%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV005-1 : 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 : n016.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 08:57:54 AM UTC 2026
% Result : Unsatisfiable 4.51s 7.55s
% Output : Refutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 242 ( 42 ~; 36 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 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 : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(n_decl,type,
n: $i ).
thf(k_decl,type,
k: $i ).
thf(l_decl,type,
l: $i ).
thf(i_decl,type,
i: $i ).
thf(one_decl,type,
one: $i ).
thf(a_decl,type,
a: $i > $i ).
thf(predecessor_decl,type,
predecessor: $i > $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(15,axiom,
! [A: $i] : ( A @ successor @ ( A @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_than_successor) ).
thf(52,plain,
! [A: $i] : ( A @ successor @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_than ) )
| ~ ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',anti_symmetry_of_less_than) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_than ) )
| ~ ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,negated_conjecture,
~ ( i @ ( k @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(28,plain,
~ ( i @ ( k @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_than ) )
| ~ ( C @ ( A @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_than) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_than ) )
| ~ ( C @ ( A @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( A @ predecessor )
!= ( B @ predecessor ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_predecessor) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( A @ predecessor )
!= ( B @ predecessor ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ predecessor @ successor )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_predecessor) ).
thf(39,plain,
! [A: $i] :
( ( A @ predecessor @ successor )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_than ) )
| ( C != B )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_and_less_than_transitivity2) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_than ) )
| ( C != B )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] :
~ ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_less_than_x) ).
thf(58,plain,
! [A: $i] :
~ ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_than ) )
| ( C != A )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_and_less_than_transitivity1) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_than ) )
| ( C != A )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,negated_conjecture,
l @ predecessor @ a @ ( k @ a @ less_than ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(24,plain,
l @ predecessor @ a @ ( k @ a @ less_than ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ successor @ predecessor )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_successor) ).
thf(37,plain,
! [A: $i] :
( ( A @ successor @ predecessor )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ~ ( A @ predecessor @ a @ ( A @ a @ less_than ) )
| ~ ( l @ ( A @ less_than ) )
| ~ ( A @ ( one @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
thf(25,plain,
! [A: $i] :
( ~ ( A @ predecessor @ a @ ( A @ a @ less_than ) )
| ~ ( l @ ( A @ less_than ) )
| ~ ( A @ ( one @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( ( A @ successor )
!= ( B @ successor ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_successor) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( ( A @ successor )
!= ( B @ successor ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,negated_conjecture,
! [A: $i] :
( ~ ( l @ predecessor @ a @ ( A @ a @ less_than ) )
| ~ ( l @ ( one @ less_than ) )
| ( A @ ( n @ less_than ) )
| ( l @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(29,plain,
! [A: $i] :
( ~ ( l @ predecessor @ a @ ( A @ a @ less_than ) )
| ~ ( l @ ( one @ less_than ) )
| ( A @ ( n @ less_than ) )
| ( l @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,negated_conjecture,
l @ ( one @ less_than ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(22,plain,
l @ ( one @ less_than ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ~ ( k @ a @ ( A @ a @ less_than ) )
| ~ ( n @ successor @ ( A @ less_than ) )
| ( l @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
thf(27,plain,
! [A: $i] :
( ~ ( k @ a @ ( A @ a @ less_than ) )
| ~ ( n @ successor @ ( A @ less_than ) )
| ( l @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
~ ( l @ ( k @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(26,plain,
~ ( l @ ( k @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_related) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
~ ( k @ ( n @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(23,plain,
~ ( k @ ( n @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
n @ ( l @ less_than ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(30,plain,
n @ ( l @ less_than ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i] : ( A @ ( A @ predecessor @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less_than) ).
thf(51,plain,
! [A: $i] : ( A @ ( A @ predecessor @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,plain,
$false,
inference(e,[status(thm)],[52,60,28,53,41,39,66,58,62,24,37,25,46,29,22,27,26,55,23,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV005-1 : 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
% 0.16/5.42 % Computer : n016.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 13:09:38 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 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
% 0.21/5.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/6.07 % [INFO] Parsing done (157ms).
% 1.38/6.08 % [INFO] Running in sequential loop mode.
% 2.16/6.46 % [INFO] eprover registered as external prover.
% 2.16/6.47 % [INFO] Scanning for conjecture ...
% 2.44/6.63 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.44/6.68 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.61/6.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.61/6.70 % [INFO] Type checking passed.
% 2.61/6.71 % [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 ...
% 4.51/7.54 % External prover 'e' found a proof!
% 4.51/7.54 % [INFO] Killing All external provers ...
% 4.51/7.54 % Time passed: 1974ms (effective reasoning time: 1458ms)
% 4.51/7.54 % Axioms used in derivation (12): well_defined_successor, all_related, predecessor_successor, predecessor_less_than, well_defined_predecessor, less_than_successor, x_not_less_than_x, successor_predecessor, anti_symmetry_of_less_than, equal_and_less_than_transitivity1, equal_and_less_than_transitivity2, transitivity_of_less_than
% 4.51/7.54 % No. of inferences in proof: 43
% 4.51/7.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1974 ms resp. 1458 ms w/o parsing
% 4.75/7.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.75/7.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------