%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA003-4 : 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 : n017.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 06:50:13 AM UTC 2026
% Result : Unsatisfiable 5.44s 3.08s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 274 ( 24 ~; 30 |; 0 &; 220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(absolute_decl,type,
absolute: $i > $i ).
thf(f_decl,type,
f: $i > $i ).
thf(xs_decl,type,
xs: $i > $i ).
thf(negate_decl,type,
negate: $i > $i ).
thf(a_real_number_decl,type,
a_real_number: $i ).
thf(g_decl,type,
g: $i > $i ).
thf(epsilon_0_decl,type,
epsilon_0: $i ).
thf(minimum_decl,type,
minimum: $i > $i > $i ).
thf(half_decl,type,
half: $i > $i ).
thf(delta_1_decl,type,
delta_1: $i > $i ).
thf(delta_2_decl,type,
delta_2: $i > $i ).
thf(7,axiom,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_1 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(25,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_1 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ ( a_real_number @ f @ negate @ ( B @ f @ add ) @ absolute @ less_or_equal ) )
| ~ ( A @ delta_1 @ ( a_real_number @ negate @ ( B @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A @ ( a_real_number @ f @ negate @ ( B @ f @ add ) @ absolute @ less_or_equal ) )
| ~ ( A @ delta_1 @ ( a_real_number @ negate @ ( B @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( epsilon_0 @ ( a_real_number @ g @ negate @ ( A @ xs @ g @ add ) @ absolute @ ( a_real_number @ f @ negate @ ( A @ xs @ f @ add ) @ absolute @ add ) @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_2) ).
thf(13,plain,
! [A: $i] :
( ~ ( epsilon_0 @ ( a_real_number @ g @ negate @ ( A @ xs @ g @ add ) @ absolute @ ( a_real_number @ f @ negate @ ( A @ xs @ f @ add ) @ absolute @ add ) @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_or_equal ) )
| ~ ( C @ ( B @ minimum ) @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum7) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_or_equal ) )
| ~ ( C @ ( B @ minimum ) @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_2 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(27,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_2 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( a_real_number @ negate @ ( A @ xs @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( a_real_number @ negate @ ( A @ xs @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ ( a_real_number @ g @ negate @ ( B @ g @ add ) @ absolute @ less_or_equal ) )
| ~ ( A @ delta_2 @ ( a_real_number @ negate @ ( B @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( a_real_number @ g @ negate @ ( B @ g @ add ) @ absolute @ less_or_equal ) )
| ~ ( A @ delta_2 @ ( a_real_number @ negate @ ( B @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( n0 @ ( A @ half @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
thf(23,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ half @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( n0 @ ( B @ ( A @ minimum ) @ less_or_equal ) )
| ( n0 @ ( B @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( n0 @ ( B @ ( A @ minimum ) @ less_or_equal ) )
| ( n0 @ ( B @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ less_or_equal ) )
| ~ ( C @ ( B @ minimum ) @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum3) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ less_or_equal ) )
| ~ ( C @ ( B @ minimum ) @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ add ) @ less_or_equal ) )
| ~ ( B @ half @ ( C @ less_or_equal ) )
| ~ ( B @ half @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ add ) @ less_or_equal ) )
| ~ ( B @ half @ ( C @ less_or_equal ) )
| ~ ( B @ half @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
~ ( n0 @ ( epsilon_0 @ less_or_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(33,plain,
~ ( n0 @ ( epsilon_0 @ less_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(61,plain,
$false,
inference(e,[status(thm)],[25,29,13,17,27,35,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.13 % 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
% 0.24/0.49 % Computer : n017.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 21:57:34 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.44/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.63 % [INFO] Parsing done (280ms).
% 1.94/1.66 % [INFO] Running in sequential loop mode.
% 2.97/2.21 % [INFO] eprover registered as external prover.
% 2.97/2.21 % [INFO] Scanning for conjecture ...
% 2.97/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.21/2.33 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.21/2.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.21/2.35 % [INFO] Type checking passed.
% 3.21/2.36 % [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 ...
% 5.44/3.08 % External prover 'e' found a proof!
% 5.44/3.08 % [INFO] Killing All external provers ...
% 5.44/3.08 % Time passed: 2371ms (effective reasoning time: 1412ms)
% 5.44/3.08 % Axioms used in derivation (11): zero_and_half, clause_2, clause_1, minimum7, clause_4, minimum3, clause_6, less_or_equal_sum_of_halves, clause_3, minimum9, clause_5
% 5.44/3.08 % No. of inferences in proof: 25
% 5.44/3.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2371 ms resp. 1412 ms w/o parsing
% 5.44/3.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.44/3.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------