%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n003.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 2.32s 1.38s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 136 ( 20 ~; 20 |; 0 &; 96 @)
% ( 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 : 10 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(d_decl,type,
d: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
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(divides_decl,type,
divides: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equalish ) )
| ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equalish ) )
| ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,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(13,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less ) )
| ~ ( A @ ( C @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,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(17,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)],[4]) ).
thf(9,axiom,
b @ ( a @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
thf(27,plain,
b @ ( a @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
~ ( d @ ( a @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_less_than_d) ).
thf(11,plain,
~ ( d @ ( a @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ divides ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_if_equal) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ divides ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ less ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_only_less_or_equal) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ less ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,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(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less ) )
| ~ ( C @ ( B @ ( A @ successor @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
d @ ( b @ divides ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_divides_d) ).
thf(28,plain,
d @ ( b @ divides ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ divides ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_if_less) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ divides ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,13,17,27,11,23,19,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 01:55:53 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/0.81 % [INFO] Parsing done (97ms).
% 0.95/0.81 % [INFO] Running in sequential loop mode.
% 1.19/1.01 % [INFO] eprover registered as external prover.
% 1.19/1.01 % [INFO] Scanning for conjecture ...
% 1.50/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.50/1.07 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.50/1.08 % [INFO] Problem is propositional (TPTP CNF).
% 1.50/1.08 % [INFO] Type checking passed.
% 1.50/1.08 % [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 ...
% 2.32/1.38 % External prover 'e' found a proof!
% 2.32/1.38 % [INFO] Killing All external provers ...
% 2.32/1.38 % Time passed: 881ms (effective reasoning time: 560ms)
% 2.32/1.38 % Axioms used in derivation (9): divides_if_less, smaller_number, less_lemma, divides_only_less_or_equal, a_less_than_b, b_divides_d, divides_if_equal, transitivity_of_less, transitivity
% 2.32/1.38 % No. of inferences in proof: 21
% 2.32/1.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 881 ms resp. 560 ms w/o parsing
% 2.75/1.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.75/1.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------