%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM425+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 8.97s 3.90s
% Output : Refutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 39 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 138 ( 12 ~; 5 |; 13 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 10 ( 0 ^; 4 !; 5 ?; 10 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_decl,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_decl,type,
aDivisorOf0: $i > $i > $o ).
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(xb_decl,type,
xb: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ) ) ).
thf(10,axiom,
( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
& ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__724) ).
thf(64,plain,
( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
& ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,plain,
( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
& ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ( ( sk2 @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( sk2 @ aInteger0 ) ),
inference(cnf,[status(esa)],[64]) ).
thf(67,plain,
( ( sk2 @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(70,plain,
( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
= ( sk2 @ ( xq @ sdtasdt0 ) ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(66,plain,
sk2 @ aInteger0,
inference(cnfConj,[status(thm)],[65]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
! [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk2 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ~ $true
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,27]) ).
thf(149,plain,
! [A: $i] :
( ( ( sk2 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
!= ( sk2 @ ( xq @ sdtasdt0 ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk2 ))]]) ).
thf(856,plain,
$false,
inference(simplifyReflect,[status(thm)],[70,150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM425+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.15/0.44 % Computer : n006.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sat Sep 26 02:40:56 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 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
% 1.00/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.24 % [INFO] Parsing done (210ms).
% 1.31/1.26 % [INFO] Running in sequential loop mode.
% 2.07/1.67 % [INFO] eprover registered as external prover.
% 2.07/1.68 % [INFO] Scanning for conjecture ...
% 2.31/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.47/1.88 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.47/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.68/1.93 % [INFO] Type checking passed.
% 2.68/1.93 % [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 ...
% 8.97/3.89 % [INFO] Killing All external provers ...
% 8.97/3.90 % Time passed: 3311ms (effective reasoning time: 2628ms)
% 8.97/3.90 % 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)>
% 8.97/3.90 % Axioms used in derivation (1): m__724
% 8.97/3.90 % No. of inferences in proof: 15
% 8.97/3.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3311 ms resp. 2628 ms w/o parsing
% 9.47/3.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.47/3.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------