%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 07:42:57 AM UTC 2026
% Result : Theorem 2.51s 6.50s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 43 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 373 ( 4 ~; 0 |; 20 &; 326 @)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 70 !; 3 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(one_decl,type,
one: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(29,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(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(89,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(32,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)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(44,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(95,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)],[20]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(38,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(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( one @ ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ leq ) )
& ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ ( one @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( one @ ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ leq ) )
& ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ ( one @ leq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( one @ ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ leq ) )
& ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ c @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ ( one @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(92,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)],[19]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(80,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(35,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(103,plain,
$false,
inference(e,[status(thm)],[56,29,89,53,77,41,32,44,86,95,50,26,83,38,21,92,65,80,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.07/5.34 % Computer : n012.cluster.edu
% 0.07/5.34 % Model : x86_64 x86_64
% 0.07/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.34 % Memory : 8046.5625MB
% 0.07/5.34 % OS : Linux 6.8.0-71-generic
% 0.07/5.34 % CPULimit : 300
% 0.07/5.34 % WCLimit : 300
% 0.07/5.34 % DateTime : Fri Sep 25 19:12:37 UTC 2026
% 0.07/5.34 % CPUTime :
% 0.07/5.34 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/5.64 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.09/5.76 % [INFO] Parsing done (112ms).
% 0.09/5.77 % [INFO] Running in sequential loop mode.
% 0.09/5.98 % [INFO] eprover registered as external prover.
% 0.09/5.98 % [INFO] Scanning for conjecture ...
% 1.30/6.04 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.30/6.08 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.30/6.10 % [INFO] Problem is first-order (TPTP FOF).
% 1.30/6.10 % [INFO] Type checking passed.
% 1.30/6.10 % [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 ...
% 2.27/6.49 % External prover 'e' found a proof!
% 2.27/6.50 % [INFO] Killing All external provers ...
% 2.27/6.50 % Time passed: 1080ms (effective reasoning time: 727ms)
% 2.27/6.50 % 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)>
% 2.51/6.50 % Axioms used in derivation (18): test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, test_deMorgan2, additive_identity, additive_idempotence, additive_associativity, order, additive_commutativity, right_annihilation, test_deMorgan1, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 2.51/6.50 % No. of inferences in proof: 40
% 2.51/6.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1080 ms resp. 727 ms w/o parsing
% 2.51/6.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.51/6.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------