%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN011-3 : 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 : 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 07:31:41 AM UTC 2026
% Result : Unsatisfiable 22.15s 18.60s
% Output : Refutation 22.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 140 ( 12 ~; 8 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(c_decl,type,
c: $i ).
thf(g_decl,type,
g: $i ).
thf(d_decl,type,
d: $i ).
thf(e_decl,type,
e: $i ).
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(identity_decl,type,
identity: $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(1,negated_conjecture,
( ( g @ ( c @ divide ) )
!= ( e @ ( d @ divide ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
thf(14,plain,
( ( g @ ( c @ divide ) )
!= ( e @ ( d @ divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
( ( a @ ( identity @ divide ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
thf(33,plain,
( ( a @ ( identity @ divide ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(17,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ divide ) )
= zero )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
( ( d @ ( identity @ divide ) )
= g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_d) ).
thf(39,plain,
( ( d @ ( identity @ divide ) )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
( ( b @ ( identity @ divide ) )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_b) ).
thf(35,plain,
( ( b @ ( identity @ divide ) )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
( ( b @ ( identity @ divide ) @ ( identity @ divide ) @ ( a @ ( identity @ divide ) @ divide ) )
!= ( a @ ( identity @ divide ) @ ( identity @ divide ) @ ( b @ ( identity @ divide ) @ divide ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_theorem) ).
thf(30,plain,
( ( b @ ( identity @ divide ) @ ( identity @ divide ) @ ( a @ ( identity @ divide ) @ divide ) )
!= ( a @ ( identity @ divide ) @ ( identity @ divide ) @ ( b @ ( identity @ divide ) @ divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(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(12,axiom,
( ( c @ ( identity @ divide ) )
= e ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_c) ).
thf(37,plain,
( ( c @ ( identity @ divide ) )
= e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(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(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/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(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(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
file('/export/starexec/sandbox2/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(3293,plain,
$false,
inference(e,[status(thm)],[14,33,17,39,35,30,24,37,25,20,29,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : HEN011-3 : TPTP v9.3.1. Released v1.0.0.
% 0.04/0.28 % 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
% 0.16/12.10 % Computer : n006.cluster.edu
% 0.16/12.10 % Model : x86_64 x86_64
% 0.16/12.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/12.10 % Memory : 8046.5625MB
% 0.16/12.10 % OS : Linux 6.8.0-71-generic
% 0.16/12.10 % CPULimit : 300
% 0.16/12.10 % WCLimit : 300
% 0.16/12.10 % DateTime : Fri Sep 25 15:58:11 UTC 2026
% 0.16/12.10 % CPUTime :
% 0.16/12.10 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
% 1.26/12.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/13.22 % [INFO] Parsing done (263ms).
% 1.73/13.25 % [INFO] Running in sequential loop mode.
% 2.84/13.85 % [INFO] eprover registered as external prover.
% 2.84/13.86 % [INFO] Scanning for conjecture ...
% 3.06/13.99 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 3.06/14.03 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 3.31/14.06 % [INFO] Problem is propositional (TPTP CNF).
% 3.31/14.07 % [INFO] Type checking passed.
% 3.31/14.08 % [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 ...
% 23.05/18.59 % External prover 'e' found a proof!
% 23.05/18.59 % [INFO] Killing All external provers ...
% 23.05/18.60 % Time passed: 6278ms (effective reasoning time: 5341ms)
% 22.15/18.60 % Axioms used in derivation (12): identity_is_largest, identity_divide_a, identity_divide_b, part_of_theorem, identity_divide_c, quotient_less_equal2, less_equal_and_equal, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property, identity_divide_d, zero_is_smallest
% 22.15/18.60 % No. of inferences in proof: 27
% 22.15/18.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6278 ms resp. 5341 ms w/o parsing
% 22.15/18.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.15/18.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------