%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN009-1 : 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 : n001.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 07:31:39 AM UTC 2026
% Result : Unsatisfiable 15.84s 5.62s
% Output : Refutation 15.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 170 ( 26 ~; 24 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(idQa_decl,type,
idQa: $i ).
thf(idQ__idQ_idQa_decl,type,
idQ__idQ_idQa: $i ).
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(quotient_decl,type,
quotient: $i > $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(identity_decl,type,
identity: $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(idQ_idQa_decl,type,
idQ_idQa: $i ).
thf(6,axiom,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
file('/export/starexec/sandbox2/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(1,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
thf(14,plain,
idQa != idQ__idQ_idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
file('/export/starexec/sandbox2/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(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_existence) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
idQ_idQa @ ( idQa @ ( identity @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
thf(35,plain,
idQ_idQa @ ( idQa @ ( identity @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
idQa @ ( a @ ( identity @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
thf(34,plain,
idQa @ ( a @ ( identity @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(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(5,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(23,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
idQ__idQ_idQa @ ( idQ_idQa @ ( identity @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
thf(36,plain,
idQ__idQ_idQa @ ( idQ_idQa @ ( identity @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
thf(30,plain,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1184,plain,
$false,
inference(e,[status(thm)],[25,14,29,21,35,31,34,17,26,23,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.11/0.50 % Computer : n001.cluster.edu
% 0.11/0.50 % Model : x86_64 x86_64
% 0.11/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.50 % Memory : 8046.5625MB
% 0.11/0.50 % OS : Linux 6.8.0-71-generic
% 0.11/0.50 % CPULimit : 300
% 0.11/0.50 % WCLimit : 300
% 0.11/0.50 % DateTime : Fri Sep 25 16:03:11 UTC 2026
% 0.11/0.51 % CPUTime :
% 0.11/0.51 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
% 1.38/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.63 % [INFO] Parsing done (274ms).
% 1.85/1.65 % [INFO] Running in sequential loop mode.
% 2.80/2.24 % [INFO] eprover registered as external prover.
% 2.80/2.25 % [INFO] Scanning for conjecture ...
% 2.98/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 3.14/2.41 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 3.14/2.44 % [INFO] Problem is propositional (TPTP CNF).
% 3.14/2.45 % [INFO] Type checking passed.
% 3.14/2.46 % [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 ...
% 15.84/5.62 % External prover 'e' found a proof!
% 15.84/5.62 % [INFO] Killing All external provers ...
% 15.84/5.62 % Time passed: 4902ms (effective reasoning time: 3961ms)
% 15.84/5.62 % Axioms used in derivation (12): quotient_property, quotient_less_equal, identity_divide_a, closure, less_equal_and_equal, identity_divide_idQ_idQa, less_equal_quotient, identity_is_largest, divisor_existence, well_defined, identity_divide_idQa, zero_is_smallest
% 15.84/5.62 % No. of inferences in proof: 27
% 15.84/5.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4902 ms resp. 3961 ms w/o parsing
% 15.84/5.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.84/5.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------