat,X1 : nat] : (($true = (less @ (pl @ X1 @ X2) @ (pl @ X0 @ X2))) | ($true != (less @ X1 @ X0)))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f17])).
% 1.69/1.33 thf(f17,plain,(
% 1.69/1.33 ! [X1 : nat,X0 : nat,X2 : nat] : (($true = (less @ X1 @ X0)) => ($true = (less @ (pl @ X1 @ X2) @ (pl @ X0 @ X2))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.33 thf(f16,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : ((less @ X1 @ X0) => (less @ (pl @ X1 @ X2) @ (pl @ X0 @ X2)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f4])).
% 1.69/1.33 thf(f4,axiom,(
% 1.69/1.33 ! [X2 : nat,X1 : nat,X3 : nat] : ((less @ X1 @ X2) => (less @ (pl @ X1 @ X3) @ (pl @ X2 @ X3)))),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz19c)).
% 1.69/1.33 thf(f43,plain,(
% 1.69/1.33 ( ! [X1 : nat] : (($true != (less @ X1 @ X1))) )),
% 1.69/1.33 inference(equality_resolution,[status(thm)],[f40])).
% 1.69/1.33 thf(f40,plain,(
% 1.69/1.33 ( ! [X0 : nat,X1 : nat] : (($true != (less @ X0 @ X1)) | (X0 != X1)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.69/1.33 thf(f29,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ((($true != (less @ X0 @ X1)) | (X0 != X1)) & (((more @ X0 @ X1) != $true) | ($true != (less @ X0 @ X1))) & ((X0 != X1) | ((more @ X0 @ X1) != $true)))),
% 1.69/1.33 inference(flattening,[status(thm)],[f28])).
% 1.69/1.33 thf(f28,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : (((($true != (less @ X0 @ X1)) | (X0 != X1)) & (((more @ X0 @ X1) != $true) | ($true != (less @ X0 @ X1)))) & ((X0 != X1) | ((more @ X0 @ X1) != $true)))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f23])).
% 1.69/1.33 thf(f23,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ((more @ X0 @ X1) != $true)) => ((((more @ X0 @ X1) = $true) => ($true != (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => (X0 != X1))))),
% 1.69/1.33 inference(flattening,[status(thm)],[f19])).
% 1.69/1.33 thf(f19,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~((more @ X0 @ X1) = $true)) => ~~((((more @ X0 @ X1) = $true) => ~($true = (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => (X0 != X1))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.33 thf(f18,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f3])).
% 1.69/1.33 thf(f3,axiom,(
% 1.69/1.33 ! [X1 : nat,X2 : nat] : ~(((X1 = X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => (X1 != X2))))),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz10b)).
% 1.69/1.33 thf(f79,plain,(
% 1.69/1.33 ($true = (less @ x @ y))),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f78,f35])).
% 1.69/1.33 thf(f35,plain,(
% 1.69/1.33 (x != y)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.69/1.33 thf(f22,plain,(
% 1.69/1.33 (x != y)),
% 1.69/1.33 inference(flattening,[status(thm)],[f8])).
% 1.69/1.33 thf(f8,negated_conjecture,(
% 1.69/1.33 ~(x = y)),
% 1.69/1.33 inference(negated_conjecture,[status(cth)],[f7])).
% 1.69/1.33 thf(f7,conjecture,(
% 1.69/1.33 (x = y)),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz20b)).
% 1.69/1.33 thf(f78,plain,(
% 1.69/1.33 (x = y) | ($true = (less @ x @ y))),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.69/1.33 thf(f77,plain,(
% 1.69/1.33 (x = y) | ($true != $true) | ($true = (less @ x @ y))),
% 1.69/1.33 inference(superposition,[status(thm)],[f76,f34])).
% 1.69/1.33 thf(f34,plain,(
% 1.69/1.33 ( ! [X0 : nat,X1 : nat] : (($true = (more @ X1 @ X0)) | ($true = (less @ X1 @ X0)) | (X0 = X1)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.33 thf(f32,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : (($true = (less @ X1 @ X0)) | ($true = (more @ X1 @ X0)) | (X0 = X1))),
% 1.69/1.33 inference(rectify,[status(thm)],[f25])).
% 1.69/1.33 thf(f25,plain,(
% 1.69/1.33 ! [X1 : nat,X0 : nat] : (($true = (less @ X0 @ X1)) | ((more @ X0 @ X1) = $true) | (X0 = X1))),
% 1.69/1.33 inference(flattening,[status(thm)],[f24])).
% 1.69/1.33 thf(f24,plain,(
% 1.69/1.33 ! [X1 : nat,X0 : nat] : ((($true = (less @ X0 @ X1)) | ((more @ X0 @ X1) = $true)) | (X0 = X1))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f21])).
% 1.69/1.33 thf(f21,plain,(
% 1.69/1.33 ! [X1 : nat,X0 : nat] : ((X0 != X1) => (((more @ X0 @ X1) != $true) => ($true = (less @ X0 @ X1))))),
% 1.69/1.33 inference(flattening,[status(thm)],[f15])).
% 1.69/1.33 thf(f15,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~((more @ X0 @ X1) = $true) => ($true = (less @ X0 @ X1))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.33 thf(f14,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f5])).
% 1.69/1.33 thf(f5,axiom,(
% 1.69/1.33 ! [X1 : nat,X2 : nat] : ((X1 != X2) => (~(more @ X1 @ X2) => (less @ X1 @ X2)))),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz10a)).
% 1.69/1.33 thf(f76,plain,(
% 1.69/1.33 ($true != (more @ x @ y))),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.69/1.33 thf(f74,plain,(
% 1.69/1.33 ($true != (more @ x @ y)) | ($true != $true)),
% 1.69/1.33 inference(superposition,[status(thm)],[f44,f52])).
% 1.69/1.33 thf(f52,plain,(
% 1.69/1.33 ( ! [X0 : nat] : (($true = (more @ (pl @ X0 @ z) @ (pl @ x @ z))) | ($true != (more @ X0 @ y))) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f41,f37])).
% 1.69/1.33 thf(f41,plain,(
% 1.69/1.33 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))) | ($true != (more @ X2 @ X0))) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f26])).
% 1.69/1.33 thf(f26,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : (($true != (more @ X2 @ X0)) | ($true = (more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.69/1.33 thf(f11,plain,(
% 1.69/1.33 ! [X2 : nat,X1 : nat,X0 : nat] : (($true = (more @ X2 @ X0)) => ($true = (more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.33 thf(f10,plain,(
% 1.69/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X2 @ X0) => (more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f6])).
% 1.69/1.33 thf(f6,axiom,(
% 1.69/1.33 ! [X2 : nat,X3 : nat,X1 : nat] : ((more @ X1 @ X2) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X3)))),
% 1.69/1.33 file('/export/starexec/sandbox/tmp/tmp.xWWK4jxpPl/DTF2THF_16696.p',satz19a)).
% 1.69/1.33 thf(f44,plain,(
% 1.69/1.33 ( ! [X1 : nat] : (($true != (more @ X1 @ X1))) )),
% 1.69/1.33 inference(equality_resolution,[status(thm)],[f38])).
% 1.69/1.33 thf(f38,plain,(
% 1.69/1.33 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ((more @ X0 @ X1) != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.69/1.33 % SZS output end Proof for DTF2THF_16696
% 1.69/1.33 % (17024)------------------------------
% 1.69/1.33 % (17024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (17024)Termination reason: Refutation
% 1.69/1.33
% 1.69/1.33 % (17024)Memory used [KB]: 5500
% 1.69/1.33 % (17024)Time elapsed: 0.010 s
% 1.69/1.33 % (17024)Instructions burned: 10 (million)
% 1.69/1.33 % (17024)------------------------------
% 1.69/1.33 % (17024)------------------------------
% 1.69/1.33 % (17023)Success in time 0.025 s
%------------------------------------------------------------------------------