%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG024-6 : 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 08:25:15 AM UTC 2026
% Result : Unsatisfiable 4.65s 8.08s
% Output : Refutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 182 ( 2 ~; 0 |; 0 &; 180 @)
% ( 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 : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(associator_decl,type,
associator: $i > $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(commutator_decl,type,
commutator: $i > $i > $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(16,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
thf(48,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,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(24,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)],[4]) ).
thf(2,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(20,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)],[2]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) @ multiply ) )
= ( B @ ( A @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_alternative) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) @ multiply ) )
= ( B @ ( A @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(38,plain,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
( ( y @ ( y @ ( x @ associator ) ) )
!= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_alternative) ).
thf(17,plain,
( ( y @ ( y @ ( x @ associator ) ) )
!= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,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(32,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ multiply ) )
= ( B @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ add ) )
= ( C @ ( B @ ( A @ add ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ add ) )
= ( C @ ( B @ ( A @ add ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,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(22,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)],[3]) ).
thf(14,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(44,plain,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,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(36,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)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(30,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,plain,
$false,
inference(e,[status(thm)],[48,42,24,20,46,28,38,17,32,34,22,44,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG024-6 : 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
% 0.22/5.48 % Computer : n018.cluster.edu
% 0.22/5.48 % Model : x86_64 x86_64
% 0.22/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.48 % Memory : 8046.5625MB
% 0.22/5.48 % OS : Linux 6.8.0-71-generic
% 0.22/5.48 % CPULimit : 300
% 0.22/5.48 % WCLimit : 300
% 0.22/5.48 % DateTime : Sat Sep 26 05:49:26 UTC 2026
% 0.22/5.49 % CPUTime :
% 0.22/5.49 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
% 1.41/6.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/6.56 % [INFO] Parsing done (250ms).
% 1.74/6.58 % [INFO] Running in sequential loop mode.
% 2.64/7.15 % [INFO] eprover registered as external prover.
% 2.84/7.16 % [INFO] Scanning for conjecture ...
% 2.91/7.28 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.06/7.36 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.06/7.39 % [INFO] Problem is propositional (TPTP CNF).
% 3.22/7.40 % [INFO] Type checking passed.
% 3.22/7.41 % [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 ...
% 4.65/8.08 % External prover 'e' found a proof!
% 4.65/8.08 % [INFO] Killing All external provers ...
% 4.65/8.08 % Time passed: 2389ms (effective reasoning time: 1495ms)
% 4.65/8.08 % Axioms used in derivation (15): distribute2, left_multiplicative_zero, right_multiplicative_zero, left_additive_identity, right_alternative, right_additive_identity, commutativity_for_addition, additive_inverse_additive_inverse, associativity_for_addition, associator, left_alternative, right_additive_inverse, left_additive_inverse, distribute1, commutator
% 4.65/8.08 % No. of inferences in proof: 33
% 4.65/8.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2389 ms resp. 1495 ms w/o parsing
% 4.86/8.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.86/8.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------