%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG008-4 : 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 : n002.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 08:25:11 AM UTC 2026
% Result : Unsatisfiable 3.53s 2.35s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 156 ( 2 ~; 0 |; 0 &; 154 @)
% ( 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 : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $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(6,axiom,
( ( additive_identity @ additive_inverse )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_identity) ).
thf(29,plain,
( ( additive_identity @ additive_inverse )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ additive_inverse @ add ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,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(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ additive_inverse @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,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(27,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)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id1) ).
thf(49,plain,
! [A: $i] :
( ( additive_identity @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( additive_identity @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ multiply ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(18,plain,
( ( b @ ( a @ multiply ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(31,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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(43,plain,
! [B: $i,A: $i] :
( ( B @ additive_inverse @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ additive_inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,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(37,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)],[10]) ).
thf(4,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(25,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)],[4]) ).
thf(17,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(51,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)],[17]) ).
thf(2,negated_conjecture,
( ( a @ ( b @ multiply ) )
!= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
thf(19,plain,
( ( a @ ( b @ multiply ) )
!= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(57,plain,
$false,
inference(e,[status(thm)],[29,33,41,45,27,49,39,35,18,31,43,23,47,37,25,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : 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
% 0.12/0.40 % Computer : n002.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 05:48:06 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (195ms).
% 1.45/1.20 % [INFO] Running in sequential loop mode.
% 1.85/1.60 % [INFO] eprover registered as external prover.
% 2.03/1.60 % [INFO] Scanning for conjecture ...
% 2.03/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.21/1.75 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.21/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.78 % [INFO] Type checking passed.
% 2.21/1.78 % [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 ...
% 3.53/2.35 % External prover 'e' found a proof!
% 3.53/2.35 % [INFO] Killing All external provers ...
% 3.53/2.35 % Time passed: 1800ms (effective reasoning time: 1142ms)
% 3.53/2.35 % Axioms used in derivation (15): additive_inverse_additive_inverse, left_identity, multiply_additive_id1, boolean_ring, multiply_additive_inverse2, additive_inverse_identity, distribute1, commutative_addition, distribute2, associative_addition, associative_multiplication, multiply_additive_id2, left_additive_inverse, distribute_additive_inverse, multiply_additive_inverse1
% 3.53/2.35 % No. of inferences in proof: 35
% 3.53/2.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1800 ms resp. 1142 ms w/o parsing
% 3.77/2.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.77/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------