%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM490+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 : 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 : Sun Sep 27 08:08:58 AM UTC 2026
% Result : Theorem 30.99s 9.05s
% Output : Refutation 30.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 60 ( 39 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 241 ( 18 ~; 14 |; 25 &; 182 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 4 !; 4 ?; 9 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_decl,type,
aNaturalNumber0: $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
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(xp_decl,type,
xp: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xr_decl,type,
xr: $i ).
thf(xn_decl,type,
xn: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( ( xm @ ( xn @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(1,conjecture,
( ( ( xm @ ( xr @ sdtasdt0 ) )
= ( xm @ ( xp @ sdtasdt0 ) @ ( xm @ ( xn @ sdtasdt0 ) @ sdtmndt0 ) ) )
| ( ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xm @ ( xn @ sdtasdt0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xm @ ( xr @ sdtasdt0 ) )
= ( xm @ ( xp @ sdtasdt0 ) @ ( xm @ ( xn @ sdtasdt0 ) @ sdtmndt0 ) ) )
| ( ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xm @ ( xn @ sdtasdt0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ ( ( ( xm @ ( xr @ sdtasdt0 ) )
= ( xm @ ( xp @ sdtasdt0 ) @ ( xm @ ( xn @ sdtasdt0 ) @ sdtmndt0 ) ) )
| ( ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xm @ ( xn @ sdtasdt0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,plain,
( ( ( xm @ ( xr @ sdtasdt0 ) )
!= ( xm @ ( xp @ sdtasdt0 ) @ ( xm @ ( xn @ sdtasdt0 ) @ sdtmndt0 ) ) )
& ( ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) )
!= ( xm @ ( xn @ sdtasdt0 ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
( ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) )
!= ( xm @ ( xn @ sdtasdt0 ) ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(53,plain,
( ( xm @ ( xn @ sdtasdt0 ) )
!= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(30,axiom,
( ( xm @ ( xn @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
& ? [A: $i] :
( ( ( xm @ ( xn @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) )
& ( xp @ isPrime0 )
& ! [A: $i] :
( ( ( ( xp @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xp
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) )
=> ( ( A = xp )
| ( A = sz10 ) ) )
& ( xp != sz10 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
thf(195,plain,
( ( xm @ ( xn @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
& ? [A: $i] :
( ( ( xm @ ( xn @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) )
& ( xp @ isPrime0 )
& ! [A: $i] :
( ( ( ( xp @ ( A @ doDivides0 ) )
| ? [B: $i] :
( ( xp
= ( B @ ( A @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) ) )
& ( A @ aNaturalNumber0 ) )
=> ( ( A = xp )
| ( A = sz10 ) ) )
& ( xp != sz10 )
& ( xp != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( xm @ ( xn @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
& ( ( xm @ ( xn @ sdtasdt0 ) )
= ( sk4 @ ( xp @ sdtasdt0 ) ) )
& ( sk4 @ aNaturalNumber0 )
& ( xp @ isPrime0 )
& ( ( A = xp )
| ( A = sz10 )
| ~ ( xp @ ( A @ doDivides0 ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( A = xp )
| ( A = sz10 )
| ( xp
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) )
& ( xp != sz10 )
& ( xp != sz00 ) ),
inference(cnf,[status(esa)],[195]) ).
thf(199,plain,
( ( xm @ ( xn @ sdtasdt0 ) )
= ( sk4 @ ( xp @ sdtasdt0 ) ) ),
inference(cnfConj,[status(thm)],[196]) ).
thf(207,plain,
( ( xm @ ( xn @ sdtasdt0 ) )
= ( sk4 @ ( xp @ sdtasdt0 ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(1577,plain,
( ( sk4 @ ( xp @ sdtasdt0 ) )
!= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
inference(rewrite,[status(thm)],[53,207]) ).
thf(31,axiom,
( ( xm @ ( xn @ sdtasdt0 ) )
= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1951) ).
thf(210,plain,
( ( xm @ ( xn @ sdtasdt0 ) )
= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(211,plain,
( ( xm @ ( xn @ sdtasdt0 ) )
= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(1662,plain,
( ( sk4 @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ sdtasdt0 ) @ ( xm @ ( xp @ sdtasdt0 ) @ sdtpldt0 ) ) ),
inference(rewrite,[status(thm)],[211,207]) ).
thf(3718,plain,
$false,
inference(simplifyReflect,[status(thm)],[1577,1662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM490+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.22/0.50 % Computer : n018.cluster.edu
% 0.22/0.50 % Model : x86_64 x86_64
% 0.22/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.50 % Memory : 8046.5625MB
% 0.22/0.50 % OS : Linux 6.8.0-71-generic
% 0.22/0.50 % CPULimit : 300
% 0.22/0.50 % WCLimit : 300
% 0.22/0.50 % DateTime : Sat Sep 26 03:00:21 UTC 2026
% 0.28/0.50 % CPUTime :
% 0.28/0.50 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
% 1.41/1.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.31/1.72 % [INFO] Parsing done (356ms).
% 2.31/1.74 % [INFO] Running in sequential loop mode.
% 3.54/2.34 % [INFO] eprover registered as external prover.
% 3.54/2.35 % [INFO] Scanning for conjecture ...
% 3.75/2.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.75/2.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.95/2.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.95/2.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.95/2.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.95/2.57 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 4.36/2.70 % [INFO] Axiom selection finished. Selected 46 axioms (removed 0 axioms).
% 4.36/2.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.36/2.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.36/2.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.36/2.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.63/2.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.63/2.83 % [INFO] Problem is first-order (TPTP FOF).
% 4.63/2.85 % [INFO] Type checking passed.
% 4.63/2.86 % [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 ...
% 30.41/9.04 % [INFO] Killing All external provers ...
% 30.99/9.05 % Time passed: 8330ms (effective reasoning time: 7292ms)
% 30.99/9.05 % 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)>
% 30.99/9.05 % Axioms used in derivation (2): m__1860, m__1951
% 30.99/9.05 % No. of inferences in proof: 17
% 30.99/9.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8330 ms resp. 7292 ms w/o parsing
% 30.99/9.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.99/9.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------