%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN006-4 : 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 : n020.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 07:31:37 AM UTC 2026
% Result : Unsatisfiable 5.54s 3.31s
% Output : Refutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 14 ~; 12 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(d_decl,type,
d: $i ).
thf(b_decl,type,
b: $i ).
thf(zero_decl,type,
zero: $i ).
thf(identity_decl,type,
identity: $i ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_equal ) )
| ~ ( C @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_equal ) )
| ~ ( C @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
~ ( b @ ( d @ ( a @ divide ) @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
thf(15,plain,
~ ( b @ ( d @ ( a @ divide ) @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ divide ) @ divide ) @ ( B @ ( C @ divide ) @ ( B @ ( A @ divide ) @ divide ) @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ divide ) @ divide ) @ ( B @ ( C @ divide ) @ ( B @ ( A @ divide ) @ divide ) @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(25,plain,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(29,plain,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ divide ) )
= zero )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ divide ) )
= zero )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( A @ divide ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
d @ ( b @ ( a @ divide ) @ less_equal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
thf(40,plain,
d @ ( b @ ( a @ divide ) @ less_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(23,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
( ( zero @ ( a @ divide ) )
= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
thf(36,plain,
( ( zero @ ( a @ divide ) )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_id_is_zero) ).
thf(30,plain,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[38,15,24,25,20,29,17,32,34,40,26,23,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n020.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 15:57:34 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.43/1.34 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.99/1.61 % [INFO] Parsing done (269ms).
% 1.99/1.63 % [INFO] Running in sequential loop mode.
% 2.98/2.24 % [INFO] eprover registered as external prover.
% 2.98/2.25 % [INFO] Scanning for conjecture ...
% 3.18/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 3.36/2.42 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 3.36/2.45 % [INFO] Problem is propositional (TPTP CNF).
% 3.36/2.46 % [INFO] Type checking passed.
% 3.36/2.47 % [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 ...
% 5.54/3.30 % External prover 'e' found a proof!
% 5.54/3.30 % [INFO] Killing All external provers ...
% 5.54/3.30 % Time passed: 2613ms (effective reasoning time: 1661ms)
% 5.54/3.30 % Axioms used in derivation (13): identity_is_largest, x_divide_x_is_zero, a_divide_b_LE_d, zero_divide_anything_is_zero, everything_divide_id_is_zero, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, x_divide_zero_is_x, quotient_less_equal1, transitivity_of_less_equal, quotient_smaller_than_numerator, quotient_property
% 5.54/3.30 % No. of inferences in proof: 29
% 5.54/3.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2613 ms resp. 1661 ms w/o parsing
% 5.54/3.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.54/3.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------