%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n009.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 07:43:19 AM UTC 2026
% Result : Theorem 6.92s 3.89s
% Output : Refutation 7.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 297 ( 2 ~; 0 |; 4 &; 282 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(strong_iteration_decl,type,
strong_iteration: $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(star_decl,type,
star: $i > $i ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) )
=> ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) )
=> ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
thf(43,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(40,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(68,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( C @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( A @ star @ ( B @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( C @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( A @ star @ ( B @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i] :
( ( zero @ ( A @ multiplication ) @ strong_iteration @ ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ leq ) )
& ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ ( zero @ ( A @ multiplication ) @ strong_iteration @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( zero @ ( A @ multiplication ) @ strong_iteration @ ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ leq ) )
& ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ ( zero @ ( A @ multiplication ) @ strong_iteration @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( zero @ ( A @ multiplication ) @ strong_iteration @ ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ leq ) )
& ( zero @ ( A @ multiplication ) @ ( one @ addition ) @ ( zero @ ( A @ multiplication ) @ strong_iteration @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
thf(71,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
thf(30,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,plain,
$false,
inference(e,[status(thm)],[74,65,77,27,35,48,43,40,68,24,37,46,57,21,33,71,54,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n009.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 19:27:44 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.44/1.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.24/1.70 % [INFO] Parsing done (314ms).
% 2.24/1.73 % [INFO] Running in sequential loop mode.
% 3.34/2.34 % [INFO] eprover registered as external prover.
% 3.34/2.35 % [INFO] Scanning for conjecture ...
% 3.77/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.95/2.61 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.95/2.68 % [INFO] Problem is first-order (TPTP FOF).
% 3.95/2.69 % [INFO] Type checking passed.
% 4.20/2.70 % [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 ...
% 6.92/3.88 % External prover 'e' found a proof!
% 6.92/3.89 % [INFO] Killing All external provers ...
% 6.92/3.89 % Time passed: 3174ms (effective reasoning time: 2149ms)
% 6.92/3.89 % 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)>
% 6.92/3.89 % Axioms used in derivation (18): additive_identity, isolation, additive_associativity, multiplicative_right_identity, star_unfold2, multiplicative_left_identity, idempotence, multiplicative_associativity, infty_unfold1, star_induction2, distributivity2, star_induction1, star_unfold1, left_annihilation, infty_coinduction, order, additive_commutativity, distributivity1
% 6.92/3.89 % No. of inferences in proof: 40
% 6.92/3.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3174 ms resp. 2149 ms w/o parsing
% 7.18/3.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.18/3.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------