%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM519+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:34:15 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 504 ( 152 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 752 ( 240 ~; 132 |; 24 &; 350 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_doDivides0,type,
doDivides0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isPrime0,type,
isPrime0: $i > $o ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtsldt0,type,
sdtsldt0: $i > $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz10,type,
sz10: $i ).
thf(tp_xk,type,
xk: $i ).
thf(tp_xm,type,
xm: $i ).
thf(tp_xn,type,
xn: $i ).
thf(tp_xp,type,
xp: $i ).
thf(tp_xr,type,
xr: $i ).
thf(6,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
thf(34,axiom,
~ ( doDivides0 @ xr @ xm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2698) ).
thf(35,axiom,
~ ( doDivides0 @ xr @ xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
thf(36,axiom,
( ( doDivides0 @ xr @ xn )
| ( doDivides0 @ xr @ xm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2449) ).
thf(43,axiom,
( ( xn != xp )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ( sdtlseqdt0 @ xm @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
thf(44,axiom,
~ ( sdtlseqdt0 @ xp @ xm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
thf(45,axiom,
~ ( sdtlseqdt0 @ xp @ xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
thf(48,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(49,conjecture,
( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(50,negated_conjecture,
( ( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) )
= $false ),
inference(negate_conjecture,[status(cth)],[49]) ).
thf(51,plain,
( ( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) )
= $false ),
inference(unfold_def,[status(thm)],[50]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(53,plain,
( ( ~ ( doDivides0 @ xr @ xm ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(54,plain,
( ( ~ ( doDivides0 @ xr @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(55,plain,
( ( ( doDivides0 @ xr @ xn )
| ( doDivides0 @ xr @ xm ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(56,plain,
( ( ( xn != xp )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ( sdtlseqdt0 @ xm @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(57,plain,
( ( ~ ( sdtlseqdt0 @ xp @ xm ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(58,plain,
( ( ~ ( sdtlseqdt0 @ xp @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(59,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(60,plain,
( ( ~ ( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(61,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ( sdtlseqdt0 @ xp @ xn ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(63,plain,
( ( ~ ( sdtlseqdt0 @ xp @ xm ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(64,plain,
( ( ( xn != xp )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ( sdtlseqdt0 @ xm @ xp ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(65,plain,
( ( ( doDivides0 @ xr @ xn )
| ( doDivides0 @ xr @ xm ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(66,plain,
( ( ~ ( doDivides0 @ xr @ xn ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(67,plain,
( ( ~ ( doDivides0 @ xr @ xm ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(69,plain,
( ( ~ ( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(70,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
| ~ ( ( xm != xp ) ) )
| ~ ( sdtlseqdt0 @ xm @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(71,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX1 @ SX2 ) )
| ( doDivides0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(73,plain,
( ( sdtlseqdt0 @ xp @ xn )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(74,plain,
( ( sdtlseqdt0 @ xp @ xm )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(75,plain,
( ( ( doDivides0 @ xr @ xn )
= $true )
| ( ( doDivides0 @ xr @ xm )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( doDivides0 @ xr @ xn )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
( ( doDivides0 @ xr @ xm )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
( ( ( doDivides0 @ xp @ xn )
| ( doDivides0 @ xp @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
| ~ ( ( xm != xp ) ) )
| ~ ( sdtlseqdt0 @ xm @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV1: $i] :
( ( ! [SY3: $i,SY4: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SY3 ) )
| ~ ( aNaturalNumber0 @ SY4 ) )
| ~ ~ ( ~ ( doDivides0 @ SV1 @ SY3 )
| ~ ( doDivides0 @ SY3 @ SY4 ) )
| ( doDivides0 @ SV1 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
( ( doDivides0 @ xp @ xn )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(83,plain,
( ( doDivides0 @ xp @ xm )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(84,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
| ~ ( ( xm != xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
( ( ~ ( sdtlseqdt0 @ xm @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(86,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
( ( ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY5: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
| ~ ( aNaturalNumber0 @ SY5 ) )
| ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SY5 ) )
| ( doDivides0 @ SV1 @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
( ( ~ ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
| ~ ( ( xm != xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(90,plain,
( ( sdtlseqdt0 @ xm @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(91,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(92,plain,
( ( aNaturalNumber0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
| ~ ( aNaturalNumber0 @ SV3 ) )
| ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
( ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
| ~ ( ( xm != xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(95,plain,
( ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(96,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
| ~ ( aNaturalNumber0 @ SV3 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(97,plain,
( ( ~ ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(98,plain,
( ( ~ ( ( xm != xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(99,plain,
( ( ~ ( aNaturalNumber0 @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(100,plain,
( ( ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
| ~ ( aNaturalNumber0 @ SV3 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
( ( ~ ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(103,plain,
( ( xm != xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(104,plain,
( ( aNaturalNumber0 @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(105,plain,
( ( aNaturalNumber0 @ xm )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
| ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(107,plain,
( ( ~ ( ( xn != xp ) )
| ~ ( sdtlseqdt0 @ xn @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
( ( xm = xp )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(110,plain,
( ( ~ ( ( xn != xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(111,plain,
( ( ~ ( sdtlseqdt0 @ xn @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(112,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
( ( xn != xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(114,plain,
( ( sdtlseqdt0 @ xn @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(115,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(116,plain,
( ( xn = xp )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(119,plain,
! [SV3: $i,SV1: $i,SV2: $i] :
( ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(120,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
| ( doDivides0 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(121,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) ) )
= $true )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(122,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) ) )
= $false )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(123,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( doDivides0 @ SV1 @ SV2 )
| ~ ( doDivides0 @ SV2 @ SV3 ) )
= $true )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(124,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( doDivides0 @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV2 @ SV3 ) )
= $true )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(125,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( doDivides0 @ SV1 @ SV2 )
= $false )
| ( ( ~ ( doDivides0 @ SV2 @ SV3 ) )
= $true )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(126,plain,
! [SV1: $i,SV3: $i,SV2: $i] :
( ( ( doDivides0 @ SV2 @ SV3 )
= $false )
| ( ( doDivides0 @ SV1 @ SV2 )
= $false )
| ( ( doDivides0 @ SV1 @ SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(127,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[73,126,116,114,108,105,104,92,90,83,82,77,76,75,74]) ).
thf(128,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM519+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 13:25:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.27
% 0.09/0.27 No.of.Axioms: 8
% 0.09/0.27
% 0.09/0.27 Length.of.Defs: 0
% 0.09/0.27
% 0.09/0.27 Contains.Choice.Funs: false
% 0.09/0.27 ..
% 0.09/0.27
% 0.09/0.27 ********************************
% 0.09/0.27 * All subproblems solved! *
% 0.09/0.27 ********************************
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:127,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.27
% 0.09/0.27 %**** End of derivation protocol ****
% 0.09/0.27 %**** no. of clauses in derivation: 88 ****
% 0.09/0.27 %**** clause counter: 127 ****
% 0.09/0.27
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:127,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------