%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM343+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n009.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 08:08:39 AM UTC 2026
% Result : Theorem 10.76s 4.08s
% Output : Refutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 11 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 138 ( 26 ~; 7 |; 15 &; 81 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 0 ^; 27 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(nn1_decl,type,
nn1: $i ).
thf(n1_decl,type,
n1: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(n21_decl,type,
n21: $i ).
thf(1,conjecture,
? [A: $i] :
( ( ( n1 @ ( A @ less ) )
& ( A @ ( nn1 @ less ) ) )
=> ( n21 @ ( A @ ( n21 @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_something_n0_samething) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( n1 @ ( A @ less ) )
& ( A @ ( nn1 @ less ) ) )
=> ( n21 @ ( A @ ( n21 @ sum ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(404,plain,
~ ? [A: $i] :
( ( ( n1 @ ( A @ less ) )
& ( A @ ( nn1 @ less ) ) )
=> ( n21 @ ( A @ ( n21 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(405,plain,
~ ( ( ! [A: $i] : ( n1 @ ( A @ less ) )
& ! [A: $i] : ( A @ ( nn1 @ less ) ) )
=> ? [A: $i] : ( n21 @ ( A @ ( n21 @ sum ) ) ) ),
inference(miniscope,[status(thm)],[404]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( n21 @ ( C @ ( n21 @ sum ) ) )
& ( n1 @ ( B @ less ) )
& ( A @ ( nn1 @ less ) ) ),
inference(cnf,[status(esa)],[405]) ).
thf(407,plain,
! [A: $i] : ( A @ ( nn1 @ less ) ),
inference(cnfConj,[status(thm)],[406]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
<=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
thf(704,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ~ ( A @ ( B @ less ) ) )
=> ( B @ ( A @ less ) ) )
& ( ( B @ ( A @ less ) )
=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(705,plain,
( ! [A: $i,B: $i] :
( ( ( B != A )
& ~ ( A @ ( B @ less ) ) )
=> ( B @ ( A @ less ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ) ),
inference(miniscope,[status(thm)],[704]) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ less ) )
| ( D = C )
| ( C @ ( D @ less ) ) )
& ( ( B != A )
| ~ ( B @ ( A @ less ) ) )
& ( ~ ( A @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ) ),
inference(cnf,[status(esa)],[705]) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( B @ ( A @ less ) ) ),
inference(cnfConj,[status(thm)],[706]) ).
thf(710,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[708]) ).
thf(711,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(simp,[status(thm)],[710]) ).
thf(878,plain,
! [B: $i,A: $i] :
( ( ( A @ ( nn1 @ less ) )
!= ( B @ ( B @ less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[407,711]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( A @ ( nn1 @ less ) )
!= ( B @ ( B @ less ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
$false,
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( nn1 )),bind(B,$thf( nn1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM343+1 : TPTP v9.3.1. Released v3.1.0.
% 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
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 02:28:29 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.32 % [INFO] Parsing done (332ms).
% 1.83/1.34 % [INFO] Running in sequential loop mode.
% 2.53/1.72 % [INFO] eprover registered as external prover.
% 2.53/1.73 % [INFO] Scanning for conjecture ...
% 3.02/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 401 axioms. Running axiom selection ...
% 3.45/2.10 % [INFO] Axiom selection finished. Selected 401 axioms (removed 0 axioms).
% 4.44/2.30 % [INFO] Problem is first-order (TPTP FOF).
% 4.44/2.32 % [INFO] Type checking passed.
% 4.44/2.32 % [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 ...
% 10.76/4.07 % [INFO] Killing All external provers ...
% 10.76/4.07 % Time passed: 3519ms (effective reasoning time: 2727ms)
% 10.76/4.07 % 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)>
% 10.76/4.07 % Axioms used in derivation (1): less_property
% 10.76/4.08 % No. of inferences in proof: 16
% 10.76/4.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3519 ms resp. 2727 ms w/o parsing
% 10.76/4.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.76/4.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------