%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG011-5 : 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 : n018.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 08:25:13 AM UTC 2026
% Result : Unsatisfiable 6.11s 3.64s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 44 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 262 ( 2 ~; 0 |; 0 &; 260 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(associator_decl,type,
associator: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(commutator_decl,type,
commutator: $i > $i > $i ).
thf(17,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id1) ).
thf(56,plain,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ associator ) ) @ ( A @ ( B @ ( A @ ( A @ associator ) ) @ multiply ) @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',middle_associator) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ associator ) ) @ ( A @ ( B @ ( A @ ( A @ associator ) ) @ multiply ) @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ commutator ) )
= ( B @ ( A @ multiply ) @ additive_inverse @ ( A @ ( B @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ commutator ) )
= ( B @ ( A @ multiply ) @ additive_inverse @ ( A @ ( B @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
( ( additive_identity @ additive_inverse )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_identity) ).
thf(60,plain,
( ( additive_identity @ additive_inverse )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ multiply ) )
= ( B @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ multiply ) )
= ( B @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) @ additive_inverse @ ( C @ ( B @ ( A @ multiply ) @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) @ additive_inverse @ ( C @ ( B @ ( A @ multiply ) @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(50,plain,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(58,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(62,plain,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ add ) @ ( A @ add ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_inverse_and_add) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ add ) @ ( A @ add ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(34,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ ( a @ associator ) ) @ ( a @ ( b @ ( a @ ( a @ associator ) ) @ multiply ) @ multiply ) )
!= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
thf(23,plain,
( ( b @ ( a @ ( a @ associator ) ) @ ( a @ ( b @ ( a @ ( a @ associator ) ) @ multiply ) @ multiply ) )
!= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverse) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) @ additive_inverse )
= ( B @ additive_inverse @ ( A @ additive_inverse @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute_additive_inverse) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) @ additive_inverse )
= ( B @ additive_inverse @ ( A @ additive_inverse @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[56,42,52,46,60,44,54,66,48,50,58,62,28,38,64,32,34,40,26,23,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.22/0.48 % Computer : n018.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 05:47:52 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.41/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.67 % [INFO] Parsing done (299ms).
% 2.23/1.70 % [INFO] Running in sequential loop mode.
% 3.14/2.34 % [INFO] eprover registered as external prover.
% 3.14/2.36 % [INFO] Scanning for conjecture ...
% 3.34/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 3.52/2.59 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.70/2.64 % [INFO] Problem is propositional (TPTP CNF).
% 3.70/2.65 % [INFO] Type checking passed.
% 3.70/2.66 % [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 ...
% 6.11/3.63 % External prover 'e' found a proof!
% 6.11/3.63 % [INFO] Killing All external provers ...
% 6.11/3.63 % Time passed: 2930ms (effective reasoning time: 1923ms)
% 6.11/3.63 % Axioms used in derivation (21): left_identity, multiply_additive_inverse2, right_identity, additive_inverse_identity, product_of_inverse, commutative_addition, middle_associator, additive_inverse_additive_inverse, multiply_additive_id1, associator, distribute2, associative_addition, right_additive_inverse, multiply_additive_id2, left_additive_inverse, distribute_additive_inverse, multiply_additive_inverse1, property_of_inverse_and_add, right_alternative, distribute1, commutator
% 6.11/3.63 % No. of inferences in proof: 45
% 6.11/3.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2930 ms resp. 1923 ms w/o parsing
% 6.34/3.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.34/3.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------