%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n006.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 07:31:40 AM UTC 2026
% Result : Unsatisfiable 5.63s 3.36s
% Output : Refutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 14 ~; 12 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(a_decl,type,
a: $i ).
thf(zero_decl,type,
zero: $i ).
thf(1,negated_conjecture,
( ( a @ ( identity @ divide ) )
!= ( a @ ( identity @ divide ) @ ( identity @ divide ) @ ( identity @ divide ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
( ( a @ ( identity @ divide ) )
!= ( a @ ( identity @ divide ) @ ( identity @ divide ) @ ( identity @ divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ divide ) )
= zero )
| ( ( C @ ( B @ divide ) )
!= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divide_to_zero) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ divide ) )
= zero )
| ( ( C @ ( B @ divide ) )
!= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(13,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ divide ) @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(15,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(22,plain,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ divide ) @ divide ) )
= zero )
| ( ( C @ ( B @ ( A @ divide ) @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ divide ) @ divide ) )
= zero )
| ( ( C @ ( B @ ( A @ divide ) @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ divide ) @ ( B @ ( C @ divide ) @ divide ) )
= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ divide ) @ ( B @ ( C @ divide ) @ divide ) )
= zero )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(19,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(39,plain,
$false,
inference(e,[status(thm)],[10,24,13,17,15,22,27,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.21/0.49 % Computer : n006.cluster.edu
% 0.21/0.49 % Model : x86_64 x86_64
% 0.21/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.49 % Memory : 8046.5625MB
% 0.21/0.49 % OS : Linux 6.8.0-71-generic
% 0.21/0.50 % CPULimit : 300
% 0.21/0.50 % WCLimit : 300
% 0.21/0.50 % DateTime : Fri Sep 25 15:57:40 UTC 2026
% 0.21/0.50 % CPUTime :
% 0.21/0.50 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
% 1.40/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.62 % [INFO] Parsing done (274ms).
% 1.94/1.64 % [INFO] Running in sequential loop mode.
% 3.06/2.26 % [INFO] eprover registered as external prover.
% 3.06/2.27 % [INFO] Scanning for conjecture ...
% 3.43/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.43/2.44 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.43/2.47 % [INFO] Problem is propositional (TPTP CNF).
% 3.43/2.48 % [INFO] Type checking passed.
% 3.43/2.48 % [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 ...
% 5.63/3.36 % External prover 'e' found a proof!
% 5.63/3.36 % [INFO] Killing All external provers ...
% 5.63/3.36 % Time passed: 2651ms (effective reasoning time: 1708ms)
% 5.63/3.36 % Axioms used in derivation (8): identity_is_largest, property_of_divide2, property_of_divide1, transitivity_of_divide_to_zero, divide_and_equal, zero_is_smallest, quotient_smaller_than_numerator, quotient_property
% 5.63/3.36 % No. of inferences in proof: 19
% 5.63/3.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2651 ms resp. 1708 ms w/o parsing
% 5.88/3.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.88/3.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------