%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n017.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 06:54:29 AM UTC 2026
% Result : Unsatisfiable 4.10s 7.12s
% Output : Refutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 154 ( 2 ~; 0 |; 0 &; 152 @)
% ( 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 : 8 ( 6 usr; 4 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(add_decl,type,
add: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ add ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( A @ ( B @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( A @ ( B @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ add ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ add ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ add ) @ ( a @ multiply ) )
!= ( a @ ( c @ multiply ) @ ( a @ ( b @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add_property) ).
thf(12,plain,
( ( c @ ( b @ add ) @ ( a @ multiply ) )
!= ( a @ ( c @ multiply ) @ ( a @ ( b @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
thf(31,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)],[10]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ add ) @ ( B @ ( A @ add ) @ multiply ) @ multiply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ add ) @ ( B @ ( A @ add ) @ multiply ) @ multiply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ add ) @ ( B @ ( A @ add ) @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ inverse @ ( A @ add ) @ ( B @ ( A @ add ) @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ multiply ) @ ( A @ add ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ multiply ) @ ( A @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ add ) @ ( B @ add ) @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ add ) @ ( B @ add ) @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(33,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)],[11]) ).
thf(98,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % 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
% 0.15/5.43 % Computer : n017.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 22:33:09 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 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
% 0.21/5.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/5.88 % [INFO] Parsing done (105ms).
% 0.21/5.89 % [INFO] Running in sequential loop mode.
% 1.54/6.18 % [INFO] eprover registered as external prover.
% 1.54/6.19 % [INFO] Scanning for conjecture ...
% 1.66/6.28 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.84/6.32 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.84/6.34 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/6.34 % [INFO] Type checking passed.
% 1.84/6.35 % [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 ...
% 4.10/7.12 % External prover 'e' found a proof!
% 4.10/7.12 % [INFO] Killing All external provers ...
% 4.10/7.12 % Time passed: 1583ms (effective reasoning time: 1224ms)
% 4.10/7.12 % Axioms used in derivation (10): b2, b1, commutativity_of_multiply, l2, l4, l3, l1, associativity_of_add, commutativity_of_add, associativity_of_multiply
% 4.10/7.12 % No. of inferences in proof: 23
% 4.10/7.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1583 ms resp. 1224 ms w/o parsing
% 4.46/7.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.46/7.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------