%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE044+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 07:43:05 AM UTC 2026
% Result : Theorem 20.99s 5.63s
% Output : Refutation 20.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 241 ( 2 ~; 0 |; 4 &; 228 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 63 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(star_decl,type,
star: $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( B @ ( C @ ( A @ star @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( B @ ( C @ ( A @ star @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,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',right_distributivity) ).
thf(60,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)],[17]) ).
thf(11,axiom,
! [A: $i] : ( A @ star @ ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
thf(45,plain,
! [A: $i] : ( A @ star @ ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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(39,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)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(63,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)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( A @ ( B @ star @ ( C @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( A @ ( B @ star @ ( C @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] : ( A @ star @ ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
thf(47,plain,
! [A: $i] : ( A @ star @ ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(42,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(25,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(5,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,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',left_distributivity) ).
thf(33,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)],[7]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(54,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ( one @ addition ) @ star @ ( A @ star @ leq ) )
& ( A @ star @ ( A @ ( one @ addition ) @ star @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ( one @ addition ) @ star @ ( A @ star @ leq ) )
& ( A @ star @ ( A @ ( one @ addition ) @ star @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] :
( ( A @ ( one @ addition ) @ star @ ( A @ star @ leq ) )
& ( A @ star @ ( A @ ( one @ addition ) @ star @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3859,plain,
$false,
inference(e,[status(thm)],[52,57,60,45,22,39,63,31,47,42,25,28,33,54,49,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n009.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 19:17:28 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.20 % [INFO] Parsing done (190ms).
% 1.44/1.21 % [INFO] Running in sequential loop mode.
% 2.17/1.61 % [INFO] eprover registered as external prover.
% 2.17/1.61 % [INFO] Scanning for conjecture ...
% 2.36/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.36/1.78 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.56/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/1.82 % [INFO] Type checking passed.
% 2.56/1.83 % [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 ...
% 20.99/5.62 % External prover 'e' found a proof!
% 20.99/5.63 % [INFO] Killing All external provers ...
% 20.99/5.63 % Time passed: 5071ms (effective reasoning time: 4411ms)
% 20.99/5.63 % 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)>
% 20.99/5.63 % Axioms used in derivation (16): additive_identity, star_induction_right, left_annihilation, star_induction_left, right_distributivity, star_unfold_left, right_annihilation, multiplicative_left_identity, additive_idempotence, additive_associativity, multiplicative_right_identity, star_unfold_right, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 20.99/5.63 % No. of inferences in proof: 36
% 20.99/5.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5071 ms resp. 4411 ms w/o parsing
% 20.99/5.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.99/5.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------