%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG024-7 : 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 : n013.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 5.16s 3.14s
% Output : Refutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 318 ( 2 ~; 0 |; 0 &; 316 @)
% ( 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 : 90 ( 0 ^; 90 !; 0 ?; 90 :)
% 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(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(commutator_decl,type,
commutator: $i > $i > $i ).
thf(23,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
thf(69,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
thf(61,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ additive_inverse @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ additive_inverse @ ( C @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference2) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ additive_inverse @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ additive_inverse @ ( C @ ( A @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(65,plain,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,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(53,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ multiply ) )
= ( B @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(49,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ additive_inverse @ ( C @ ( A @ multiply ) @ additive_inverse @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference4) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ ( A @ add ) @ multiply ) )
= ( C @ ( B @ multiply ) @ additive_inverse @ ( C @ ( A @ multiply ) @ additive_inverse @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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(35,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)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ additive_inverse @ multiply ) )
= ( C @ ( A @ multiply ) @ additive_inverse @ ( B @ ( A @ multiply ) @ additive_inverse @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference3) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ additive_inverse @ multiply ) )
= ( C @ ( A @ multiply ) @ additive_inverse @ ( B @ ( A @ multiply ) @ additive_inverse @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,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(55,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)],[16]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,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(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) @ multiply ) )
= ( B @ ( A @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( y @ ( y @ ( x @ associator ) ) )
!= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_alternative) ).
thf(24,plain,
( ( y @ ( y @ ( x @ associator ) ) )
!= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ add ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ additive_inverse @ ( B @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ add ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ additive_inverse @ ( B @ ( A @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,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(57,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)],[17]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(59,plain,
! [A: $i] :
( ( A @ additive_inverse @ ( A @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
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(27,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(22,axiom,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(67,plain,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,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(31,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)],[4]) ).
thf(77,plain,
$false,
inference(e,[status(thm)],[69,61,33,65,53,41,45,49,39,35,63,43,55,51,47,24,37,57,29,59,27,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 05:46:37 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.14/1.13 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.43 % [INFO] Parsing done (286ms).
% 1.70/1.45 % [INFO] Running in sequential loop mode.
% 2.81/2.07 % [INFO] eprover registered as external prover.
% 2.81/2.08 % [INFO] Scanning for conjecture ...
% 3.10/2.22 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 3.10/2.29 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 3.29/2.32 % [INFO] Problem is propositional (TPTP CNF).
% 3.29/2.33 % [INFO] Type checking passed.
% 3.29/2.33 % [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 ...
% 5.16/3.14 % External prover 'e' found a proof!
% 5.16/3.14 % [INFO] Killing All external provers ...
% 5.16/3.14 % Time passed: 2558ms (effective reasoning time: 1679ms)
% 5.16/3.14 % Axioms used in derivation (22): distributivity_of_difference2, distributivity_of_difference3, product_of_inverses, left_multiplicative_zero, right_multiplicative_zero, inverse_product2, left_additive_identity, right_alternative, inverse_product1, commutativity_for_addition, additive_inverse_additive_inverse, associativity_for_addition, associator, left_alternative, distribute2, distributivity_of_difference4, right_additive_inverse, left_additive_inverse, distributivity_of_difference1, right_additive_identity, distribute1, commutator
% 5.16/3.14 % No. of inferences in proof: 47
% 5.16/3.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2558 ms resp. 1679 ms w/o parsing
% 5.69/3.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.69/3.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------