%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:08:07 AM UTC 2026
% Result : Unsatisfiable 3.13s 12.69s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 200 ( 22 ~; 18 |; 0 &; 160 @)
% ( 0 <=>; 0 =>; 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 : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(predecessor_of_1st_minus_2nd_decl,type,
predecessor_of_1st_minus_2nd: $i > $i > $i ).
thf(4,axiom,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(20,plain,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] : ( A @ successor @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_less_than_its_successor) ).
thf(39,plain,
! [A: $i] : ( A @ successor @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
thf(18,plain,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
~ ( a @ successor @ ( n0 @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_less_than_all_successors) ).
thf(16,plain,
~ ( a @ successor @ ( n0 @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less ) )
| ~ ( A @ ( C @ less ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less ) )
| ~ ( A @ ( C @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_first_number) ).
thf(37,plain,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less ) )
| ~ ( C @ ( B @ ( A @ successor @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less ) )
| ~ ( C @ ( B @ ( A @ successor @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(21,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ predecessor_of_1st_minus_2nd ) @ successor @ add ) @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ predecessor_of_1st_minus_2nd ) @ successor @ add ) @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(19,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,plain,
$false,
inference(e,[status(thm)],[20,32,22,39,35,18,16,26,24,37,28,21,33,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/10.56 % Computer : n017.cluster.edu
% 0.14/10.56 % Model : x86_64 x86_64
% 0.14/10.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.56 % Memory : 8046.5625MB
% 0.14/10.56 % OS : Linux 6.8.0-71-generic
% 0.14/10.56 % CPULimit : 300
% 0.14/10.56 % WCLimit : 300
% 0.14/10.56 % DateTime : Sat Sep 26 01:49:30 UTC 2026
% 0.14/10.56 % CPUTime :
% 0.14/10.56 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.78/11.08 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.03/11.29 % [INFO] Parsing done (207ms).
% 1.20/11.32 % [INFO] Running in sequential loop mode.
% 1.89/11.82 % [INFO] eprover registered as external prover.
% 1.89/11.82 % [INFO] Scanning for conjecture ...
% 1.89/11.89 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.06/11.91 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.06/11.94 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/11.95 % [INFO] Type checking passed.
% 2.06/11.95 % [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 ...
% 3.13/12.69 % External prover 'e' found a proof!
% 3.13/12.69 % [INFO] Killing All external provers ...
% 3.13/12.69 % Time passed: 2022ms (effective reasoning time: 1372ms)
% 3.13/12.69 % Axioms used in derivation (14): successor_equality1, smaller_number, less_lemma, zero_is_first_number, successor_substitution, reflexivity, addition, times_zero, times, transitivity_of_less, transitivity, symmetry, adding_zero, numbers_less_than_its_successor
% 3.13/12.69 % No. of inferences in proof: 31
% 3.13/12.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2022 ms resp. 1372 ms w/o parsing
% 3.34/12.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/12.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------