%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:08:57 AM UTC 2026
% Result : Theorem 15.23s 4.76s
% Output : Refutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 204 ( 78 equ; 0 cnn)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 441 ( 79 ~; 92 |; 54 &; 204 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 2 ^; 31 !; 13 ?; 48 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_decl,type,
aNaturalNumber0: $i > $o ).
thf(doDivides0_decl,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(isPrime0_decl,type,
isPrime0: $i > $o ).
thf(sz10_decl,type,
sz10: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( A @ ( B @ doDivides0 ) )
& ? [C: $i] :
( ( A
= ( C @ ( B @ sdtasdt0 ) ) )
& ( C @ aNaturalNumber0 ) )
& ( B @ aNaturalNumber0 ) )
=> ( ( B = A )
| ( B = sz10 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ( A
= ( B @ ( A @ sk2 @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) ) ) ).
thf(36,axiom,
xk @ aNaturalNumber0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
thf(239,plain,
xk @ aNaturalNumber0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
& ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(249,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
& ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(250,plain,
! [A: $i] :
( ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( sz10 @ ( A @ sdtasdt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [A: $i] :
( ( ( sz10 @ ( A @ sdtasdt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[250]) ).
thf(253,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(2602,plain,
! [A: $i] :
( ( ( xk @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[239,253]) ).
thf(2603,plain,
! [A: $i] :
( ( ( xk @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(simp,[status(thm)],[2602]) ).
thf(2604,plain,
( ( sz10 @ ( xk @ sdtasdt0 ) )
= xk ),
inference(pattern_uni,[status(thm)],[2603:[bind(A,$thf( xk ))]]) ).
thf(1,conjecture,
( ( ( xk @ isPrime0 )
& ! [A: $i] :
( ( ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) )
=> ( ( A = xk )
| ( A = sz10 ) ) ) )
=> ? [A: $i] :
( ( ( A @ isPrime0 )
| ( ! [B: $i] :
( ( ( A @ ( B @ doDivides0 ) )
& ? [C: $i] :
( ( A
= ( C @ ( B @ sdtasdt0 ) ) )
& ( C @ aNaturalNumber0 ) )
& ( B @ aNaturalNumber0 ) )
=> ( ( B = A )
| ( B = sz10 ) ) )
& ( A != sz10 )
& ( A != sz00 ) ) )
& ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xk @ isPrime0 )
& ! [A: $i] :
( ( ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) )
=> ( ( A = xk )
| ( A = sz10 ) ) ) )
=> ? [A: $i] :
( ( ( A @ isPrime0 )
| ( ! [B: $i] :
( ( ( A @ ( B @ doDivides0 ) )
& ? [C: $i] :
( ( A
= ( C @ ( B @ sdtasdt0 ) ) )
& ( C @ aNaturalNumber0 ) )
& ( B @ aNaturalNumber0 ) )
=> ( ( B = A )
| ( B = sz10 ) ) )
& ( A != sz10 )
& ( A != sz00 ) ) )
& ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ( ( ( xk @ isPrime0 )
& ! [A: $i] :
( ( ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) )
=> ( ( A = xk )
| ( A = sz10 ) ) ) )
=> ? [A: $i] :
( ( ( A @ isPrime0 )
| ( ! [B: $i] :
( ( ( A @ ( B @ doDivides0 ) )
& ? [C: $i] :
( ( A
= ( C @ ( B @ sdtasdt0 ) ) )
& ( C @ aNaturalNumber0 ) )
& ( B @ aNaturalNumber0 ) )
=> ( ( B = A )
| ( B = sz10 ) ) )
& ( A != sz10 )
& ( A != sz00 ) ) )
& ( ( xk @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xk
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( C @ isPrime0 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( ( C @ sk2 )
!= C )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( ( C @ sk2 )
!= sz10 )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( C @ ( C @ sk2 @ doDivides0 ) )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( C
= ( C @ sk3 @ ( C @ sk2 @ sdtasdt0 ) ) )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( C @ sk3 @ aNaturalNumber0 )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ( C @ sk2 @ aNaturalNumber0 )
| ( C = sz10 )
| ( C = sz00 )
| ( C @ sk1 )
| ~ ( C @ aNaturalNumber0 ) )
& ( ~ ( C @ sk1 )
| ~ ( xk @ ( C @ doDivides0 ) )
| ~ ( C @ aNaturalNumber0 ) )
& ( ~ ( C @ sk1 )
| ( xk
!= ( D @ ( C @ sdtasdt0 ) ) )
| ~ ( D @ aNaturalNumber0 )
| ~ ( C @ aNaturalNumber0 ) )
& ( xk @ isPrime0 )
& ( ( A = xk )
| ( A = sz10 )
| ~ ( xk @ ( A @ doDivides0 ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( A = xk )
| ( A = sz10 )
| ( xk
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk1 )
| ( xk
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk1 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ( ( B @ ( A @ sdtasdt0 ) )
!= xk ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk1 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ( ( B @ ( A @ sdtasdt0 ) )
!= xk ) ),
inference(simp,[status(thm)],[72]) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ( ( sz10 @ ( xk @ sdtasdt0 ) )
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( A @ sk1 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ( xk != xk ) ),
inference(paramod_ordered,[status(thm)],[2604,73]) ).
thf(2924,plain,
! [B: $i,A: $i] :
( ( ( sz10 @ ( xk @ sdtasdt0 ) )
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( A @ sk1 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2925,plain,
( ~ ( xk @ sk1 )
| ~ ( sz10 @ aNaturalNumber0 )
| ~ ( xk @ aNaturalNumber0 ) ),
inference(pattern_uni,[status(thm)],[2924:[bind(A,$thf( xk )),bind(B,$thf( sz10 ))]]) ).
thf(53,plain,
xk @ isPrime0,
inference(cnfConj,[status(thm)],[44]) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ isPrime0 )
| ( A @ sk1 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(74,plain,
! [A: $i] :
( ~ ( A @ isPrime0 )
| ( A @ sk1 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[49]) ).
thf(297,plain,
! [A: $i] :
( ( ( xk @ isPrime0 )
!= ( A @ isPrime0 ) )
| ~ $true
| ( A @ sk1 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[53,74]) ).
thf(298,plain,
! [A: $i] :
( ( ( xk @ isPrime0 )
!= ( A @ isPrime0 ) )
| ( A @ sk1 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
( ( xk @ sk1 )
| ~ ( xk @ aNaturalNumber0 ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( xk ))]]) ).
thf(419,plain,
( ( xk @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[299,239]) ).
thf(420,plain,
xk @ sk1,
inference(simp,[status(thm)],[419]) ).
thf(6,axiom,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(87,plain,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,plain,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
sz10 @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[88]) ).
thf(3035,plain,
( ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2925,420,89,239]) ).
thf(3036,plain,
$false,
inference(simp,[status(thm)],[3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 26 02:55:35 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.62/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/0.97 % [INFO] Parsing done (190ms).
% 0.93/0.98 % [INFO] Running in sequential loop mode.
% 1.78/1.31 % [INFO] eprover registered as external prover.
% 1.78/1.31 % [INFO] Scanning for conjecture ...
% 1.78/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.78/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.78/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.78/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 2.21/1.51 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.21/1.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.58 % [INFO] Type checking passed.
% 2.21/1.58 % [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 ...
% 15.23/4.76 % [INFO] Killing All external provers ...
% 15.23/4.76 % Time passed: 4324ms (effective reasoning time: 3770ms)
% 15.23/4.76 % 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)>
% 15.23/4.76 % Axioms used in derivation (3): m__1716, m_MulUnit, mSortsC_01
% 15.23/4.76 % No. of inferences in proof: 34
% 15.23/4.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4324 ms resp. 3770 ms w/o parsing
% 15.72/4.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.72/4.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------