%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM432+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 08:08:49 AM UTC 2026
% Result : Theorem 51.72s 18.13s
% Output : Refutation 51.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 248 ( 29 ~; 21 |; 13 &; 183 @)
% ( 0 <=>; 2 =>; 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 : 15 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 15 !; 3 ?; 18 :)
% 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(xc_decl,type,
xc: $i ).
thf(xb_decl,type,
xb: $i ).
thf(xn_decl,type,
xn: $i ).
thf(xm_decl,type,
xm: $i ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( B @ aInteger0 )
& ( A @ aInteger0 ) )
=> ( B @ ( A @ sdtpldt0 ) @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( B @ aInteger0 )
& ( A @ aInteger0 ) )
=> ( B @ ( A @ sdtpldt0 ) @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sdtpldt0 ) @ aInteger0 )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(cnf,[status(esa)],[71]) ).
thf(25,axiom,
( ( xm @ ( xn @ sdtpldt0 ) @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__924) ).
thf(138,plain,
( ( xm @ ( xn @ sdtpldt0 ) @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(139,plain,
( ( xm @ ( xn @ sdtpldt0 ) @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(1,conjecture,
( ( xq @ ( xc @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xc @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xq @ ( xc @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xc @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ( ( xq @ ( xc @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xc @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
! [A: $i] :
( ~ ( xq @ ( xc @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
& ~ ( xc @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(31512,plain,
! [A: $i] :
( ( ( xm @ ( xn @ sdtpldt0 ) @ ( xq @ sdtasdt0 ) )
!= ( A @ ( xq @ sdtasdt0 ) ) )
| ~ ( A @ aInteger0 )
| ( ( xc @ smndt0 @ ( xa @ sdtpldt0 ) )
!= ( xc @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,34]) ).
thf(31513,plain,
! [A: $i] :
( ( ( xm @ ( xn @ sdtpldt0 ) @ ( xq @ sdtasdt0 ) )
!= ( A @ ( xq @ sdtasdt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[31512]) ).
thf(31514,plain,
~ ( xm @ ( xn @ sdtpldt0 ) @ aInteger0 ),
inference(pattern_uni,[status(thm)],[31513:[bind(A,$thf( xm @ ( xn @ sdtpldt0 ) ))]]) ).
thf(33195,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aInteger0 )
!= ( xm @ ( xn @ sdtpldt0 ) @ aInteger0 ) )
| ~ $true
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(paramod_ordered,[status(thm)],[72,31514]) ).
thf(33196,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aInteger0 )
!= ( xm @ ( xn @ sdtpldt0 ) @ aInteger0 ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[33195]) ).
thf(33197,plain,
( ~ ( xm @ aInteger0 )
| ~ ( xn @ aInteger0 ) ),
inference(pattern_uni,[status(thm)],[33196:[bind(A,$thf( xn )),bind(B,$thf( xm ))]]) ).
thf(19,axiom,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__876) ).
thf(112,plain,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(113,plain,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
inference(cnf,[status(esa)],[112]) ).
thf(114,plain,
xn @ aInteger0,
inference(cnfConj,[status(thm)],[113]) ).
thf(28,axiom,
( ( ( xm @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( xm @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__899) ).
thf(147,plain,
( ( ( xm @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( xm @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(148,plain,
( ( ( xm @ ( xq @ sdtasdt0 ) )
= ( xc @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( xm @ aInteger0 ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
xm @ aInteger0,
inference(cnfConj,[status(thm)],[148]) ).
thf(33629,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[33197,114,149]) ).
thf(33630,plain,
$false,
inference(simp,[status(thm)],[33629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM432+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 02:44:52 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.20 % [INFO] Parsing done (205ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 2.06/1.61 % [INFO] eprover registered as external prover.
% 2.06/1.62 % [INFO] Scanning for conjecture ...
% 2.24/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.43/1.83 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.43/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/1.89 % [INFO] Type checking passed.
% 2.65/1.90 % [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 ...
% 51.55/18.12 % [INFO] Killing All external provers ...
% 51.55/18.13 % Time passed: 17584ms (effective reasoning time: 16907ms)
% 51.55/18.13 % 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)>
% 51.72/18.13 % Axioms used in derivation (4): mIntPlus, m__924, m__876, m__899
% 51.72/18.13 % No. of inferences in proof: 28
% 51.72/18.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17584 ms resp. 16907 ms w/o parsing
% 51.72/18.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.72/18.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------