%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM427+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 : n008.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 109.62s 48.65s
% Output : Refutation 109.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 37 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 380 ( 52 ~; 42 |; 13 &; 267 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 40 ( 0 ^; 37 !; 3 ?; 40 :)
% 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(xb_decl,type,
xb: $i ).
thf(xa_decl,type,
xa: $i ).
thf(sz10_decl,type,
sz10: $i ).
thf(xn_decl,type,
xn: $i ).
thf(19,axiom,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
thf(100,plain,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(101,plain,
( ( ( xn @ ( xq @ sdtasdt0 ) )
= ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
& ( xn @ aInteger0 ) ),
inference(cnf,[status(esa)],[100]) ).
thf(102,plain,
xn @ aInteger0,
inference(cnfConj,[status(thm)],[101]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( ( A @ smndt0 )
= ( sz10 @ smndt0 @ ( A @ sdtasdt0 ) ) )
& ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
thf(33,plain,
! [A: $i] :
( ( A @ aInteger0 )
=> ( ( ( A @ smndt0 )
= ( sz10 @ smndt0 @ ( A @ sdtasdt0 ) ) )
& ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,plain,
! [A: $i] :
( ( ( ( A @ smndt0 )
= ( sz10 @ smndt0 @ ( A @ sdtasdt0 ) ) )
| ~ ( A @ aInteger0 ) )
& ( ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(154,plain,
! [A: $i] :
( ( ( xn @ aInteger0 )
!= ( A @ aInteger0 ) )
| ~ $true
| ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) ) ),
inference(paramod_ordered,[status(thm)],[102,37]) ).
thf(155,plain,
! [A: $i] :
( ( ( xn @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( ( A @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( A @ smndt0 ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
( ( xn @ ( sz10 @ smndt0 @ sdtasdt0 ) )
= ( xn @ smndt0 ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( xn ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ aInteger0 )
& ( A @ aInteger0 ) )
=> ( B @ ( A @ sdtasdt0 ) @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( B @ aInteger0 )
& ( A @ aInteger0 ) )
=> ( B @ ( A @ sdtasdt0 ) @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(cnf,[status(esa)],[39]) ).
thf(1,conjecture,
( ( xq @ ( xa @ ( xb @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xb @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xq @ ( xa @ ( xb @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xb @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ( ( xq @ ( xa @ ( xb @ sdteqdtlpzmzozddtrp0 ) ) )
| ( xa @ smndt0 @ ( xb @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
& ( A @ aInteger0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
! [A: $i] :
( ~ ( xq @ ( xa @ ( xb @ sdteqdtlpzmzozddtrp0 ) ) )
& ~ ( xa @ smndt0 @ ( xb @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
& ( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(32,plain,
! [A: $i] :
( ~ ( A @ aInteger0 )
| ( ( A @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
!= ( C @ aInteger0 ) )
| ~ $true
| ( ( C @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(paramod_ordered,[status(thm)],[40,32]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
!= ( C @ aInteger0 ) )
| ( ( C @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[392]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ sdtasdt0 ) ))]]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
!= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[394]) ).
thf(22,axiom,
( ( xn @ smndt0 @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
thf(117,plain,
( ( xn @ smndt0 @ ( xq @ sdtasdt0 ) )
= ( xa @ smndt0 @ ( xb @ sdtpldt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,plain,
( ( xa @ smndt0 @ ( xb @ sdtpldt0 ) )
= ( xn @ smndt0 @ ( xq @ sdtasdt0 ) ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(124853,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
!= ( xn @ smndt0 @ ( xq @ sdtasdt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(rewrite,[status(thm)],[414,118]) ).
thf(125170,plain,
! [B: $i,A: $i] :
( ( ( xn @ ( sz10 @ smndt0 @ sdtasdt0 ) )
!= ( B @ ( A @ sdtasdt0 ) ) )
| ( ( xn @ smndt0 @ ( xq @ sdtasdt0 ) )
!= ( xn @ smndt0 @ ( xq @ sdtasdt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(paramod_ordered,[status(thm)],[156,124853]) ).
thf(125171,plain,
! [B: $i,A: $i] :
( ( ( xn @ ( sz10 @ smndt0 @ sdtasdt0 ) )
!= ( B @ ( A @ sdtasdt0 ) ) )
| ~ ( B @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(simp,[status(thm)],[125170]) ).
thf(125172,plain,
( ~ ( xn @ aInteger0 )
| ~ ( sz10 @ smndt0 @ aInteger0 ) ),
inference(pattern_uni,[status(thm)],[125171:[bind(A,$thf( sz10 @ smndt0 )),bind(B,$thf( xn ))]]) ).
thf(15,axiom,
sz10 @ aInteger0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
thf(90,plain,
sz10 @ aInteger0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ aInteger0 )
=> ( A @ smndt0 @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
thf(55,plain,
! [A: $i] :
( ( A @ aInteger0 )
=> ( A @ smndt0 @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,plain,
! [A: $i] :
( ( A @ smndt0 @ aInteger0 )
| ~ ( A @ aInteger0 ) ),
inference(cnf,[status(esa)],[55]) ).
thf(2886,plain,
! [A: $i] :
( ( ( sz10 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( A @ smndt0 @ aInteger0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,56]) ).
thf(2887,plain,
! [A: $i] :
( ( ( sz10 @ aInteger0 )
!= ( A @ aInteger0 ) )
| ( A @ smndt0 @ aInteger0 ) ),
inference(simp,[status(thm)],[2886]) ).
thf(2888,plain,
sz10 @ smndt0 @ aInteger0,
inference(pattern_uni,[status(thm)],[2887:[bind(A,$thf( sz10 ))]]) ).
thf(133145,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[125172,102,2888]) ).
thf(133146,plain,
$false,
inference(simp,[status(thm)],[133145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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 : n008.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 02:42:10 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.20 % [INFO] Parsing done (211ms).
% 1.41/1.22 % [INFO] Running in sequential loop mode.
% 2.18/1.62 % [INFO] eprover registered as external prover.
% 2.18/1.63 % [INFO] Scanning for conjecture ...
% 2.37/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.37/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.37/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 24 axioms. Running axiom selection ...
% 2.56/1.85 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.56/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.90 % [INFO] Problem is first-order (TPTP FOF).
% 2.79/1.91 % [INFO] Type checking passed.
% 2.79/1.91 % [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 ...
% 109.62/48.65 % [INFO] Killing All external provers ...
% 109.62/48.65 % Time passed: 48103ms (effective reasoning time: 47422ms)
% 109.62/48.65 % 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)>
% 109.62/48.65 % Axioms used in derivation (6): m__767, mIntMult, mIntNeg, mIntOne, mMulMinOne, m__747
% 109.62/48.65 % No. of inferences in proof: 42
% 109.62/48.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 48103 ms resp. 47422 ms w/o parsing
% 109.62/48.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 109.62/48.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------