%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : 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 08:25:12 AM UTC 2026
% Result : Unsatisfiable 5.33s 8.32s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 24
% Syntax : Number of formulae : 49 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 52 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 344 ( 12 ~; 4 |; 0 &; 328 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(associator_decl,type,
associator: $i > $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(cx_decl,type,
cx: $i ).
thf(cy_decl,type,
cy: $i ).
thf(cz_decl,type,
cz: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
!= ( A @ ( B @ ( C @ associator ) ) @ additive_inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
!= ( A @ ( B @ ( C @ associator ) ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',associator) ).
thf(74,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)],[21]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ multiply ) @ multiply ) )
!= ( A @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_law) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ multiply ) @ multiply ) )
!= ( A @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) @ multiply ) )
= ( B @ ( A @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) @ multiply ) )
= ( B @ ( A @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add2) ).
thf(58,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)],[13]) ).
thf(3,axiom,
( ( additive_identity @ additive_inverse )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_additive_identity) ).
thf(30,plain,
( ( additive_identity @ additive_inverse )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverse) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( cz @ ( cy @ ( cx @ ( cx @ multiply ) @ associator ) ) )
!= ( cz @ ( cy @ ( cx @ associator ) ) @ ( cx @ multiply ) @ ( cx @ ( cz @ ( cy @ ( cx @ associator ) ) @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_skew_symmetry) ).
thf(25,plain,
( ( cz @ ( cy @ ( cx @ ( cx @ multiply ) @ associator ) ) )
!= ( cz @ ( cy @ ( cx @ associator ) ) @ ( cx @ multiply ) @ ( cx @ ( cz @ ( cy @ ( cx @ associator ) ) @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(28,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ multiply ) @ ( A @ multiply ) @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_moufang) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ multiply ) @ ( A @ multiply ) @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
!= ( C @ ( A @ ( B @ associator ) ) @ additive_inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ associator ) ) )
!= ( C @ ( A @ ( B @ associator ) ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(64,plain,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add1) ).
thf(54,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(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ add ) )
!= ( B @ ( C @ add ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation_for_addition) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ add ) )
!= ( B @ ( C @ add ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ add ) )
= ( C @ ( B @ ( A @ add ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
thf(81,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)],[24]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ multiply ) )
= ( B @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
thf(76,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(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ add ) )
!= ( C @ ( A @ add ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation_for_addition) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ add ) )
!= ( C @ ( A @ add ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( B @ ( C @ ( B @ ( A @ multiply ) @ multiply ) @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_moufang) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( B @ ( C @ ( B @ ( A @ multiply ) @ multiply ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) @ additive_inverse )
= ( B @ additive_inverse @ ( A @ additive_inverse @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_of_inverses) ).
thf(68,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)],[18]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(83,plain,
$false,
inference(e,[status(thm)],[56,78,74,60,44,66,35,72,58,30,37,25,28,70,32,64,54,49,81,76,39,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % 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
% 0.16/5.58 % Computer : n009.cluster.edu
% 0.16/5.58 % Model : x86_64 x86_64
% 0.16/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.58 % Memory : 8046.5625MB
% 0.16/5.58 % OS : Linux 6.8.0-71-generic
% 0.16/5.58 % CPULimit : 300
% 0.16/5.58 % WCLimit : 300
% 0.16/5.58 % DateTime : Sat Sep 26 05:44:51 UTC 2026
% 0.16/5.58 % CPUTime :
% 0.16/5.58 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
% 1.23/6.33 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/6.55 % [INFO] Parsing done (220ms).
% 1.58/6.57 % [INFO] Running in sequential loop mode.
% 2.36/7.04 % [INFO] eprover registered as external prover.
% 2.66/7.06 % [INFO] Scanning for conjecture ...
% 2.91/7.20 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 2.91/7.29 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 3.09/7.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.09/7.36 % [INFO] Type checking passed.
% 3.09/7.37 % [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 ...
% 5.33/8.31 % External prover 'e' found a proof!
% 5.33/8.31 % [INFO] Killing All external provers ...
% 5.33/8.31 % Time passed: 2524ms (effective reasoning time: 1735ms)
% 5.33/8.32 % Axioms used in derivation (23): sum_of_inverses, associator_skew_symmetry1, middle_law, inverse_additive_identity, left_moufang, multiply_over_add2, right_multiplicative_zero, inverse_product2, right_alternative, commutativity_for_addition, additive_inverse_additive_inverse, associativity_for_addition, associator, left_alternative, right_moufang, left_cancellation_for_addition, associator_skew_symmetry2, right_cancellation_for_addition, left_multiplicative_zero, left_additive_identity, multiply_over_add1, add_inverse, inverse_product1
% 5.33/8.32 % No. of inferences in proof: 49
% 5.33/8.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2524 ms resp. 1735 ms w/o parsing
% 5.53/8.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.53/8.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------