%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM859+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n012.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 08:10:13 AM UTC 2026
% Result : Theorem 2.46s 16.53s
% Output : Refutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 317 ( 6 ~; 6 |; 24 &; 246 @)
% ( 9 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 82 ( 0 ^; 79 !; 3 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(minsol_model_ub_decl,type,
minsol_model_ub: $i > $i > $i > $o ).
thf(minsol_model_max_decl,type,
minsol_model_max: $i > $i > $i > $o ).
thf(lesseq_decl,type,
lesseq: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(summation_decl,type,
summation: $i > $i ).
thf(max_decl,type,
max: $i > $i > $i ).
thf(ub_decl,type,
ub: $i > $i > $i > $o ).
thf(model_max_decl,type,
model_max: $i > $i > $i > $o ).
thf(model_ub_decl,type,
model_ub: $i > $i > $i > $o ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( C @ ( A @ lesseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( C @ ( A @ lesseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_max ) ) )
<=> ( C @ ( B @ ( A @ max ) @ lesseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_2) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ max ) @ lesseq ) )
=> ( C @ ( B @ ( A @ model_max ) ) ) )
& ( ( C @ ( B @ ( A @ model_max ) ) )
=> ( C @ ( B @ ( A @ max ) @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ lesseq ) )
<=> ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_monotone_1) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ( ( B @ ( A @ lesseq ) )
=> ( B @ ( C @ sum ) @ ( A @ ( C @ sum ) @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ model_ub ) ) )
<=> ? [D: $i] :
( ( C @ ( D @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_2) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C @ ( D @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) )
=> ( C @ ( B @ ( A @ model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ model_ub ) ) )
=> ? [D: $i] :
( ( C @ ( D @ lesseq ) )
& ( D @ ( B @ ( A @ ub ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ lesseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
thf(23,plain,
! [A: $i] : ( A @ ( A @ lesseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ lesseq ) )
| ( B @ ( A @ lesseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_ub ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_ub ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
thf(47,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ lesseq ) )
| ( ( B @ ( A @ max ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lesseq ) )
<=> ( B @ summation @ ( A @ summation @ lesseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',summation_monotone) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( B @ summation @ ( A @ summation @ lesseq ) )
=> ( B @ ( A @ lesseq ) ) )
& ( ( B @ ( A @ lesseq ) )
=> ( B @ summation @ ( A @ summation @ lesseq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_max ) ) )
<=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ model_max ) ) )
=> ( D @ ( C @ lesseq ) ) )
& ( C @ ( B @ ( A @ model_max ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ lesseq ) )
| ( ( B @ ( A @ max ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ lesseq ) )
& ( B @ ( A @ lesseq ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ub ) ) )
<=> ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) )
=> ( C @ ( B @ ( A @ ub ) ) ) )
& ( ( C @ ( B @ ( A @ ub ) ) )
=> ( ( C @ ( B @ lesseq ) )
& ( C @ ( A @ lesseq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
<=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ minsol_model_max ) ) )
=> ( C @ ( B @ ( A @ minsol_model_ub ) ) ) )
& ( ( C @ ( B @ ( A @ minsol_model_ub ) ) )
=> ( C @ ( B @ ( A @ minsol_model_max ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(177,plain,
$false,
inference(e,[status(thm)],[25,57,32,63,23,30,79,47,38,70,44,27,50,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM859+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % 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
% 0.07/15.34 % Computer : n012.cluster.edu
% 0.07/15.34 % Model : x86_64 x86_64
% 0.07/15.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/15.34 % Memory : 8046.5625MB
% 0.07/15.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.34 % CPULimit : 300
% 0.07/15.34 % WCLimit : 300
% 0.07/15.34 % DateTime : Sat Sep 26 04:13:51 UTC 2026
% 0.07/15.34 % CPUTime :
% 0.07/15.34 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
% 0.09/15.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.09/15.72 % [INFO] Parsing done (90ms).
% 0.09/15.72 % [INFO] Running in sequential loop mode.
% 0.09/15.91 % [INFO] eprover registered as external prover.
% 0.09/15.91 % [INFO] Scanning for conjecture ...
% 0.09/15.96 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 0.09/15.97 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 0.09/15.99 % [INFO] Problem is first-order (TPTP FOF).
% 0.09/16.00 % [INFO] Type checking passed.
% 0.09/16.00 % [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 ...
% 2.46/16.53 % External prover 'e' found a proof!
% 2.46/16.53 % [INFO] Killing All external provers ...
% 2.46/16.53 % Time passed: 1104ms (effective reasoning time: 803ms)
% 2.46/16.53 % Solved by 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)>
% 2.46/16.53 % Axioms used in derivation (13): summation_monotone, lesseq_ref, max_1, lesseq_trans, model_max_2, max_2, ub, lesseq_total, model_ub_2, sum_monotone_1, minsol_model_max, lesseq_antisymmetric, minsol_model_ub
% 2.46/16.53 % No. of inferences in proof: 30
% 2.46/16.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1104 ms resp. 803 ms w/o parsing
% 2.46/16.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.46/16.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------