%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed 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 : n004.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 08:08:08 AM UTC 2026
% Result : Unsatisfiable 5.30s 13.47s
% Output : Refutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 292 ( 34 ~; 30 |; 0 &; 228 @)
% ( 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 : 11 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(n0_decl,type,
n0: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(predecessor_of_1st_minus_2nd_decl,type,
predecessor_of_1st_minus_2nd: $i > $i > $i ).
thf(20,axiom,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
thf(56,plain,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_equality1) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times) ).
thf(39,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_preserved_over_times) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_and_equal) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ less ) )
| ( n0 @ ( C @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_lemma) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ less ) )
| ( n0 @ ( C @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
~ ( a @ ( b @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_less_than_a) ).
thf(24,plain,
~ ( a @ ( b @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ( A @ ( B @ equalish ) )
| ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ( A @ ( B @ equalish ) )
| ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
c @ ( a @ multiply ) @ ( c @ ( b @ multiply ) @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
thf(46,plain,
c @ ( a @ multiply ) @ ( c @ ( b @ multiply ) @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition) ).
thf(57,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_not_less_than_itself) ).
thf(28,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less ) )
| ~ ( C @ ( B @ ( A @ successor @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_number) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less ) )
| ~ ( C @ ( B @ ( A @ successor @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
~ ( n0 @ ( c @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_0) ).
thf(22,plain,
~ ( n0 @ ( c @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ predecessor_of_1st_minus_2nd ) @ successor @ add ) @ equalish ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_lemma) ).
thf(54,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)],[19]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_the_first_number) ).
thf(40,plain,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less ) )
| ~ ( A @ ( C @ less ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/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)],[3]) ).
thf(5,axiom,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_zero) ).
thf(30,plain,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(51,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[56,52,39,35,31,47,42,24,37,46,57,28,33,22,44,54,49,40,26,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed 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
% 0.24/10.51 % Computer : n004.cluster.edu
% 0.24/10.51 % Model : x86_64 x86_64
% 0.24/10.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/10.51 % Memory : 8046.5625MB
% 0.24/10.51 % OS : Linux 6.8.0-71-generic
% 0.24/10.51 % CPULimit : 300
% 0.24/10.51 % WCLimit : 300
% 0.24/10.51 % DateTime : Sat Sep 26 01:54:48 UTC 2026
% 0.24/10.52 % CPUTime :
% 0.24/10.52 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
% 1.35/11.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/11.69 % [INFO] Parsing done (299ms).
% 2.04/11.71 % [INFO] Running in sequential loop mode.
% 2.98/12.34 % [INFO] eprover registered as external prover.
% 2.98/12.35 % [INFO] Scanning for conjecture ...
% 3.17/12.48 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.35/12.57 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 3.52/12.61 % [INFO] Problem is propositional (TPTP CNF).
% 3.52/12.61 % [INFO] Type checking passed.
% 3.52/12.62 % [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 ...
% 5.30/13.47 % External prover 'e' found a proof!
% 5.30/13.47 % [INFO] Killing All external provers ...
% 5.30/13.47 % Time passed: 2740ms (effective reasoning time: 1750ms)
% 5.30/13.47 % Axioms used in derivation (20): numbers_either_less_or_equal, successor_equality1, equality_preserved_over_times, less_lemma, successor_substitution, reflexivity, addition, times_zero, not_less_and_equal, adding_zero, number_not_less_than_itself, transitivity, multiply_lemma, symmetry, smaller_number, b_times_c_less_than_a_times_c, b_not_less_than_a, times, transitivity_of_less, zero_is_the_first_number
% 5.30/13.47 % No. of inferences in proof: 43
% 5.30/13.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2740 ms resp. 1750 ms w/o parsing
% 5.70/13.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.70/13.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------