%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 3.51s 2.31s
% Output : Refutation 3.51s
% 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 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 176 ( 26 ~; 24 |; 0 &; 126 @)
% ( 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 : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(quotient_decl,type,
quotient: $i > $i > $i > $o ).
thf(x_decl,type,
x: $i ).
thf(zero_decl,type,
zero: $i ).
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(identity_decl,type,
identity: $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(1,negated_conjecture,
~ ( x @ ( zero @ ( x @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divde_zero_is_x) ).
thf(14,plain,
~ ( x @ ( zero @ ( x @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [A: $i] : ( zero @ ( A @ ( zero @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(34,plain,
! [A: $i] : ( zero @ ( A @ ( zero @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(22,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,
! [A: $i] : ( zero @ ( A @ ( A @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(35,plain,
! [A: $i] : ( zero @ ( A @ ( A @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
thf(30,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(6,axiom,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(24,plain,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(25,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,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
thf(20,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(9,axiom,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(29,plain,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(28,plain,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i] : ( zero @ ( identity @ ( A @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(33,plain,
! [A: $i] : ( zero @ ( identity @ ( A @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[14,34,22,35,18,16,30,24,25,20,29,28,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n011.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 15:55:59 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.18 % [INFO] Parsing done (182ms).
% 1.21/1.19 % [INFO] Running in sequential loop mode.
% 1.81/1.59 % [INFO] eprover registered as external prover.
% 1.81/1.60 % [INFO] Scanning for conjecture ...
% 2.00/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.15/1.71 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.15/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.74 % [INFO] Type checking passed.
% 2.15/1.75 % [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 ...
% 3.51/2.30 % External prover 'e' found a proof!
% 3.51/2.30 % [INFO] Killing All external provers ...
% 3.51/2.30 % Time passed: 1765ms (effective reasoning time: 1106ms)
% 3.51/2.30 % Axioms used in derivation (12): quotient_property, closure, everything_divide_identity_is_zero, zero_divide_anything_is_zero, less_equal_and_equal, zero_is_smallest, less_equal_quotient, identity_is_largest, x_divide_x_is_zero, quotient_less_equal, divisor_existence, well_defined
% 3.51/2.30 % No. of inferences in proof: 27
% 3.51/2.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1765 ms resp. 1106 ms w/o parsing
% 3.51/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------