%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO009-2 : 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 : n016.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 06:54:24 AM UTC 2026
% Result : Unsatisfiable 3.71s 2.39s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 146 ( 2 ~; 0 |; 0 &; 144 @)
% ( 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 : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(7,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',distributivity4) ).
thf(29,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)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( multiplicative_identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( multiplicative_identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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',distributivity3) ).
thf(27,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(12,axiom,
! [A: $i] :
( ( multiplicative_identity @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(39,plain,
! [A: $i] :
( ( multiplicative_identity @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(35,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
thf(43,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ add ) )
= ( C @ ( B @ add ) @ ( C @ ( A @ add ) @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ add ) )
= ( C @ ( B @ add ) @ ( C @ ( A @ add ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ add ) )
= ( C @ ( A @ add ) @ ( B @ ( A @ add ) @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ add ) )
= ( C @ ( A @ add ) @ ( B @ ( A @ add ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( A @ ( B @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( A @ ( B @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ add ) )
= multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ add ) )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ add ) @ ( a @ multiply ) )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_operation) ).
thf(16,plain,
( ( b @ ( a @ add ) @ ( a @ multiply ) )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(31,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,39,35,43,23,19,37,25,21,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 22:39:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.17 % [INFO] Parsing done (192ms).
% 1.30/1.18 % [INFO] Running in sequential loop mode.
% 1.91/1.59 % [INFO] eprover registered as external prover.
% 2.10/1.60 % [INFO] Scanning for conjecture ...
% 2.10/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.28/1.72 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.28/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.28/1.75 % [INFO] Type checking passed.
% 2.28/1.75 % [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 ...
% 3.71/2.39 % External prover 'e' found a proof!
% 3.71/2.39 % [INFO] Killing All external provers ...
% 3.71/2.39 % Time passed: 1867ms (effective reasoning time: 1201ms)
% 3.71/2.39 % Axioms used in derivation (14): distributivity3, distributivity2, multiplicative_inverse2, multiplicative_id2, multiplicative_inverse1, commutativity_of_add, multiplicative_id1, additive_inverse2, additive_inverse1, distributivity1, commutativity_of_multiply, additive_id2, distributivity4, additive_id1
% 3.71/2.39 % No. of inferences in proof: 31
% 3.71/2.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1867 ms resp. 1201 ms w/o parsing
% 3.97/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.97/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------