%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN003-4 : 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 : n002.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 07:31:35 AM UTC 2026
% Result : Unsatisfiable 3.13s 2.23s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 10 ~; 8 |; 0 &; 76 @)
% ( 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 : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(zero_decl,type,
zero: $i ).
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(identity_decl,type,
identity: $i ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ divide ) )
= zero )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ divide ) )
= zero )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(21,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(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ( ( B @ ( A @ divide ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( a @ ( a @ divide ) )
!= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
thf(11,plain,
( ( a @ ( a @ divide ) )
!= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(20,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( zero @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(22,plain,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',everything_divide_id_is_zero) ).
thf(27,plain,
! [A: $i] :
( ( identity @ ( A @ divide ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(26,plain,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(23,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(31,plain,
$false,
inference(e,[status(thm)],[14,21,17,11,20,29,22,27,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n002.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 : Fri Sep 25 15:58:19 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.16 % [INFO] Parsing done (181ms).
% 1.20/1.18 % [INFO] Running in sequential loop mode.
% 1.80/1.57 % [INFO] eprover registered as external prover.
% 1.80/1.58 % [INFO] Scanning for conjecture ...
% 2.00/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.00/1.69 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.15/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.71 % [INFO] Type checking passed.
% 2.15/1.72 % [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 ...
% 3.13/2.22 % External prover 'e' found a proof!
% 3.13/2.22 % [INFO] Killing All external provers ...
% 3.13/2.22 % Time passed: 1687ms (effective reasoning time: 1038ms)
% 3.13/2.22 % Axioms used in derivation (9): identity_is_largest, zero_divide_anything_is_zero, everything_divide_id_is_zero, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property
% 3.13/2.22 % No. of inferences in proof: 21
% 3.13/2.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1687 ms resp. 1038 ms w/o parsing
% 3.13/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.13/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------