%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA004-4 : 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 : n015.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 06:50:14 AM UTC 2026
% Result : Unsatisfiable 4.17s 2.51s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 298 ( 26 ~; 32 |; 0 &; 240 @)
% ( 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 : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(absolute_decl,type,
absolute: $i > $i ).
thf(add_decl,type,
add: $i > $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(6,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(24,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)],[6]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( epsilon_0 @ ( a_real_number @ g @ negate @ ( A @ xs @ g @ add ) @ ( a_real_number @ f @ negate @ ( A @ xs @ f @ add ) @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_1) ).
thf(14,plain,
! [A: $i] :
( ~ ( epsilon_0 @ ( a_real_number @ g @ negate @ ( A @ xs @ g @ add ) @ ( a_real_number @ f @ negate @ ( A @ xs @ f @ add ) @ add ) @ absolute @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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(20,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)],[4]) ).
thf(5,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(22,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)],[5]) ).
thf(3,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(18,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)],[3]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ absolute @ less_or_equal ) )
| ~ ( C @ ( B @ absolute @ ( A @ absolute @ add ) @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ absolute @ less_or_equal ) )
| ~ ( C @ ( B @ absolute @ ( A @ absolute @ add ) @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,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(26,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ half @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,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(28,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_1 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,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(38,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)],[13]) ).
thf(10,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(32,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)],[10]) ).
thf(11,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(34,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)],[11]) ).
thf(12,axiom,
~ ( n0 @ ( epsilon_0 @ less_or_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(36,plain,
~ ( n0 @ ( epsilon_0 @ less_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,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(30,plain,
! [A: $i] :
( ~ ( n0 @ ( A @ delta_2 @ less_or_equal ) )
| ( n0 @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,plain,
$false,
inference(e,[status(thm)],[24,14,20,22,18,16,26,28,38,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA004-4 : 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
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 22:05:59 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 1.04/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.29 % [INFO] Parsing done (192ms).
% 1.58/1.31 % [INFO] Running in sequential loop mode.
% 2.27/1.73 % [INFO] eprover registered as external prover.
% 2.27/1.74 % [INFO] Scanning for conjecture ...
% 2.48/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.48/1.87 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.48/1.90 % [INFO] Problem is propositional (TPTP CNF).
% 2.67/1.90 % [INFO] Type checking passed.
% 2.67/1.90 % [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 ...
% 4.17/2.51 % External prover 'e' found a proof!
% 4.17/2.51 % [INFO] Killing All external provers ...
% 4.17/2.51 % Time passed: 1899ms (effective reasoning time: 1195ms)
% 4.17/2.51 % Axioms used in derivation (12): zero_and_half, absolute_sum_less_or_equal_sum_of_absolutes2, clause_2, clause_1, minimum7, clause_4, minimum3, clause_6, less_or_equal_sum_of_halves, clause_3, minimum9, clause_5
% 4.17/2.51 % No. of inferences in proof: 27
% 4.17/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1899 ms resp. 1195 ms w/o parsing
% 4.17/2.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.17/2.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------