%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN006-5 : TPTP v9.3.1. Released v1.0.0.
% 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 : n012.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 1.64s 1.24s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 6 ~; 4 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
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(8,axiom,
( ( d @ ( b @ ( a @ divide ) @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_divide_d_is_zero) ).
thf(25,plain,
( ( d @ ( b @ ( a @ divide ) @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ divide ) @ divide ) @ ( B @ ( C @ divide ) @ ( B @ ( A @ divide ) @ divide ) @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ divide ) @ divide ) @ ( B @ ( C @ divide ) @ ( B @ ( A @ divide ) @ divide ) @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(21,plain,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( b @ ( d @ ( a @ divide ) @ divide ) )
!= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_divide1) ).
thf(9,plain,
( ( b @ ( d @ ( a @ divide ) @ divide ) )
!= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ divide ) @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ divide ) @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( B @ divide ) )
!= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( B @ divide ) )
!= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i] :
( ( zero @ ( A @ divide ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
thf(23,plain,
! [A: $i] :
( ( zero @ ( A @ divide ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[25,14,21,9,12,18,16,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN006-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Fri Sep 25 15:56:21 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.33 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
% 0.38/0.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.70 % [INFO] Parsing done (86ms).
% 0.67/0.70 % [INFO] Running in sequential loop mode.
% 0.85/0.89 % [INFO] eprover registered as external prover.
% 0.85/0.89 % [INFO] Scanning for conjecture ...
% 1.01/0.94 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.01/0.95 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.01/0.96 % [INFO] Problem is propositional (TPTP CNF).
% 1.01/0.96 % [INFO] Type checking passed.
% 1.01/0.96 % [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 ...
% 1.64/1.24 % External prover 'e' found a proof!
% 1.64/1.24 % [INFO] Killing All external provers ...
% 1.64/1.24 % Time passed: 841ms (effective reasoning time: 536ms)
% 1.64/1.24 % Axioms used in derivation (7): a_divide_b_divide_d_is_zero, identity_is_largest, divide_and_equal, zero_is_smallest, x_divide_zero_is_x, quotient_smaller_than_numerator, quotient_property
% 1.64/1.24 % No. of inferences in proof: 17
% 1.64/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 841 ms resp. 536 ms w/o parsing
% 1.64/1.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.64/1.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------