%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 : Sun Sep 27 08:08:48 AM UTC 2026
% Result : Theorem 64.36s 17.87s
% Output : Refutation 64.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 260 ( 38 ~; 26 |; 17 &; 175 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 0 ^; 19 !; 3 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_decl,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_decl,type,
aDivisorOf0: $i > $i > $o ).
thf(sz00_decl,type,
sz00: $i ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_decl,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(smndt0_decl,type,
smndt0: $i > $i ).
thf(xq_decl,type,
xq: $i ).
thf(xa_decl,type,
xa: $i ).
thf(20,axiom,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
thf(101,plain,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,plain,
! [A: $i] :
( ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
| ~ ( A @ aInteger0 ) )
& ( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(103,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[102]) ).
thf(105,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(22,axiom,
sz00 @ aInteger0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
thf(113,plain,
sz00 @ aInteger0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
( ( xq @ ( xa @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xq @ ( xa @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ( ( xq @ ( xa @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [A: $i] :
( ~ ( xq @ ( xa @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
& ~ ( xa @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(117,plain,
! [A: $i] :
( ( ( sz00 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ~ $true
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[113,28]) ).
thf(118,plain,
! [A: $i] :
( ( ( sz00 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
( ( xa @ smndt0 @ ( xa @ sdtpldt0 ) )
!= ( sz00 @ ( xq @ sdtasdt0 ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sz00 ))]]) ).
thf(18,axiom,
( ( xq != sz00 )
& ( xq @ aInteger0 )
& ( xa @ aInteger0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
thf(89,plain,
( ( xq != sz00 )
& ( xq @ aInteger0 )
& ( xa @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(90,plain,
( ( xq != sz00 )
& ( xq @ aInteger0 )
& ( xa @ aInteger0 ) ),
inference(cnf,[status(esa)],[89]) ).
thf(91,plain,
xa @ aInteger0,
inference(cnfConj,[status(thm)],[90]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( sz00
= ( A @ ( A @ smndt0 @ sdtpldt0 ) ) )
& ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
thf(95,plain,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( sz00
= ( A @ ( A @ smndt0 @ sdtpldt0 ) ) )
& ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,plain,
! [A: $i] :
( ( ( sz00
= ( A @ ( A @ smndt0 @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) )
& ( ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(99,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(18688,plain,
! [A: $i] :
( ( ( xa @ aInteger0 )
!= ( A @ aInteger0 ) )
| ~ $true
| ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[91,99]) ).
thf(18689,plain,
! [A: $i] :
( ( ( xa @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( ( A @ smndt0 @ ( A @ sdtpldt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[18688]) ).
thf(18690,plain,
( ( xa @ smndt0 @ ( xa @ sdtpldt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[18689:[bind(A,$thf( xa ))]]) ).
thf(20103,plain,
( ( sz00 @ ( xq @ sdtasdt0 ) )
!= sz00 ),
inference(rewrite,[status(thm)],[119,18690]) ).
thf(20892,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtasdt0 ) )
!= ( sz00 @ ( xq @ sdtasdt0 ) ) )
| ( sz00 != sz00 )
| ~ ( A @ aInteger0 ) ),
inference(paramod_ordered,[status(thm)],[105,20103]) ).
thf(20893,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtasdt0 ) )
!= ( sz00 @ ( xq @ sdtasdt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[20892]) ).
thf(20894,plain,
~ ( xq @ aInteger0 ),
inference(pattern_uni,[status(thm)],[20893:[bind(A,$thf( xq ))]]) ).
thf(92,plain,
xq @ aInteger0,
inference(cnfConj,[status(thm)],[90]) ).
thf(21037,plain,
~ $true,
inference(rewrite,[status(thm)],[20894,92]) ).
thf(21038,plain,
$false,
inference(simp,[status(thm)],[21037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50 % Computer : n006.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 02:40:26 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.41/1.38 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.18/1.70 % [INFO] Parsing done (312ms).
% 2.18/1.72 % [INFO] Running in sequential loop mode.
% 3.21/2.38 % [INFO] eprover registered as external prover.
% 3.21/2.39 % [INFO] Scanning for conjecture ...
% 3.61/2.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.61/2.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.61/2.59 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 4.03/2.71 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 4.03/2.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.03/2.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.03/2.77 % [INFO] Problem is first-order (TPTP FOF).
% 4.03/2.78 % [INFO] Type checking passed.
% 4.03/2.79 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 64.36/17.86 % [INFO] Killing All external provers ...
% 64.36/17.87 % Time passed: 17151ms (effective reasoning time: 16134ms)
% 64.36/17.87 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 64.36/17.87 % Axioms used in derivation (4): mMulZero, mIntZero, m__671, mAddNeg
% 64.36/17.87 % No. of inferences in proof: 35
% 64.36/17.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17151 ms resp. 16134 ms w/o parsing
% 64.58/17.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.58/17.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------