%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM691^1 : 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 : n018.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 1.64s 1.35s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 312 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 503 ( 80 ~; 55 |; 7 &; 322 @)
% ( 2 <=>; 37 =>; 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 : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% 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(f98,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f62,f75,f89,f97]) ).
thf(f97,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f94,f55]) ).
thf(f55,plain,
( ( ( more @ z @ u )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_1
<=> ( ( more @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f94,plain,
( ( ( more @ z @ u )
!= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( more @ z @ u )
!= $true )
| ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f78,f48]) ).
thf(f48,plain,
! [X2: nat,X3: nat,X0: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X3 @ X0 ) ) )
| ( $true
!= ( more @ X2 @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
!= ( more @ X2 @ X0 ) )
| ( X1 != X3 )
| ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X3 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( more @ X2 @ X0 ) )
| ( ( $true
!= ( more @ X1 @ X3 ) )
& ( X1 != X3 ) )
| ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X3 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
! [X3: nat,X1: nat,X2: nat,X0: nat] :
( ( $true
!= ( more @ X2 @ X3 ) )
| ( ( $true
!= ( more @ X1 @ X0 ) )
& ( X0 != X1 ) )
| ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
! [X3: nat,X2: nat,X1: nat,X0: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) )
| ( $true
!= ( more @ X2 @ X3 ) )
| ( ( $true
!= ( more @ X1 @ X0 ) )
& ( X0 != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X3: nat,X2: nat,X1: nat,X0: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( X0 = X1 ) )
=> ( ( $true
= ( more @ X2 @ X3 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( X0 = X1 ) )
=> ( ( $true
= ( more @ X2 @ X3 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ~ ( more @ X1 @ X0 )
=> ( X0 = X1 ) )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X1: nat,X3: nat,X4: nat] :
( ( ~ ( more @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz22a) ).
thf(f78,plain,
( ( ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) )
!= $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f37,f77]) ).
thf(f77,plain,
( ( x = y )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( x = y )
| ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f60,f45]) ).
thf(f45,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',m) ).
thf(f60,plain,
( ( ( more @ x @ y )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_2
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f37,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( pl @ x @ z )
!= ( pl @ y @ u ) )
& ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz23) ).
thf(f89,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f88]) ).
thf(f88,plain,
( $false
| spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( pl @ x @ z )
!= ( pl @ x @ z ) )
| spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f79,f64]) ).
thf(f64,plain,
( ( z = u )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( z = u )
| spl0_1 ),
inference(superposition,[status(thm)],[f56,f41]) ).
thf(f41,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,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.8y8FY8P18I/DTF2THF_32726.p',n) ).
thf(f56,plain,
( ( ( more @ z @ u )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f79,plain,
( ( ( pl @ x @ z )
!= ( pl @ x @ u ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f38,f77]) ).
thf(f38,plain,
( ( pl @ x @ z )
!= ( pl @ y @ u ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f75,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f72,f54,f58]) ).
thf(f72,plain,
( ( ( more @ x @ y )
!= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( ( more @ x @ y )
!= $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f66,f46]) ).
thf(f46,plain,
! [X2: nat,X3: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X1 ) ) )
| ( $true
!= ( more @ X3 @ X2 ) ) ),
inference(equality_resolution,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) ) )
| ( $true
!= ( more @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
& ( X0 != X1 ) )
| ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) ) )
| ( $true
!= ( more @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ( ( $true
!= ( more @ X3 @ X0 ) )
& ( X0 != X3 ) )
| ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( $true
!= ( more @ X3 @ X0 ) )
& ( X0 != X3 ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( ( more @ X1 @ X2 )
= $true )
=> ( ( ( $true
!= ( more @ X3 @ X0 ) )
=> ( X0 = X3 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( more @ X1 @ X2 )
= $true )
=> ( ( ( $true
!= ( more @ X3 @ X0 ) )
=> ( X0 = X3 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( ( ~ ( more @ X3 @ X0 )
=> ( X0 = X3 ) )
=> ( 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 )
=> ( X3 = X4 ) )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz22b) ).
thf(f66,plain,
( ( $true
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f37,f64]) ).
thf(f62,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f51,f58,f54]) ).
thf(f51,plain,
( ( ( more @ x @ y )
!= $true )
| ( ( more @ z @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true )
| ( ( more @ z @ u )
!= $true ) ),
inference(superposition,[status(thm)],[f37,f40]) ).
thf(f40,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) ) )
| ( $true
!= ( more @ X3 @ X2 ) )
| ( $true
!= ( more @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM691^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.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 11:11:01 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : NUM691^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Number Theory
% 0.31/0.46 % Problem : Landau theorem 23
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : ~(more (pl x z) (pl y u)) -> pl x z = pl y u
% 0.31/0.46
% 0.31/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : satz23 [Lan30]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % : Without extensionality : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 13 ( 0 unt; 7 typ; 0 def)
% 0.31/0.46 % Number of atoms : 14 ( 5 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 2 avg)
% 0.31/0.46 % Number of connectives : 51 ( 7 ~; 0 |; 0 &; 34 @)
% 0.31/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(nat_type,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(x,type,
% 0.31/0.46 x: nat ).
% 0.31/0.46
% 0.31/0.46 thf(y,type,
% 0.31/0.46 y: nat ).
% 0.31/0.46
% 0.31/0.46 thf(z,type,
% 0.31/0.46 z: nat ).
% 0.31/0.46
% 0.31/0.46 thf(u,type,
% 0.31/0.46 u: nat ).
% 0.31/0.46
% 0.31/0.46 thf(more,type,
% 0.31/0.46 more: nat > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(m,axiom,
% 0.31/0.46 ( ~ ( more @ x @ y )
% 0.31/0.46 => ( x = y ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(n,axiom,
% 0.31/0.46 ( ~ ( more @ z @ u )
% 0.31/0.46 => ( z = u ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(pl,type,
% 0.31/0.46 pl: nat > nat > nat ).
% 0.31/0.46
% 0.31/0.46 thf(et,axiom,
% 0.31/0.46 ! [Xa: $o] :
% 0.31/0.46 ( ~ ~ Xa
% 0.31/0.46 => Xa ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz22a,axiom,
% 0.31/0.46 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.31/0.46 ( ( ~ ( more @ Xx @ Xy )
% 0.31/0.46 => ( Xx = Xy ) )
% 0.31/0.46 => ( ( more @ Xz @ Xu )
% 0.31/0.46 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz22b,axiom,
% 0.31/0.46 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.31/0.46 ( ( more @ Xx @ Xy )
% 0.31/0.46 => ( ( ~ ( more @ Xz @ Xu )
% 0.31/0.46 => ( Xz = Xu ) )
% 0.31/0.46 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz23,conjecture,
% 0.31/0.46 ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
% 0.31/0.46 => ( ( pl @ x @ z )
% 0.31/0.46 = ( pl @ y @ u ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.64/1.32 ---- Embedded in THF ---
% 1.64/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.32 %%% Generated on Tue Feb 24 11:11:02 EST 2026
% 1.64/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.32 %%% Logic specification used:
% 1.64/1.32 %%% thf(spec, logic, $$dhol).
% 1.64/1.32
% 1.64/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2DTF32726.p
% See solution above
% 1.64/1.32 ------------------------
% 1.64/1.33 ---- Cleaned THF ---
% 1.64/1.33 thf(nat_type,type,
% 1.64/1.33 nat: $tType ).
% 1.64/1.33
% 1.64/1.33 thf(x,type,
% 1.64/1.33 x: nat ).
% 1.64/1.33
% 1.64/1.33 thf(y,type,
% 1.64/1.33 y: nat ).
% 1.64/1.33
% 1.64/1.33 thf(z,type,
% 1.64/1.33 z: nat ).
% 1.64/1.33
% 1.64/1.33 thf(u,type,
% 1.64/1.33 u: nat ).
% 1.64/1.33
% 1.64/1.33 thf(more,type,
% 1.64/1.33 more: nat > nat > $o ).
% 1.64/1.33
% 1.64/1.33 thf(m,axiom,
% 1.64/1.33 ( ~ ( more @ x @ y )
% 1.64/1.33 => ( x = y ) ) ).
% 1.64/1.33
% 1.64/1.33 thf(n,axiom,
% 1.64/1.33 ( ~ ( more @ z @ u )
% 1.64/1.33 => ( z = u ) ) ).
% 1.64/1.33
% 1.64/1.33 thf(pl,type,
% 1.64/1.33 pl: nat > nat > nat ).
% 1.64/1.33
% 1.64/1.33 thf(et,axiom,
% 1.64/1.33 ! [Xa: $o] :
% 1.64/1.33 ( ~ ~ Xa
% 1.64/1.33 => Xa ) ).
% 1.64/1.33
% 1.64/1.33 thf(satz22a,axiom,
% 1.64/1.33 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.64/1.33 ( ( ~ ( more @ Xx @ Xy )
% 1.64/1.33 => ( Xx = Xy ) )
% 1.64/1.33 => ( ( more @ Xz @ Xu )
% 1.64/1.33 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 1.64/1.33
% 1.64/1.33 thf(satz22b,axiom,
% 1.64/1.33 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.64/1.33 ( ( more @ Xx @ Xy )
% 1.64/1.33 => ( ( ~ ( more @ Xz @ Xu )
% 1.64/1.33 => ( Xz = Xu ) )
% 1.64/1.33 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 1.64/1.33
% 1.64/1.33 thf(satz23,conjecture,
% 1.64/1.33 ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
% 1.64/1.33 => ( ( pl @ x @ z )
% 1.64/1.33 = ( pl @ y @ u ) ) ) ).
% 1.64/1.33 ------------------------
% 1.64/1.34 % (588)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_32726 for (2999ds/275Mi)
% 1.64/1.35 % (588)First to succeed.
% 1.64/1.35 % (588)Refutation found. Thanks to Tanya!
% 1.64/1.35 % SZS status Theorem for DTF2THF_32726
% 1.64/1.35 % SZS output start Proof for DTF2THF_32726
% 1.64/1.35 thf(type_def_5, type, nat: $tType).
% 1.64/1.35 thf(func_def_0, type, nat: $tType).
% 1.64/1.35 thf(func_def_1, type, x: nat).
% 1.64/1.35 thf(func_def_2, type, y: nat).
% 1.64/1.35 thf(func_def_3, type, z: nat).
% 1.64/1.35 thf(func_def_4, type, u: nat).
% 1.64/1.35 thf(func_def_5, type, more: nat > nat > $o).
% 1.64/1.35 thf(func_def_7, type, pl: nat > nat > nat).
% 1.64/1.35 thf(f98,plain,(
% 1.64/1.35 $false),
% 1.64/1.35 inference(avatar_sat_refutation,[status(thm)],[f62,f75,f89,f97])).
% 1.64/1.35 thf(f97,plain,(
% 1.64/1.35 ~spl0_1 | spl0_2),
% 1.64/1.35 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.64/1.35 thf(f96,plain,(
% 1.64/1.35 $false | (~spl0_1 | spl0_2)),
% 1.64/1.35 inference(subsumption_resolution,[status(thm)],[f94,f55])).
% 1.64/1.35 thf(f55,plain,(
% 1.64/1.35 ((more @ z @ u) = $true) | ~spl0_1),
% 1.64/1.35 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.64/1.35 thf(f54,definition,(
% 1.64/1.35 spl0_1 <=> ((more @ z @ u) = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.64/1.35 thf(f94,plain,(
% 1.64/1.35 ((more @ z @ u) != $true) | spl0_2),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.64/1.35 thf(f92,plain,(
% 1.64/1.35 ((more @ z @ u) != $true) | ($true != $true) | spl0_2),
% 1.64/1.35 inference(superposition,[status(thm)],[f78,f48])).
% 1.64/1.35 thf(f48,plain,(
% 1.64/1.35 ( ! [X2 : nat,X3 : nat,X0 : nat] : (($true = (more @ (pl @ X3 @ X2) @ (pl @ X3 @ X0))) | ($true != (more @ X2 @ X0))) )),
% 1.64/1.35 inference(equality_resolution,[status(thm)],[f43])).
% 1.64/1.35 thf(f43,plain,(
% 1.64/1.35 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != (more @ X2 @ X0)) | (X1 != X3) | ($true = (more @ (pl @ X1 @ X2) @ (pl @ X3 @ X0)))) )),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f36])).
% 1.64/1.35 thf(f36,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true != (more @ X2 @ X0)) | (($true != (more @ X1 @ X3)) & (X1 != X3)) | ($true = (more @ (pl @ X1 @ X2) @ (pl @ X3 @ X0))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f31])).
% 1.64/1.35 thf(f31,plain,(
% 1.64/1.35 ! [X3 : nat,X1 : nat,X2 : nat,X0 : nat] : (($true != (more @ X2 @ X3)) | (($true != (more @ X1 @ X0)) & (X0 != X1)) | ($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))))),
% 1.64/1.35 inference(flattening,[status(thm)],[f30])).
% 1.64/1.35 thf(f30,plain,(
% 1.64/1.35 ! [X3 : nat,X2 : nat,X1 : nat,X0 : nat] : ((($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))) | ($true != (more @ X2 @ X3))) | (($true != (more @ X1 @ X0)) & (X0 != X1)))),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f26])).
% 1.64/1.35 thf(f26,plain,(
% 1.64/1.35 ! [X3 : nat,X2 : nat,X1 : nat,X0 : nat] : ((($true != (more @ X1 @ X0)) => (X0 = X1)) => (($true = (more @ X2 @ X3)) => ($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3)))))),
% 1.64/1.35 inference(flattening,[status(thm)],[f10])).
% 1.64/1.35 thf(f10,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((~($true = (more @ X1 @ X0)) => (X0 = X1)) => (($true = (more @ X2 @ X3)) => ($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3)))))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.35 thf(f9,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((~(more @ X1 @ X0) => (X0 = X1)) => ((more @ X2 @ X3) => (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f4])).
% 1.64/1.35 thf(f4,axiom,(
% 1.64/1.35 ! [X2 : nat,X1 : nat,X3 : nat,X4 : nat] : ((~(more @ X1 @ X2) => (X1 = X2)) => ((more @ X3 @ X4) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X4))))),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz22a)).
% 1.64/1.35 thf(f78,plain,(
% 1.64/1.35 ((more @ (pl @ x @ z) @ (pl @ x @ u)) != $true) | spl0_2),
% 1.64/1.35 inference(superposition,[status(thm)],[f37,f77])).
% 1.64/1.35 thf(f77,plain,(
% 1.64/1.35 (x = y) | spl0_2),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.64/1.35 thf(f76,plain,(
% 1.64/1.35 (x = y) | ($true != $true) | spl0_2),
% 1.64/1.35 inference(superposition,[status(thm)],[f60,f45])).
% 1.64/1.35 thf(f45,plain,(
% 1.64/1.35 ((more @ x @ y) = $true) | (x = y)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.35 thf(f27,plain,(
% 1.64/1.35 ((more @ x @ y) = $true) | (x = y)),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f23])).
% 1.64/1.35 thf(f23,plain,(
% 1.64/1.35 ((more @ x @ y) != $true) => (x = y)),
% 1.64/1.35 inference(flattening,[status(thm)],[f16])).
% 1.64/1.35 thf(f16,plain,(
% 1.64/1.35 ~((more @ x @ y) = $true) => (x = y)),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f15])).
% 1.64/1.35 thf(f15,plain,(
% 1.64/1.35 ~(more @ x @ y) => (x = y)),
% 1.64/1.35 inference(rectify,[status(thm)],[f1])).
% 1.64/1.35 thf(f1,axiom,(
% 1.64/1.35 ~(more @ x @ y) => (x = y)),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',m)).
% 1.64/1.35 thf(f60,plain,(
% 1.64/1.35 ((more @ x @ y) != $true) | spl0_2),
% 1.64/1.35 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.64/1.35 thf(f58,definition,(
% 1.64/1.35 spl0_2 <=> ((more @ x @ y) = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.64/1.35 thf(f37,plain,(
% 1.64/1.35 ((more @ (pl @ x @ z) @ (pl @ y @ u)) != $true)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f29,plain,(
% 1.64/1.35 ((pl @ x @ z) != (pl @ y @ u)) & ((more @ (pl @ x @ z) @ (pl @ y @ u)) != $true)),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f21])).
% 1.64/1.35 thf(f21,plain,(
% 1.64/1.35 ~(((more @ (pl @ x @ z) @ (pl @ y @ u)) != $true) => ((pl @ x @ z) = (pl @ y @ u)))),
% 1.64/1.35 inference(flattening,[status(thm)],[f14])).
% 1.64/1.35 thf(f14,plain,(
% 1.64/1.35 ~(~((more @ (pl @ x @ z) @ (pl @ y @ u)) = $true) => ((pl @ x @ z) = (pl @ y @ u)))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.35 thf(f13,plain,(
% 1.64/1.35 ~(~(more @ (pl @ x @ z) @ (pl @ y @ u)) => ((pl @ x @ z) = (pl @ y @ u)))),
% 1.64/1.35 inference(rectify,[status(thm)],[f7])).
% 1.64/1.35 thf(f7,negated_conjecture,(
% 1.64/1.35 ~(~(more @ (pl @ x @ z) @ (pl @ y @ u)) => ((pl @ x @ z) = (pl @ y @ u)))),
% 1.64/1.35 inference(negated_conjecture,[status(cth)],[f6])).
% 1.64/1.35 thf(f6,conjecture,(
% 1.64/1.35 ~(more @ (pl @ x @ z) @ (pl @ y @ u)) => ((pl @ x @ z) = (pl @ y @ u))),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz23)).
% 1.64/1.35 thf(f89,plain,(
% 1.64/1.35 spl0_1 | spl0_2),
% 1.64/1.35 inference(avatar_contradiction_clause,[status(thm)],[f88])).
% 1.64/1.35 thf(f88,plain,(
% 1.64/1.35 $false | (spl0_1 | spl0_2)),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.64/1.35 thf(f87,plain,(
% 1.64/1.35 ((pl @ x @ z) != (pl @ x @ z)) | (spl0_1 | spl0_2)),
% 1.64/1.35 inference(forward_demodulation,[status(thm)],[f79,f64])).
% 1.64/1.35 thf(f64,plain,(
% 1.64/1.35 (z = u) | spl0_1),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.64/1.35 thf(f63,plain,(
% 1.64/1.35 ($true != $true) | (z = u) | spl0_1),
% 1.64/1.35 inference(superposition,[status(thm)],[f56,f41])).
% 1.64/1.35 thf(f41,plain,(
% 1.64/1.35 ((more @ z @ u) = $true) | (z = u)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f28])).
% 1.64/1.35 thf(f28,plain,(
% 1.64/1.35 ((more @ z @ u) = $true) | (z = u)),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f24])).
% 1.64/1.35 thf(f24,plain,(
% 1.64/1.35 ((more @ z @ u) != $true) => (z = u)),
% 1.64/1.35 inference(flattening,[status(thm)],[f12])).
% 1.64/1.35 thf(f12,plain,(
% 1.64/1.35 ~((more @ z @ u) = $true) => (z = u)),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.35 thf(f11,plain,(
% 1.64/1.35 ~(more @ z @ u) => (z = u)),
% 1.64/1.35 inference(rectify,[status(thm)],[f2])).
% 1.64/1.35 thf(f2,axiom,(
% 1.64/1.35 ~(more @ z @ u) => (z = u)),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',n)).
% 1.64/1.35 thf(f56,plain,(
% 1.64/1.35 ((more @ z @ u) != $true) | spl0_1),
% 1.64/1.35 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.64/1.35 thf(f79,plain,(
% 1.64/1.35 ((pl @ x @ z) != (pl @ x @ u)) | spl0_2),
% 1.64/1.35 inference(superposition,[status(thm)],[f38,f77])).
% 1.64/1.35 thf(f38,plain,(
% 1.64/1.35 ((pl @ x @ z) != (pl @ y @ u))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f75,plain,(
% 1.64/1.35 ~spl0_2 | spl0_1),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f72,f54,f58])).
% 1.64/1.35 thf(f72,plain,(
% 1.64/1.35 ((more @ x @ y) != $true) | spl0_1),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.64/1.35 thf(f69,plain,(
% 1.64/1.35 ($true != $true) | ((more @ x @ y) != $true) | spl0_1),
% 1.64/1.35 inference(superposition,[status(thm)],[f66,f46])).
% 1.64/1.35 thf(f46,plain,(
% 1.64/1.35 ( ! [X2 : nat,X3 : nat,X1 : nat] : (($true = (more @ (pl @ X3 @ X1) @ (pl @ X2 @ X1))) | ($true != (more @ X3 @ X2))) )),
% 1.64/1.35 inference(equality_resolution,[status(thm)],[f39])).
% 1.64/1.35 thf(f39,plain,(
% 1.64/1.35 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((X0 != X1) | ($true = (more @ (pl @ X3 @ X1) @ (pl @ X2 @ X0))) | ($true != (more @ X3 @ X2))) )),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.35 thf(f35,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true != (more @ X1 @ X0)) & (X0 != X1)) | ($true = (more @ (pl @ X3 @ X1) @ (pl @ X2 @ X0))) | ($true != (more @ X3 @ X2)))),
% 1.64/1.35 inference(rectify,[status(thm)],[f34])).
% 1.64/1.35 thf(f34,plain,(
% 1.64/1.35 ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((($true != (more @ X3 @ X0)) & (X0 != X3)) | ($true = (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0))) | ((more @ X1 @ X2) != $true))),
% 1.64/1.35 inference(flattening,[status(thm)],[f33])).
% 1.64/1.35 thf(f33,plain,(
% 1.64/1.35 ! [X2 : nat,X0 : nat,X3 : nat,X1 : nat] : ((($true = (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0))) | (($true != (more @ X3 @ X0)) & (X0 != X3))) | ((more @ X1 @ X2) != $true))),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f25])).
% 1.64/1.35 thf(f25,plain,(
% 1.64/1.35 ! [X2 : nat,X0 : nat,X3 : nat,X1 : nat] : (((more @ X1 @ X2) = $true) => ((($true != (more @ X3 @ X0)) => (X0 = X3)) => ($true = (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)))))),
% 1.64/1.35 inference(flattening,[status(thm)],[f18])).
% 1.64/1.35 thf(f18,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((more @ X1 @ X2) = $true) => ((~($true = (more @ X3 @ X0)) => (X0 = X3)) => ($true = (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0)))))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f17])).
% 1.64/1.35 thf(f17,plain,(
% 1.64/1.35 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X1 @ X2) => ((~(more @ X3 @ X0) => (X0 = X3)) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X0))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f5])).
% 1.64/1.35 thf(f5,axiom,(
% 1.64/1.35 ! [X4 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X1 @ X2) => ((~(more @ X3 @ X4) => (X3 = X4)) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X4))))),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.8y8FY8P18I/DTF2THF_32726.p',satz22b)).
% 1.64/1.35 thf(f66,plain,(
% 1.64/1.35 ($true != (more @ (pl @ x @ z) @ (pl @ y @ z))) | spl0_1),
% 1.64/1.35 inference(superposition,[status(thm)],[f37,f64])).
% 1.64/1.35 thf(f62,plain,(
% 1.64/1.35 ~spl0_1 | ~spl0_2),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f51,f58,f54])).
% 1.64/1.35 thf(f51,plain,(
% 1.64/1.35 ((more @ x @ y) != $true) | ((more @ z @ u) != $true)),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.64/1.35 thf(f50,plain,(
% 1.64/1.35 ((more @ x @ y) != $true) | ($true != $true) | ((more @ z @ u) != $true)),
% 1.64/1.35 inference(superposition,[status(thm)],[f37,f40])).
% 1.64/1.35 thf(f40,plain,(
% 1.64/1.35 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X3 @ X1) @ (pl @ X2 @ X0))) | ($true != (more @ X3 @ X2)) | ($true != (more @ X1 @ X0))) )),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.35 % SZS output end Proof for DTF2THF_32726
% 1.64/1.35 % (588)------------------------------
% 1.64/1.35 % (588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (588)Termination reason: Refutation
% 1.64/1.35
% 1.64/1.35 % (588)Memory used [KB]: 5500
% 1.64/1.35 % (588)Time elapsed: 0.005 s
% 1.64/1.35 % (588)Instructions burned: 6 (million)
% 1.64/1.35 % (588)------------------------------
% 1.64/1.35 % (588)------------------------------
% 1.64/1.35 % (582)Success in time 0.016 s
%------------------------------------------------------------------------------